CINXE.COM

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: compressible Euler equations</title> <meta name="description" content="Search results for: compressible Euler equations"> <meta name="keywords" content="compressible Euler equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="compressible Euler equations" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="compressible Euler equations"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1962</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: compressible Euler equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1962</span> A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xijun%20Yu">Xijun Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhenzhen%20Li"> Zhenzhen Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Zupeng%20Jia"> Zupeng Jia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cell-centered%20Lagrangian%20scheme" title="cell-centered Lagrangian scheme">cell-centered Lagrangian scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations" title=" compressible Euler equations"> compressible Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=RKDG%20method" title=" RKDG method"> RKDG method</a> </p> <a href="https://publications.waset.org/abstracts/3584/a-runge-kutta-discontinuous-galerkin-method-for-lagrangian-compressible-euler-equations-in-two-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3584.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">546</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1961</span> An Inviscid Compressible Flow Solver Based on Unstructured OpenFOAM Mesh Format</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Utkan%20Caliskan">Utkan Caliskan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cell%20centered%20finite%20volume%20method" title="cell centered finite volume method">cell centered finite volume method</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations" title=" compressible Euler equations"> compressible Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=OpenFOAM%20mesh%20format" title=" OpenFOAM mesh format"> OpenFOAM mesh format</a>, <a href="https://publications.waset.org/abstracts/search?q=OpenMP" title=" OpenMP"> OpenMP</a> </p> <a href="https://publications.waset.org/abstracts/73005/an-inviscid-compressible-flow-solver-based-on-unstructured-openfoam-mesh-format" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73005.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">319</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1960</span> Numerical Analysis of Gas-Particle Mixtures through Pipelines</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20Judakova">G. Judakova</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Bause"> M. Bause</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The ability to model and simulate numerically natural gas flow in pipelines has become of high importance for the design of pipeline systems. The understanding of the formation of hydrate particles and their dynamical behavior is of particular interest, since these processes govern the operation properties of the systems and are responsible for system failures by clogging of the pipelines under certain conditions. Mathematically, natural gas flow can be described by multiphase flow models. Using the two-fluid modeling approach, the gas phase is modeled by the compressible Euler equations and the particle phase is modeled by the pressureless Euler equations. The numerical simulation of compressible multiphase flows is an important research topic. It is well known that for nonlinear fluxes, even for smooth initial data, discontinuities in the solution are likely to occur in finite time. They are called shock waves or contact discontinuities. For hyperbolic and singularly perturbed parabolic equations the standard application of the Galerkin finite element method (FEM) leads to spurious oscillations (e.g. Gibb's phenomenon). In our approach, we use stabilized FEM, the streamline upwind Petrov-Galerkin (SUPG) method, where artificial diffusion acting only in the direction of the streamlines and using a special treatment of the boundary conditions in inviscid convective terms, is added. Numerical experiments show that the numerical solution obtained and stabilized by SUPG captures discontinuities or steep gradients of the exact solution in layers. However, within this layer the approximate solution may still exhibit overshoots or undershoots. To suitably reduce these artifacts we add a discontinuity capturing or shock capturing term. The performance properties of our numerical scheme are illustrated for two-phase flow problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-phase%20flow" title="two-phase flow">two-phase flow</a>, <a href="https://publications.waset.org/abstracts/search?q=gas-particle%20mixture" title=" gas-particle mixture"> gas-particle mixture</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20two-fluid%20model" title=" inviscid two-fluid model"> inviscid two-fluid model</a>, <a href="https://publications.waset.org/abstracts/search?q=euler%20equation" title=" euler equation"> euler equation</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=streamline%20upwind%20petrov-galerkin" title=" streamline upwind petrov-galerkin"> streamline upwind petrov-galerkin</a>, <a href="https://publications.waset.org/abstracts/search?q=shock%20capturing" title=" shock capturing"> shock capturing</a> </p> <a href="https://publications.waset.org/abstracts/41971/numerical-analysis-of-gas-particle-mixtures-through-pipelines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41971.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">311</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1959</span> An Axisymmetric Finite Element Method for Compressible Swirling Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Raphael%20Zanella">Raphael Zanella</a>, <a href="https://publications.waset.org/abstracts/search?q=Todd%20A.%20Oliver"> Todd A. Oliver</a>, <a href="https://publications.waset.org/abstracts/search?q=Karl%20W.%20Schulz"> Karl W. Schulz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=axisymmetric%20problem" title="axisymmetric problem">axisymmetric problem</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20Navier-Stokes%20equations" title=" compressible Navier-Stokes equations"> compressible Navier-Stokes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20finite%20elements" title=" continuous finite elements"> continuous finite elements</a>, <a href="https://publications.waset.org/abstracts/search?q=swirling%20flow" title=" swirling flow"> swirling flow</a> </p> <a href="https://publications.waset.org/abstracts/143638/an-axisymmetric-finite-element-method-for-compressible-swirling-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143638.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">174</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1958</span> Application of the MOOD Technique to the Steady-State Euler Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gaspar%20J.%20Machado">Gaspar J. Machado</a>, <a href="https://publications.waset.org/abstracts/search?q=St%C3%A9phane%20Clain"> Stéphane Clain</a>, <a href="https://publications.waset.org/abstracts/search?q=Raphael%20Loub%C3%A8re"> Raphael Loubère</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20equations" title="Euler equations">Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20volume" title=" finite volume"> finite volume</a>, <a href="https://publications.waset.org/abstracts/search?q=MOOD" title=" MOOD"> MOOD</a>, <a href="https://publications.waset.org/abstracts/search?q=steady-state" title=" steady-state"> steady-state</a> </p> <a href="https://publications.waset.org/abstracts/52830/application-of-the-mood-technique-to-the-steady-state-euler-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52830.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">277</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1957</span> Fractional Euler Method and Finite Difference Formula Using Conformable Fractional Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramzi%20B.%20Albadarneh">Ramzi B. Albadarneh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conformable%20fractional%20derivative" title="conformable fractional derivative">conformable fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20derivative" title=" fractional derivative"> fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20formula" title=" finite difference formula"> finite difference formula</a> </p> <a href="https://publications.waset.org/abstracts/37072/fractional-euler-method-and-finite-difference-formula-using-conformable-fractional-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37072.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1956</span> Comparing Numerical Accuracy of Solutions of Ordinary Differential Equations (ODE) Using Taylor's Series Method, Euler's Method and Runge-Kutta (RK) Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Palwinder%20Singh">Palwinder Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Munish%20Sandhir"> Munish Sandhir</a>, <a href="https://publications.waset.org/abstracts/search?q=Tejinder%20Singh"> Tejinder Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ordinary%20differential%20equations%20%28ODE%29" title="Ordinary differential equations (ODE)">Ordinary differential equations (ODE)</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%E2%80%99s%20Series%20Method" title=" Taylor’s Series Method"> Taylor’s Series Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%E2%80%99s%20Method" title=" Euler’s Method"> Euler’s Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Runge-Kutta%20Fourth%20Order%20Method" title=" Runge-Kutta Fourth Order Method"> Runge-Kutta Fourth Order Method</a> </p> <a href="https://publications.waset.org/abstracts/56685/comparing-numerical-accuracy-of-solutions-of-ordinary-differential-equations-ode-using-taylors-series-method-eulers-method-and-runge-kutta-rk-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56685.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">358</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1955</span> Student Project on Using a Spreadsheet for Solving Differential Equations by Euler's Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andriy%20Didenko">Andriy Didenko</a>, <a href="https://publications.waset.org/abstracts/search?q=Zanin%20Kavazovic"> Zanin Kavazovic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=student%20project" title="student project">student project</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%27s%20method" title=" Euler's method"> Euler's method</a>, <a href="https://publications.waset.org/abstracts/search?q=spreadsheet" title=" spreadsheet"> spreadsheet</a>, <a href="https://publications.waset.org/abstracts/search?q=engineering%20education" title=" engineering education"> engineering education</a> </p> <a href="https://publications.waset.org/abstracts/112422/student-project-on-using-a-spreadsheet-for-solving-differential-equations-by-eulers-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/112422.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1954</span> The Observable Method for the Regularization of Shock-Interface Interactions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teng%20Li">Teng Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Kamran%20Mohseni"> Kamran Mohseni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an inviscid regularization technique that is capable of regularizing the shocks and sharp interfaces simultaneously in the shock-interface interaction simulations. The direct numerical simulation of flows involving shocks has been investigated for many years and a lot of numerical methods were developed to capture the shocks. However, most of these methods rely on the numerical dissipation to regularize the shocks. Moreover, in high Reynolds number flows, the nonlinear terms in hyperbolic Partial Differential Equations (PDE) dominates, constantly generating small scale features. This makes direct numerical simulation of shocks even harder. The same difficulty happens in two-phase flow with sharp interfaces where the nonlinear terms in the governing equations keep sharpening the interfaces to discontinuities. The main idea of the proposed technique is to average out the small scales that is below the resolution (observable scale) of the computational grid by filtering the convective velocity in the nonlinear terms in the governing PDE. This technique is named “observable method” and it results in a set of hyperbolic equations called observable equations, namely, observable Navier-Stokes or Euler equations. The observable method has been applied to the flow simulations involving shocks, turbulence, and two-phase flows, and the results are promising. In the current paper, the observable method is examined on the performance of regularizing shocks and interfaces at the same time in shock-interface interaction problems. Bubble-shock interactions and Richtmyer-Meshkov instability are particularly chosen to be studied. Observable Euler equations will be numerically solved with pseudo-spectral discretization in space and third order Total Variation Diminishing (TVD) Runge Kutta method in time. Results are presented and compared with existing publications. The interface acceleration and deformation and shock reflection are particularly examined. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressible%20flow%20simulation" title="compressible flow simulation">compressible flow simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20regularization" title=" inviscid regularization"> inviscid regularization</a>, <a href="https://publications.waset.org/abstracts/search?q=Richtmyer-Meshkov%20instability" title=" Richtmyer-Meshkov instability"> Richtmyer-Meshkov instability</a>, <a href="https://publications.waset.org/abstracts/search?q=shock-bubble%20interactions." title=" shock-bubble interactions. "> shock-bubble interactions. </a> </p> <a href="https://publications.waset.org/abstracts/37215/the-observable-method-for-the-regularization-of-shock-interface-interactions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37215.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">349</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1953</span> Euler-Bernoulli’s Approach for Buckling Analysis of Thick Rectangular Plates Using Alternative I Refined Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Owus%20Mathias%20Ibearugbulem">Owus Mathias Ibearugbulem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study presents Euler-Bernoulli’s approach for buckling analysis of thick rectangular plates using alternative I refined theory. No earlier study, to the best knowledge of the author, based on the literature available to this research, applied Euler-Bernoulli’s approach in the alternative I refined theory for buckling analysis of thick rectangular plates. In this study, basic kinematics and constitutive relations for thick rectangular plates are employed in the differential equations of equilibrium of stresses in a deformable elemental body to obtain alternative I governing differential equations of thick rectangular plates and the corresponding compatibility equations. Solving these equations resulted in a general deflection function of a thick rectangular plate. Using this function and satisfying the boundary conditions of three plates, their peculiar deflection functions are obtained. Going further, the study determined the non-dimensional critical buckling loads of the six plates. Values of the non-dimensional critical buckling load from the present study are compared with those from a three-dimensional buckling analysis of a thick plate. The highest percentage difference recorded for the plates: all edges simply supported (ssss), all edges clamped (cccc) and adjacent edges clamped with the other edges simply supported (ccss) are 3.31%, 5.57% and 3.38% respectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli" title="Euler-Bernoulli">Euler-Bernoulli</a>, <a href="https://publications.waset.org/abstracts/search?q=buckling" title=" buckling"> buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=alternative%20I" title=" alternative I"> alternative I</a>, <a href="https://publications.waset.org/abstracts/search?q=kinematics" title=" kinematics"> kinematics</a>, <a href="https://publications.waset.org/abstracts/search?q=constitutive%20relation" title=" constitutive relation"> constitutive relation</a>, <a href="https://publications.waset.org/abstracts/search?q=governing%20differential%20equation" title=" governing differential equation"> governing differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=compatibility%20equation" title=" compatibility equation"> compatibility equation</a>, <a href="https://publications.waset.org/abstracts/search?q=thick%20plate" title=" thick plate"> thick plate</a> </p> <a href="https://publications.waset.org/abstracts/188996/euler-bernoullis-approach-for-buckling-analysis-of-thick-rectangular-plates-using-alternative-i-refined-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188996.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">30</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1952</span> Non–Geometric Sensitivities Using the Adjoint Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marcelo%20Hayashi">Marcelo Hayashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Jo%C3%A3o%20Lima"> João Lima</a>, <a href="https://publications.waset.org/abstracts/search?q=Bruno%20Chieregatti"> Bruno Chieregatti</a>, <a href="https://publications.waset.org/abstracts/search?q=Ernani%20Volpe"> Ernani Volpe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adjoint%20method" title="adjoint method">adjoint method</a>, <a href="https://publications.waset.org/abstracts/search?q=aerodynamics" title=" aerodynamics"> aerodynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20theory" title=" sensitivity theory"> sensitivity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=non-geometric%20sensitivities" title=" non-geometric sensitivities"> non-geometric sensitivities</a> </p> <a href="https://publications.waset.org/abstracts/42509/non-geometric-sensitivities-using-the-adjoint-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42509.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">547</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1951</span> A Parallel Computation Based on GPU Programming for a 3D Compressible Fluid Flow Simulation </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sugeng%20Rianto">Sugeng Rianto</a>, <a href="https://publications.waset.org/abstracts/search?q=P.W.%20Arinto%20Yudi"> P.W. Arinto Yudi</a>, <a href="https://publications.waset.org/abstracts/search?q=Soemarno%20%20Muhammad%20Nurhuda"> Soemarno Muhammad Nurhuda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A computation of a 3D compressible fluid flow for virtual environment with haptic interaction can be a non-trivial issue. This is especially how to reach good performances and balancing between visualization, tactile feedback interaction, and computations. In this paper, we describe our approach of computation methods based on parallel programming on a GPU. The 3D fluid flow solvers have been developed for smoke dispersion simulation by using combinations of the cubic interpolated propagation (CIP) based fluid flow solvers and the advantages of the parallelism and programmability of the GPU. The fluid flow solver is generated in the GPU-CPU message passing scheme to get rapid development of haptic feedback modes for fluid dynamic data. A rapid solution in fluid flow solvers is developed by applying cubic interpolated propagation (CIP) fluid flow solvers. From this scheme, multiphase fluid flow equations can be solved simultaneously. To get more acceleration in the computation, the Navier-Stoke Equations (NSEs) is packed into channels of texel, where computation models are performed on pixels that can be considered to be a grid of cells. Therefore, despite of the complexity of the obstacle geometry, processing on multiple vertices and pixels can be done simultaneously in parallel. The data are also shared in global memory for CPU to control the haptic in providing kinaesthetic interaction and felling. The results show that GPU based parallel computation approaches provide effective simulation of compressible fluid flow model for real-time interaction in 3D computer graphic for PC platform. This report has shown the feasibility of a new approach of solving the compressible fluid flow equations on the GPU. The experimental tests proved that the compressible fluid flowing on various obstacles with haptic interactions on the few model obstacles can be effectively and efficiently simulated on the reasonable frame rate with a realistic visualization. These results confirm that good performances and balancing between visualization, tactile feedback interaction, and computations can be applied successfully. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CIP" title="CIP">CIP</a>, <a href="https://publications.waset.org/abstracts/search?q=compressible%20fluid" title=" compressible fluid"> compressible fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=GPU%20programming" title=" GPU programming"> GPU programming</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20computation" title=" parallel computation"> parallel computation</a>, <a href="https://publications.waset.org/abstracts/search?q=real-time%20visualisation" title=" real-time visualisation"> real-time visualisation</a> </p> <a href="https://publications.waset.org/abstracts/3308/a-parallel-computation-based-on-gpu-programming-for-a-3d-compressible-fluid-flow-simulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3308.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">432</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1950</span> An Alternative Framework of Multi-Resolution Nested Weighted Essentially Non-Oscillatory Schemes for Solving Euler Equations with Adaptive Order</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhenming%20Wang">Zhenming Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jun%20Zhu"> Jun Zhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuchen%20Yang"> Yuchen Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ning%20Zhao"> Ning Zhao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, an alternative framework is proposed to construct a class of finite difference multi-resolution nested weighted essentially non-oscillatory (WENO) schemes with an increasingly higher order of accuracy for solving inviscid Euler equations. These WENO schemes firstly obtain a set of reconstruction polynomials by a hierarchy of nested central spatial stencils, and then recursively achieve a higher order approximation through the lower-order precision WENO schemes. The linear weights of such WENO schemes can be set as any positive numbers with a requirement that their sum equals one and they will not pollute the optimal order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near discontinuities. Numerical results obtained indicate that these alternative finite-difference multi-resolution nested WENO schemes with different accuracies are very robust with low dissipation and use as few reconstruction stencils as possible while maintaining the same efficiency, achieving the high-resolution property without any equivalent multi-resolution representation. Besides, its finite volume form is easier to implement in unstructured grids. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite-difference" title="finite-difference">finite-difference</a>, <a href="https://publications.waset.org/abstracts/search?q=WENO%20schemes" title=" WENO schemes"> WENO schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20order" title=" high order"> high order</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20Euler%20equations" title=" inviscid Euler equations"> inviscid Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-resolution" title=" multi-resolution "> multi-resolution </a> </p> <a href="https://publications.waset.org/abstracts/111223/an-alternative-framework-of-multi-resolution-nested-weighted-essentially-non-oscillatory-schemes-for-solving-euler-equations-with-adaptive-order" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/111223.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">145</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1949</span> Load Maximization of Two-Link Flexible Manipulator Using Suppression Vibration with Piezoelectric Transducer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamidreza%20Heidari">Hamidreza Heidari</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdollah%20Malmir%20Nasab"> Abdollah Malmir Nasab</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the energy equations of a two-link flexible manipulator were extracted using the Euler-Bernoulli beam hypotheses. Applying Assumed mode and considering some finite degrees of freedom, we could obtain dynamic motions of each manipulator using Euler-Lagrange equations. Using its claws, the robots can carry a certain load with the ached control of vibrations for robot flexible links during the travelling path using the piezoceramics transducer; dynamic load carrying capacity increase. The traveling path of flexible robot claw has been taken from that of equivalent rigid manipulator and coupled; therefore to avoid the role of Euler-Bernoulli beam assumptions and linear strains, material and physical characteristics selection of robot cause deflection of link ends not exceed 5% of link length. To do so, the maximum load carrying capacity of robot is calculated at the horizontal plan. The increasing of robot load carrying capacity with vibration control is 53%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flexible%20link" title="flexible link">flexible link</a>, <a href="https://publications.waset.org/abstracts/search?q=DLCC" title=" DLCC"> DLCC</a>, <a href="https://publications.waset.org/abstracts/search?q=active%20control%20vibration" title=" active control vibration"> active control vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=assumed%20mode%20method" title=" assumed mode method"> assumed mode method</a> </p> <a href="https://publications.waset.org/abstracts/54871/load-maximization-of-two-link-flexible-manipulator-using-suppression-vibration-with-piezoelectric-transducer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54871.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1948</span> Compressible Flow Modeling in Pipes and Porous Media during Blowdown Experiment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Thomas%20Paris">Thomas Paris</a>, <a href="https://publications.waset.org/abstracts/search?q=Vincent%20Bruyere"> Vincent Bruyere</a>, <a href="https://publications.waset.org/abstracts/search?q=Patrick%20Namy"> Patrick Namy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A numerical model is developed to simulate gas blowdowns through a thin tube and a filter (porous media), separating a high pressure gas filled reservoir to low pressure ones. Based on a previous work, a one-dimensional approach is developed by using the finite element method to solve the transient compressible flow and to predict the pressure and temperature evolution in space and time. Mass, momentum, and energy conservation equations are solved in a fully coupled way in the reservoirs, the pipes and the porous media. Numerical results, such as pressure and temperature evolutions, are firstly compared with experimental data to validate the model for different configurations. Couplings between porous media and pipe flow are then validated by checking mass balance. The influence of the porous media and the nature of the gas is then studied for different initial high pressure values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressible%20flow" title="compressible flow">compressible flow</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid%20mechanics" title=" fluid mechanics"> fluid mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=porous%20media" title=" porous media"> porous media</a> </p> <a href="https://publications.waset.org/abstracts/95747/compressible-flow-modeling-in-pipes-and-porous-media-during-blowdown-experiment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/95747.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">406</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1947</span> Kirchoff Type Equation Involving the p-Laplacian on the Sierpinski Gasket Using Nehari Manifold Technique</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abhilash%20Sahu">Abhilash Sahu</a>, <a href="https://publications.waset.org/abstracts/search?q=Amit%20Priyadarshi"> Amit Priyadarshi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20functional" title="Euler functional">Euler functional</a>, <a href="https://publications.waset.org/abstracts/search?q=p-Laplacian" title=" p-Laplacian"> p-Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=p-energy" title=" p-energy"> p-energy</a>, <a href="https://publications.waset.org/abstracts/search?q=Sierpinski%20gasket" title=" Sierpinski gasket"> Sierpinski gasket</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solution" title=" weak solution"> weak solution</a> </p> <a href="https://publications.waset.org/abstracts/89044/kirchoff-type-equation-involving-the-p-laplacian-on-the-sierpinski-gasket-using-nehari-manifold-technique" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89044.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">234</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1946</span> Investigating the Form of the Generalised Equations of Motion of the N-Bob Pendulum and Computing Their Solution Using MATLAB</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Divij%20Gupta">Divij Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=classical%20mechanics" title="classical mechanics">classical mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=lagrangian%20analysis" title=" lagrangian analysis"> lagrangian analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=pendulum" title=" pendulum"> pendulum</a> </p> <a href="https://publications.waset.org/abstracts/113019/investigating-the-form-of-the-generalised-equations-of-motion-of-the-n-bob-pendulum-and-computing-their-solution-using-matlab" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">208</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1945</span> Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gholamreza%20Koochaki">Gholamreza Koochaki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=buckling" title="buckling">buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beams" title=" functionally graded beams"> functionally graded beams</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle" title=" Hamilton's principle"> Hamilton's principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20beam" title=" Euler-Bernoulli beam"> Euler-Bernoulli beam</a> </p> <a href="https://publications.waset.org/abstracts/30892/thermal-buckling-analysis-of-functionally-graded-beams-with-various-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30892.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">392</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1944</span> Compressible Lattice Boltzmann Method for Turbulent Jet Flow Simulations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Noah">K. Noah</a>, <a href="https://publications.waset.org/abstracts/search?q=F.-S.%20Lien"> F.-S. Lien</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compressible%20lattice%20Boltzmann%20method" title="compressible lattice Boltzmann method">compressible lattice Boltzmann method</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20relaxation%20times" title=" multiple relaxation times"> multiple relaxation times</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20eddy%20simulation" title=" large eddy simulation"> large eddy simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulent%20jet%20flows" title=" turbulent jet flows"> turbulent jet flows</a> </p> <a href="https://publications.waset.org/abstracts/89310/compressible-lattice-boltzmann-method-for-turbulent-jet-flow-simulations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89310.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">274</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1943</span> Closed-Form Solutions for Nanobeams Based on the Nonlocal Euler-Bernoulli Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francesco%20Marotti%20de%20Sciarra">Francesco Marotti de Sciarra</a>, <a href="https://publications.waset.org/abstracts/search?q=Raffaele%20Barretta"> Raffaele Barretta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernoulli-Euler%20beams" title="Bernoulli-Euler beams">Bernoulli-Euler beams</a>, <a href="https://publications.waset.org/abstracts/search?q=nanobeams" title=" nanobeams"> nanobeams</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20elasticity" title=" nonlocal elasticity"> nonlocal elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=closed-form%20solutions" title=" closed-form solutions "> closed-form solutions </a> </p> <a href="https://publications.waset.org/abstracts/24524/closed-form-solutions-for-nanobeams-based-on-the-nonlocal-euler-bernoulli-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24524.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">370</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1942</span> Implementation and Modeling of a Quadrotor</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ersan%20Aktas">Ersan Aktas</a>, <a href="https://publications.waset.org/abstracts/search?q=Eren%20Turano%C4%9Fuz"> Eren Turanoğuz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the quad-electrical rotor driven unmanned aerial vehicle system is designed and modeled using fundamental dynamic equations. After that, mechanical, electronical and control system of the air vehicle are designed and implemented. Brushless motor speeds are altered via electronic speed controllers in order to achieve desired controllability. The vehicle's fundamental Euler angles (i.e., roll angle, pitch angle, and yaw angle) are obtained via AHRS sensor. These angles are provided as an input to the control algorithm that run on soft the processor on the electronic card. The vehicle control algorithm is implemented in the electronic card. Controller is designed and improved for each Euler angles. Finally, flight tests have been performed to observe and improve the flight characteristics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=quadrotor" title="quadrotor">quadrotor</a>, <a href="https://publications.waset.org/abstracts/search?q=UAS%20applications" title=" UAS applications"> UAS applications</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20architectures" title=" control architectures"> control architectures</a>, <a href="https://publications.waset.org/abstracts/search?q=PID" title=" PID"> PID</a> </p> <a href="https://publications.waset.org/abstracts/48615/implementation-and-modeling-of-a-quadrotor" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48615.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">365</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1941</span> Regularized Euler Equations for Incompressible Two-Phase Flow Simulations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teng%20Li">Teng Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Kamran%20Mohseni"> Kamran Mohseni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Euler%20equations" title="Euler equations">Euler equations</a>, <a href="https://publications.waset.org/abstracts/search?q=incompressible%20flow%20simulation" title=" incompressible flow simulation"> incompressible flow simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20regularization%20technique" title=" inviscid regularization technique"> inviscid regularization technique</a>, <a href="https://publications.waset.org/abstracts/search?q=two-phase%20flow" title=" two-phase flow"> two-phase flow</a> </p> <a href="https://publications.waset.org/abstracts/37217/regularized-euler-equations-for-incompressible-two-phase-flow-simulations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37217.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">502</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1940</span> Direct Compression Formulation of Poorly Compressible Drugs to Minimize the Tablet Defects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abhishek%20Pandey">Abhishek Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Capping and lamination are the most common tablet defects with poorly compressible drugs the common example of that Ibuprofen and Acetaminophen. Generally both these drugs are compressed by wet granulation method which is very time consuming process Ibuprofen and Acetaminophen is widely used as prescription & non-prescription medicine. Ibuprofen mainly used in the treatment of mild to moderate pain related to headache, migraine, postoperative condition and in the management of spondylitis, osteoarthritis Acetaminophen used as an analgesic and antipyretic drug. Ibuprofen having high tendency of sticking to punches of tablet punching machine while Acetaminophen is not ordinarily compressible to tablet formulation because Acetaminophen crystals are very hard and brittle in nature and fracture very easily when compressed producing capping and laminating tablet defects therefore wet granulation method is used to make them compressible. The aim of study was to prepare Ibuprofen and Acetaminophen tablets by direct compression technique and their evaluation. In this Investigation tablets were prepared by using directly compressible grade excipients. Dibasic calcium phosphate, lactose anhydrous (DCL21), microcrystalline cellulose (Avicel PH 101). In order to obtain best or optimize formulation nine different formulations were generated among them batch F5, F6, F7 shows good results and within the acceptable limit. Formulation (F7) selected as optimize product on the basis of evaluation parameters. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=capping" title="capping">capping</a>, <a href="https://publications.waset.org/abstracts/search?q=lamination" title=" lamination"> lamination</a>, <a href="https://publications.waset.org/abstracts/search?q=tablet%20defects" title=" tablet defects"> tablet defects</a>, <a href="https://publications.waset.org/abstracts/search?q=direct%20compression" title=" direct compression"> direct compression</a> </p> <a href="https://publications.waset.org/abstracts/38039/direct-compression-formulation-of-poorly-compressible-drugs-to-minimize-the-tablet-defects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38039.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">438</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1939</span> Implementation of Fuzzy Version of Block Backward Differentiation Formulas for Solving Fuzzy Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Z.%20B.%20Ibrahim">Z. B. Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Ismail"> N. Ismail</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20I.%20Othman"> K. I. Othman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block" title="block">block</a>, <a href="https://publications.waset.org/abstracts/search?q=backward%20differentiation%20formulas" title=" backward differentiation formulas"> backward differentiation formulas</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20order" title=" first order"> first order</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20differential%20equations" title=" fuzzy differential equations"> fuzzy differential equations</a> </p> <a href="https://publications.waset.org/abstracts/47384/implementation-of-fuzzy-version-of-block-backward-differentiation-formulas-for-solving-fuzzy-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47384.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">319</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1938</span> Energy Separation Mechanism in Uni-Flow Vortex Tube Using Compressible Vortex Flow </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hiroshi%20Katanoda">Hiroshi Katanoda</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Hazwan%20bin%20Yusof"> Mohd Hazwan bin Yusof</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A theoretical investigation from the viewpoint of gas-dynamics and thermodynamics was carried out, in order to clarify the energy separation mechanism in a viscous compressible vortex, as a primary flow element in a uni-flow vortex tube. The mathematical solutions of tangential velocity, density and temperature in a viscous compressible vortical flow were used in this study. It is clear that a total temperature in the vortex core falls well below that distant from the vortex core in the radial direction, causing a region with higher total temperature, compared to the distant region, peripheral to the vortex core. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=energy%20separation%20mechanism" title="energy separation mechanism">energy separation mechanism</a>, <a href="https://publications.waset.org/abstracts/search?q=theoretical%20analysis" title=" theoretical analysis"> theoretical analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex%20tube" title=" vortex tube"> vortex tube</a>, <a href="https://publications.waset.org/abstracts/search?q=vortical%20flow" title=" vortical flow"> vortical flow</a> </p> <a href="https://publications.waset.org/abstracts/10251/energy-separation-mechanism-in-uni-flow-vortex-tube-using-compressible-vortex-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10251.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">399</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1937</span> Stochastic Variation of the Hubble's Parameter Using Ornstein-Uhlenbeck Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mary%20Chriselda%20A">Mary Chriselda A</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chapman%20Kolmogorov%20forward%20differential%20equations" title="Chapman Kolmogorov forward differential equations">Chapman Kolmogorov forward differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20transformation" title=" fourier transformation"> fourier transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=hubble%27s%20parameter" title=" hubble's parameter"> hubble's parameter</a>, <a href="https://publications.waset.org/abstracts/search?q=ornstein-uhlenbeck%20process" title=" ornstein-uhlenbeck process "> ornstein-uhlenbeck process </a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations "> stochastic differential equations </a> </p> <a href="https://publications.waset.org/abstracts/116444/stochastic-variation-of-the-hubbles-parameter-using-ornstein-uhlenbeck-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/116444.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">201</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1936</span> A Comparison Between Different Discretization Techniques for the Doyle-Fuller-Newman Li+ Battery Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Davide%20Gotti">Davide Gotti</a>, <a href="https://publications.waset.org/abstracts/search?q=Milan%20Prodanovic"> Milan Prodanovic</a>, <a href="https://publications.waset.org/abstracts/search?q=Sergio%20Pinilla"> Sergio Pinilla</a>, <a href="https://publications.waset.org/abstracts/search?q=David%20Mu%C3%B1oz-Torrero"> David Muñoz-Torrero</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Since its proposal, the Doyle-Fuller-Newman (DFN) lithium-ion battery model has gained popularity in the electrochemical field. In fact, this model provides the user with theoretical support for designing the lithium-ion battery parameters, such as the material particle or the diffusion coefficient adjustment direction. However, the model is mathematically complex as it is composed of several partial differential equations (PDEs) such as Fick’s law of diffusion, the MacInnes and Ohm’s equations, among other phenomena. Thus, to efficiently use the model in a time-domain simulation environment, the selection of the discretization technique is of a pivotal importance. There are several numerical methods available in the literature that can be used to carry out this task. In this study, a comparison between the explicit Euler, Crank-Nicolson, and Chebyshev discretization methods is proposed. These three methods are compared in terms of accuracy, stability, and computational times. Firstly, the explicit Euler discretization technique is analyzed. This method is straightforward to implement and is computationally fast. In this work, the accuracy of the method and its stability properties are shown for the electrolyte diffusion partial differential equation. Subsequently, the Crank-Nicolson method is considered. It represents a combination of the implicit and explicit Euler methods that has the advantage of being of the second order in time and is intrinsically stable, thus overcoming the disadvantages of the simpler Euler explicit method. As shown in the full paper, the Crank-Nicolson method provides accurate results when applied to the DFN model. Its stability does not depend on the integration time step, thus it is feasible for both short- and long-term tests. This last remark is particularly important as this discretization technique would allow the user to implement parameter estimation and optimization techniques such as system or genetic parameter identification methods using this model. Finally, the Chebyshev discretization technique is implemented in the DFN model. This discretization method features swift convergence properties and, as other spectral methods used to solve differential equations, achieves the same accuracy with a smaller number of discretization nodes. However, as shown in the literature, these methods are not suitable for handling sharp gradients, which are common during the first instants of the charge and discharge phases of the battery. The numerical results obtained and presented in this study aim to provide the guidelines on how to select the adequate discretization technique for the DFN model according to the type of application to be performed, highlighting the pros and cons of the three methods. Specifically, the non-eligibility of the simple Euler method for longterm tests will be presented. Afterwards, the Crank-Nicolson and the Chebyshev discretization methods will be compared in terms of accuracy and computational times under a wide range of battery operating scenarios. These include both long-term simulations for aging tests, and short- and mid-term battery charge/discharge cycles, typically relevant in battery applications like grid primary frequency and inertia control and electrical vehicle breaking and acceleration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Doyle-Fuller-Newman%20battery%20model" title="Doyle-Fuller-Newman battery model">Doyle-Fuller-Newman battery model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=discretization" title=" discretization"> discretization</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods" title=" numerical methods"> numerical methods</a> </p> <a href="https://publications.waset.org/abstracts/190331/a-comparison-between-different-discretization-techniques-for-the-doyle-fuller-newman-li-battery-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/190331.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">23</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1935</span> 3D Codes for Unsteady Interaction Problems of Continuous Mechanics in Euler Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Abuziarov">M. Abuziarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The designed complex is intended for the numerical simulation of fast dynamic processes of interaction of heterogeneous environments susceptible to the significant formability. The main challenges in solving such problems are associated with the construction of the numerical meshes. Currently, there are two basic approaches to solve this problem. One is using of Lagrangian or Lagrangian Eulerian grid associated with the boundaries of media and the second is associated with the fixed Eulerian mesh, boundary cells of which cut boundaries of the environment medium and requires the calculation of these cut volumes. Both approaches require the complex grid generators and significant time for preparing the code’s data for simulation. In this codes these problems are solved using two grids, regular fixed and mobile local Euler Lagrange - Eulerian (ALE approach) accompanying the contact and free boundaries, the surfaces of shock waves and phase transitions, and other possible features of solutions, with mutual interpolation of integrated parameters. For modeling of both liquids and gases, and deformable solids the Godunov scheme of increased accuracy is used in Lagrangian - Eulerian variables, the same for the Euler equations and for the Euler- Cauchy, describing the deformation of the solid. The increased accuracy of the scheme is achieved by using 3D spatial time dependent solution of the discontinuity problem (3D space time dependent Riemann's Problem solver). The same solution is used to calculate the interaction at the liquid-solid surface (Fluid Structure Interaction problem). The codes does not require complex 3D mesh generators, only the surfaces of the calculating objects as the STL files created by means of engineering graphics are given by the user, which greatly simplifies the preparing the task and makes it convenient to use directly by the designer at the design stage. The results of the test solutions and applications related to the generation and extension of the detonation and shock waves, loading the constructions are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fluid%20structure%20interaction" title="fluid structure interaction">fluid structure interaction</a>, <a href="https://publications.waset.org/abstracts/search?q=Riemann%27s%20solver" title=" Riemann's solver"> Riemann's solver</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%20variables" title=" Euler variables"> Euler variables</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20codes" title=" 3D codes"> 3D codes</a> </p> <a href="https://publications.waset.org/abstracts/17837/3d-codes-for-unsteady-interaction-problems-of-continuous-mechanics-in-euler-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17837.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1934</span> Prediction of Finned Projectile Aerodynamics Using a Lattice-Boltzmann Method CFD Solution</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zaki%20Abiza">Zaki Abiza</a>, <a href="https://publications.waset.org/abstracts/search?q=Miguel%20Chavez"> Miguel Chavez</a>, <a href="https://publications.waset.org/abstracts/search?q=David%20M.%20Holman"> David M. Holman</a>, <a href="https://publications.waset.org/abstracts/search?q=Ruddy%20Brionnaud"> Ruddy Brionnaud</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CFD" title="CFD">CFD</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20fluid%20dynamics" title=" computational fluid dynamics"> computational fluid dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=drag" title=" drag"> drag</a>, <a href="https://publications.waset.org/abstracts/search?q=finned%20projectile" title=" finned projectile"> finned projectile</a>, <a href="https://publications.waset.org/abstracts/search?q=lattice-boltzmann%20method" title=" lattice-boltzmann method"> lattice-boltzmann method</a>, <a href="https://publications.waset.org/abstracts/search?q=LBM" title=" LBM"> LBM</a>, <a href="https://publications.waset.org/abstracts/search?q=lift" title=" lift"> lift</a>, <a href="https://publications.waset.org/abstracts/search?q=mach" title=" mach"> mach</a>, <a href="https://publications.waset.org/abstracts/search?q=pitch" title=" pitch"> pitch</a> </p> <a href="https://publications.waset.org/abstracts/42078/prediction-of-finned-projectile-aerodynamics-using-a-lattice-boltzmann-method-cfd-solution" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42078.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">421</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1933</span> Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Carla%20E.%20O.%20de%20Moraes">Carla E. O. de Moraes</a>, <a href="https://publications.waset.org/abstracts/search?q=Gladson%20O.%20Antunes"> Gladson O. Antunes</a>, <a href="https://publications.waset.org/abstracts/search?q=Mauro%20A.%20Rincon"> Mauro A. Rincon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernoulli-Euler%20plate%20equation" title="Bernoulli-Euler plate equation">Bernoulli-Euler plate equation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulations" title=" numerical simulations"> numerical simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20decay" title=" energy decay"> energy decay</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title=" finite difference method"> finite difference method</a> </p> <a href="https://publications.waset.org/abstracts/7035/stabilization-of-the-bernoulli-euler-plate-equation-numerical-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7035.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">416</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=10">10</a></li> <li class="page-item disabled"><span class="page-link">...</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=65">65</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=66">66</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=compressible%20Euler%20equations&page=2" rel="next">&rsaquo;</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>