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: numerical</title> <meta name="description" content="Search results for: numerical"> <meta name="keywords" content="numerical"> <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="numerical" 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="numerical"> <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> 3545</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: numerical</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3545</span> Optimization of the Numerical Fracture Mechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Hentati">H. Hentati</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Abdelmoula"> R. Abdelmoula</a>, <a href="https://publications.waset.org/abstracts/search?q=Li%20Jia"> Li Jia</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Maalej"> A. Maalej</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fracture%20mechanics" title="fracture mechanics">fracture mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=variation%20approach" title=" variation approach"> variation approach</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanic" title=" mechanic"> mechanic</a> </p> <a href="https://publications.waset.org/abstracts/5187/optimization-of-the-numerical-fracture-mechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5187.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">606</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">3544</span> Some Results on the Generalized Higher Rank Numerical Ranges</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Zahraei">Mohsen Zahraei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> ‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8E%E2%80%8ERank-k%20numerical%20range%E2%80%8E" title="‎‎Rank-k numerical range‎">‎‎Rank-k numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eisometry%E2%80%8E" title=" ‎isometry‎"> ‎isometry‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Enumerical%20range%E2%80%8E" title=" ‎numerical range‎"> ‎numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Erectangular%20matrix%20polynomials" title=" ‎rectangular matrix polynomials"> ‎rectangular matrix polynomials</a> </p> <a href="https://publications.waset.org/abstracts/28955/some-results-on-the-generalized-higher-rank-numerical-ranges" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28955.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">459</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">3543</span> Using Derivative Free Method to Improve the Error Estimation of Numerical Quadrature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chin-Yun%20Chen">Chin-Yun Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20quadrature" title="numerical quadrature">numerical quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimation" title=" error estimation"> error estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=derivative%20free%20method" title=" derivative free method"> derivative free method</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20computation" title=" interval computation "> interval computation </a> </p> <a href="https://publications.waset.org/abstracts/17210/using-derivative-free-method-to-improve-the-error-estimation-of-numerical-quadrature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17210.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">463</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">3542</span> Improvement of the Numerical Integration's Quality in Meshless Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahlem%20Mougaida">Ahlem Mougaida</a>, <a href="https://publications.waset.org/abstracts/search?q=Hedi%20Bel%20Hadj%20Salah"> Hedi Bel Hadj Salah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20methods" title="adaptive methods">adaptive methods</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless" title=" meshless"> meshless</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20integration" title=" numerical integration"> numerical integration</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20quadrature" title=" rational quadrature"> rational quadrature</a> </p> <a href="https://publications.waset.org/abstracts/46442/improvement-of-the-numerical-integrations-quality-in-meshless-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46442.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">364</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">3541</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> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3540</span> Numerical Methods versus Bjerksund and Stensland Approximations for American Options Pricing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marasovic%20Branka">Marasovic Branka</a>, <a href="https://publications.waset.org/abstracts/search?q=Aljinovic%20Zdravka"> Aljinovic Zdravka</a>, <a href="https://publications.waset.org/abstracts/search?q=Poklepovic%20Tea"> Poklepovic Tea</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time? <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bjerksund%20and%20Stensland%20approximations" title="Bjerksund and Stensland approximations">Bjerksund and Stensland approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20analysis" title=" computational analysis"> computational analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=finance" title=" finance"> finance</a>, <a href="https://publications.waset.org/abstracts/search?q=options%20pricing" title=" options pricing"> options pricing</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/2832/numerical-methods-versus-bjerksund-and-stensland-approximations-for-american-options-pricing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2832.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">456</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">3539</span> Numerical Simulations for Nitrogen Flow in Piezoelectric Valve</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pawel%20Flaszynski">Pawel Flaszynski</a>, <a href="https://publications.waset.org/abstracts/search?q=Piotr%20Doerffer"> Piotr Doerffer</a>, <a href="https://publications.waset.org/abstracts/search?q=Jan%20Holnicki-Szulc"> Jan Holnicki-Szulc</a>, <a href="https://publications.waset.org/abstracts/search?q=Grzegorz%20Mikulowski"> Grzegorz Mikulowski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pneumatic%20valve" title="pneumatic valve">pneumatic valve</a>, <a href="https://publications.waset.org/abstracts/search?q=transonic%20flow" title=" transonic flow"> transonic flow</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=piezoelectric%20valve" title=" piezoelectric valve"> piezoelectric valve</a> </p> <a href="https://publications.waset.org/abstracts/29877/numerical-simulations-for-nitrogen-flow-in-piezoelectric-valve" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29877.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">513</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">3538</span> Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuziyah%20Ishak">Fuziyah Ishak</a>, <a href="https://publications.waset.org/abstracts/search?q=Siti%20Norazura%20Ahmad"> Siti Norazura Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=accuracy" title="accuracy">accuracy</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20trapezoidal%20method" title=" extended trapezoidal method"> extended trapezoidal method</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integro-differential%20equations" title=" Volterra integro-differential equations"> Volterra integro-differential equations</a> </p> <a href="https://publications.waset.org/abstracts/52856/development-of-extended-trapezoidal-method-for-numerical-solution-of-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52856.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">424</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">3537</span> 3-D Numerical Model for Wave-Induced Seabed Response around an Offshore Pipeline</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zuodong%20Liang">Zuodong Liang</a>, <a href="https://publications.waset.org/abstracts/search?q=Dong-Sheng%20Jeng"> Dong-Sheng Jeng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pore%20pressure" title="pore pressure">pore pressure</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20wave%20model" title=" 3D wave model"> 3D wave model</a>, <a href="https://publications.waset.org/abstracts/search?q=seabed%20liquefaction" title=" seabed liquefaction"> seabed liquefaction</a>, <a href="https://publications.waset.org/abstracts/search?q=pipeline" title=" pipeline"> pipeline</a> </p> <a href="https://publications.waset.org/abstracts/76992/3-d-numerical-model-for-wave-induced-seabed-response-around-an-offshore-pipeline" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76992.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">372</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">3536</span> Solving Mean Field Problems: A Survey of Numerical Methods and Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amal%20Machtalay">Amal Machtalay</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mean-field%20games" title="mean-field games">mean-field games</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20schemes" title=" numerical schemes"> numerical schemes</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=complex%20systems" title=" complex systems"> complex systems</a>, <a href="https://publications.waset.org/abstracts/search?q=machine%20learning" title=" machine learning"> machine learning</a> </p> <a href="https://publications.waset.org/abstracts/153744/solving-mean-field-problems-a-survey-of-numerical-methods-and-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/153744.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">113</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">3535</span> Three Dimensional Numerical Analysis for Longitudinal Seismic Response of Tunnels under Asynchronous Earthquake</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Peng%20Li">Peng Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Er-xiang%20Song"> Er-xiang Song</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asynchronous%20input" title="asynchronous input">asynchronous input</a>, <a href="https://publications.waset.org/abstracts/search?q=longitudinal%20seismic%20response" title=" longitudinal seismic response"> longitudinal seismic response</a>, <a href="https://publications.waset.org/abstracts/search?q=tunnel%20structure" title=" tunnel structure"> tunnel structure</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=traveling%20wave%20effect" title=" traveling wave effect"> traveling wave effect</a> </p> <a href="https://publications.waset.org/abstracts/9730/three-dimensional-numerical-analysis-for-longitudinal-seismic-response-of-tunnels-under-asynchronous-earthquake" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9730.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">437</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">3534</span> Study on the Effect of Coupling Fluid Compressible-Deformable Wall on the Flow of Molten Polymers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Driouich">Mohamed Driouich</a>, <a href="https://publications.waset.org/abstracts/search?q=Kamal%20Gueraoui"> Kamal Gueraoui</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Sammouda"> Mohamed Sammouda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20code" title="numerical code">numerical code</a>, <a href="https://publications.waset.org/abstracts/search?q=molten%20polymers" title=" molten polymers"> molten polymers</a>, <a href="https://publications.waset.org/abstracts/search?q=deformable%20pipes" title=" deformable pipes"> deformable pipes</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20differences" title=" finite differences"> finite differences</a> </p> <a href="https://publications.waset.org/abstracts/8493/study-on-the-effect-of-coupling-fluid-compressible-deformable-wall-on-the-flow-of-molten-polymers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8493.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">574</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">3533</span> The Different Improvement of Numerical Magnitude and Spatial Representation of Numbers to Symbolic Approximate Arithmetic: A Training Study of Preschooler</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yu%20Liang">Yu Liang</a>, <a href="https://publications.waset.org/abstracts/search?q=Wei%20Wei"> Wei Wei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximate%20arithmetic" title="approximate arithmetic">approximate arithmetic</a>, <a href="https://publications.waset.org/abstracts/search?q=mental%20number%20line" title=" mental number line"> mental number line</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20magnitude" title=" numerical magnitude"> numerical magnitude</a>, <a href="https://publications.waset.org/abstracts/search?q=preschooler" title=" preschooler"> preschooler</a> </p> <a href="https://publications.waset.org/abstracts/72817/the-different-improvement-of-numerical-magnitude-and-spatial-representation-of-numbers-to-symbolic-approximate-arithmetic-a-training-study-of-preschooler" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72817.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">251</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">3532</span> Numerical Modeling the Cavitating Flow in Injection Nozzle Holes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ridha%20Zgolli">Ridha Zgolli</a>, <a href="https://publications.waset.org/abstracts/search?q=Hatem%20Kanfoudi"> Hatem Kanfoudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A 2D numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier-Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density which is expressed as function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term TEM. The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in details. The numerical simulations are in good agreement with the experimental data for steady flow. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cavitation" title="cavitation">cavitation</a>, <a href="https://publications.waset.org/abstracts/search?q=injection%20nozzle" title=" injection nozzle"> injection nozzle</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=k%E2%80%93%CF%89" title=" k–ω"> k–ω</a> </p> <a href="https://publications.waset.org/abstracts/8089/numerical-modeling-the-cavitating-flow-in-injection-nozzle-holes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8089.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">401</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">3531</span> Numerical Study for Structural Design of Composite Rotor with Crack Initiation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Chellil">A. Chellil</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Nour"> A. Nour</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Lecheb"> S. Lecheb</a>, <a href="https://publications.waset.org/abstracts/search?q=H.Mechakra"> H.Mechakra</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Bouderba"> A. Bouderba</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Kebir"> H. Kebir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the numerical study for the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor is developed. The use of the composite material for the rotor, offers a good Stability. Numerical calculations on the model develop of three dimensions prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed to determine the vibratory responses due to various excitations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=rotor" title="rotor">rotor</a>, <a href="https://publications.waset.org/abstracts/search?q=composite" title=" composite"> composite</a>, <a href="https://publications.waset.org/abstracts/search?q=damage" title=" damage"> damage</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical" title=" numerical"> numerical</a> </p> <a href="https://publications.waset.org/abstracts/19109/numerical-study-for-structural-design-of-composite-rotor-with-crack-initiation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19109.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">488</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">3530</span> Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ogunrinde%20Roseline%20Bosede">Ogunrinde Roseline Bosede</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title="differential equations">differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical" title=" numerical"> numerical</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial" title=" polynomial"> polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problem" title=" initial value problem"> initial value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a> </p> <a href="https://publications.waset.org/abstracts/23505/inverse-polynomial-numerical-scheme-for-the-solution-of-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23505.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">447</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">3529</span> The Impact of Modeling Method of Moisture Emission from the Swimming Pool on the Accuracy of Numerical Calculations of Air Parameters in Ventilated Natatorium</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Piotr%20Ciuman">Piotr Ciuman</a>, <a href="https://publications.waset.org/abstracts/search?q=Barbara%20Lipska"> Barbara Lipska</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of presented research was to improve numerical predictions of air parameters distribution in the actual natatorium by the selection of calculation formula of mass flux of moisture emitted from the pool. Selected correlation should ensure the best compliance of numerical results with the measurements' results of these parameters in the facility. The numerical model of the natatorium was developed, for which boundary conditions were prepared on the basis of measurements' results carried out in the actual facility. Numerical calculations were carried out with the use of ANSYS CFX software, with six formulas being implemented, which in various ways made the moisture emission dependent on water surface temperature and air parameters in the natatorium. The results of calculations with the use of these formulas were compared for air parameters' distributions: Specific humidity, velocity and temperature in the facility. For the selection of the best formula, numerical results of these parameters in occupied zone were validated by comparison with the measurements' results carried out at selected points of this zone. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=experimental%20validation" title="experimental validation">experimental validation</a>, <a href="https://publications.waset.org/abstracts/search?q=indoor%20swimming%20pool" title=" indoor swimming pool"> indoor swimming pool</a>, <a href="https://publications.waset.org/abstracts/search?q=moisture%20emission" title=" moisture emission"> moisture emission</a>, <a href="https://publications.waset.org/abstracts/search?q=natatorium" title=" natatorium"> natatorium</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20calculations%20CFD" title=" numerical calculations CFD"> numerical calculations CFD</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20and%20humidity%20conditions" title=" thermal and humidity conditions"> thermal and humidity conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=ventilation" title=" ventilation"> ventilation</a> </p> <a href="https://publications.waset.org/abstracts/39922/the-impact-of-modeling-method-of-moisture-emission-from-the-swimming-pool-on-the-accuracy-of-numerical-calculations-of-air-parameters-in-ventilated-natatorium" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39922.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">411</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">3528</span> Numerical Investigation of Wave Interaction with Double Vertical Slotted Walls</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Ahmed">H. Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Schlenkhoff"> A. Schlenkhoff</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, permeable breakwaters have been suggested to overcome the disadvantages of fully protection breakwaters. These protection structures have minor impacts on the coastal environment and neighboring beaches where they provide a more economical protection from waves and currents. For regular waves, a numerical model is used (FLOW-3D, VOF) to investigate the hydraulic performance of a permeable breakwater. The model of permeable breakwater consists of a pair of identical vertical slotted walls with an impermeable upper and lower part, where the draft is a decimal multiple of the total depth. The middle part is permeable with a porosity of 50%. The second barrier is located at distant of 0.5 and 1.5 of the water depth from the first one. The numerical model is validated by comparisons with previous laboratory data and semi-analytical results of the same model. A good agreement between the numerical results and both laboratory data and semi-analytical results has been shown and the results indicate the applicability of the numerical model to reproduce most of the important features of the interaction. Through the numerical investigation, the friction factor of the model is carefully discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coastal%20structures" title="coastal structures">coastal structures</a>, <a href="https://publications.waset.org/abstracts/search?q=permeable%20breakwater" title=" permeable breakwater"> permeable breakwater</a>, <a href="https://publications.waset.org/abstracts/search?q=slotted%20wall" title=" slotted wall"> slotted wall</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20model" title=" numerical model"> numerical model</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20dissipation%20coefficient" title=" energy dissipation coefficient"> energy dissipation coefficient</a> </p> <a href="https://publications.waset.org/abstracts/12807/numerical-investigation-of-wave-interaction-with-double-vertical-slotted-walls" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12807.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">391</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">3527</span> On Constructing a Cubically Convergent Numerical Method for Multiple Roots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Young%20Hee%20Geum">Young Hee Geum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20error%20constant" title="asymptotic error constant">asymptotic error constant</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20method" title=" iterative method"> iterative method</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20root" title=" multiple root"> multiple root</a>, <a href="https://publications.waset.org/abstracts/search?q=root-finding" title=" root-finding"> root-finding</a> </p> <a href="https://publications.waset.org/abstracts/4187/on-constructing-a-cubically-convergent-numerical-method-for-multiple-roots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4187.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">220</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">3526</span> Impact Characteristics of Fragile Cover Based on Numerical Simulation and Experimental Verification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dejin%20Chen">Dejin Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Bin%20Lin"> Bin Lin</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaohui%20LI"> Xiaohui LI</a>, <a href="https://publications.waset.org/abstracts/search?q=Haobin%20Tian"> Haobin Tian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to acquire stable impact performance of cover, the factors influencing the impact force of the cover were analyzed and researched. The influence of impact factors such as impact velocity, impact weight and fillet radius of warhead was studied by Orthogonal experiment. Through the range analysis and numerical simulation, the results show that the impact velocity has significant influences on impact force of cover. The impact force decreases with the increase of impact velocity and impact weight. The test results are similar to the numerical simulation. The cover broke up into four parts along the groove. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fragile%20cover" title="fragile cover">fragile cover</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=impact%20force" title=" impact force"> impact force</a>, <a href="https://publications.waset.org/abstracts/search?q=epoxy%20foam" title=" epoxy foam"> epoxy foam</a> </p> <a href="https://publications.waset.org/abstracts/136873/impact-characteristics-of-fragile-cover-based-on-numerical-simulation-and-experimental-verification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/136873.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">263</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">3525</span> Study of Heat Transfer by Natural Convection in Overhead Storage Tank of LNG</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hariti%20Rafika">Hariti Rafika</a>, <a href="https://publications.waset.org/abstracts/search?q=Fekih%20Malika"> Fekih Malika</a>, <a href="https://publications.waset.org/abstracts/search?q=Saighi%20Mohamed"> Saighi Mohamed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During the period storage of liquefied natural gas, stability is necessarily affected by natural convection along the walls of the tank with thermal insulation is not perfectly efficient. In this paper, we present the numerical simulation of heat transfert by natural convection double diffusion,in unsteady laminar regime in a storage tank. The storage tank contains a liquefied natural gas (LNG) in its gaseous phase. Fluent, a commercial CFD package, based on the numerical finite volume method, is used to simulate the flow. The gas is just on the surface of the liquid phase. This numerical simulation allowed us to determine the temperature profiles, the stream function, the velocity vectors and the variation of the heat flux density in the vapor phase in the LNG storage tank volume. The results obtained for a general configuration, by numerical simulation were compared to those found in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title="numerical simulation">numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=natural%20convection" title=" natural convection"> natural convection</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20gains" title=" heat gains"> heat gains</a>, <a href="https://publications.waset.org/abstracts/search?q=storage%20tank" title=" storage tank"> storage tank</a>, <a href="https://publications.waset.org/abstracts/search?q=liquefied%20natural%20gas" title=" liquefied natural gas"> liquefied natural gas</a> </p> <a href="https://publications.waset.org/abstracts/27792/study-of-heat-transfer-by-natural-convection-in-overhead-storage-tank-of-lng" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27792.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">482</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">3524</span> Numerical Modeling for Water Engineering and Obstacle Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mounir%20Adal">Mounir Adal</a>, <a href="https://publications.waset.org/abstracts/search?q=Baalal%20Azeddine"> Baalal Azeddine</a>, <a href="https://publications.waset.org/abstracts/search?q=Afifi%20Moulay%20Larbi"> Afifi Moulay Larbi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20analysis%20methods" title="numerical analysis methods">numerical analysis methods</a>, <a href="https://publications.waset.org/abstracts/search?q=obstacles%20solving" title=" obstacles solving"> obstacles solving</a>, <a href="https://publications.waset.org/abstracts/search?q=engineering" title=" engineering"> engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20modeling" title=" numerical modeling"> numerical modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=iteration" title=" iteration"> iteration</a>, <a href="https://publications.waset.org/abstracts/search?q=computer" title=" computer"> computer</a>, <a href="https://publications.waset.org/abstracts/search?q=MATLAB" title=" MATLAB"> MATLAB</a>, <a href="https://publications.waset.org/abstracts/search?q=water" title=" water"> water</a>, <a href="https://publications.waset.org/abstracts/search?q=underground" title=" underground"> underground</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity" title=" velocity"> velocity</a> </p> <a href="https://publications.waset.org/abstracts/32980/numerical-modeling-for-water-engineering-and-obstacle-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32980.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">462</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">3523</span> Groundwater Seepage Estimation into Amirkabir Tunnel Using Analytical Methods and DEM and SGR Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hadi%20Farhadian">Hadi Farhadian</a>, <a href="https://publications.waset.org/abstracts/search?q=Homayoon%20Katibeh"> Homayoon Katibeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above-mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm the high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occurred in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=water%20Seepage" title="water Seepage">water Seepage</a>, <a href="https://publications.waset.org/abstracts/search?q=Amirkabir%20Tunnel" title=" Amirkabir Tunnel"> Amirkabir Tunnel</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20method" title=" analytical method"> analytical method</a>, <a href="https://publications.waset.org/abstracts/search?q=DEM" title=" DEM"> DEM</a>, <a href="https://publications.waset.org/abstracts/search?q=SGR" title=" SGR"> SGR</a> </p> <a href="https://publications.waset.org/abstracts/26677/groundwater-seepage-estimation-into-amirkabir-tunnel-using-analytical-methods-and-dem-and-sgr-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26677.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">476</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">3522</span> A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cletus%20Abhulimen">Cletus Abhulimen</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20A.%20Ukpebor"> L. A. Ukpebor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=third%20derivative%20four-step" title="third derivative four-step">third derivative four-step</a>, <a href="https://publications.waset.org/abstracts/search?q=exponentially%20fitted" title=" exponentially fitted"> exponentially fitted</a>, <a href="https://publications.waset.org/abstracts/search?q=a-stable" title=" a-stable"> a-stable</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20differential%20equations" title=" stiff differential equations"> stiff differential equations</a> </p> <a href="https://publications.waset.org/abstracts/74060/a-class-of-third-derivative-four-step-exponential-fitting-numerical-integrator-for-stiff-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74060.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">265</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">3521</span> Numerical Simulation of Punching Shear of Flat Plates with Low Reinforcement</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fatema-Tuz-Zahura">Fatema-Tuz-Zahura</a>, <a href="https://publications.waset.org/abstracts/search?q=Raquib%20Ahsan"> Raquib Ahsan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Punching shear failure is usually the governing failure mode of flat plate structures. Punching failure is brittle in nature which induces more vulnerability to this type of structure. In the present study, a 3D finite element model of a flat plate with low reinforcement ratio and without any transverse reinforcement has been developed. Punching shear stress and the deflection data were obtained on the surface of the flat plate as well as through the thickness of the model from numerical simulations. The obtained data were compared with the experimental results. Variation of punching stress with respect to deflection as obtained from numerical results is found to be in good agreement with the experimental results; the range of variation of punching stress is within 5%. The numerical simulation shows an early and gradual onset of nonlinearity, whereas the same is late and abrupt as observed in the experimental results. The range of variation of punching stress for different slab thicknesses between experimental and numerical results is less than 15%. The developed numerical model is useful to complement available punching test series performed in the past. The results obtained from the numerical model will be helpful for designing retrofitting schemes of flat plates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flat%20plate" title="flat plate">flat plate</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20model" title=" finite element model"> finite element model</a>, <a href="https://publications.waset.org/abstracts/search?q=punching%20shear" title=" punching shear"> punching shear</a>, <a href="https://publications.waset.org/abstracts/search?q=reinforcement%20ratio" title=" reinforcement ratio"> reinforcement ratio</a> </p> <a href="https://publications.waset.org/abstracts/45233/numerical-simulation-of-punching-shear-of-flat-plates-with-low-reinforcement" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45233.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">257</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">3520</span> A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jyh-Yang%20Wu">Jyh-Yang Wu</a>, <a href="https://publications.waset.org/abstracts/search?q=Sheng-Gwo%20Chen"> Sheng-Gwo Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conservation%20laws" title="conservation laws">conservation laws</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equations" title=" diffusion equations"> diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Cahn-Hilliard%20equations" title=" Cahn-Hilliard equations"> Cahn-Hilliard equations</a>, <a href="https://publications.waset.org/abstracts/search?q=evolving%20surfaces" title=" evolving surfaces"> evolving surfaces</a> </p> <a href="https://publications.waset.org/abstracts/56432/a-numerical-method-for-diffusion-and-cahn-hilliard-equations-on-evolving-spherical-surfaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56432.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">494</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">3519</span> Numerical and Analytical Approach for Film Condensation on Different Forms of Surfaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Kazemi%20Jouybari">A. Kazemi Jouybari</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Mirabdolah%20Lavasani"> A. Mirabdolah Lavasani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper seeks to the solution of condensation around of a flat plate, circular and elliptical tube in way of numerical and analytical methods. Also, it calculates the entropy production rates. The first, problem was solved by using mesh dynamic and rational assumptions, next it was compared with the numerical solution that the result had acceptable errors. An additional supporting relation was applied based on a characteristic of condensation phenomenon for condensing elements. As it has been shown here, due to higher rates of heat transfer for elliptical tubes, they have more entropy production rates, in comparison to circular ones. Findings showed that two methods were efficient. Furthermore, analytical methods can be used to optimize the problem and reduce the entropy production rate. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=condensation" title="condensation">condensation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=entropy%20rate" title=" entropy rate"> entropy rate</a> </p> <a href="https://publications.waset.org/abstracts/94520/numerical-and-analytical-approach-for-film-condensation-on-different-forms-of-surfaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94520.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">216</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">3518</span> Thermomechanical Damage Modeling of F114 Carbon Steel</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20El%20Amri">A. El Amri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20El%20Yakhloufi%20Haddou"> M. El Yakhloufi Haddou</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Khamlichi"> A. Khamlichi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The numerical simulation based on the Finite Element Method (FEM) is widely used in academic institutes and in the industry. It is a useful tool to predict many phenomena present in the classical manufacturing forming processes such as fracture. But, the results of such numerical model depend strongly on the parameters of the constitutive behavior model. The influences of thermal and mechanical loads cause damage. The temperature and strain rate dependent materials’ properties and their modelling are discussed. A Johnson-Cook Model of damage has been selected for the numerical simulations. Virtual software called the ABAQUS 6.11 is used for finite element analysis. This model was introduced in order to give information concerning crack initiation during thermal and mechanical loads. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=thermo-mechanical%20fatigue" title="thermo-mechanical fatigue">thermo-mechanical fatigue</a>, <a href="https://publications.waset.org/abstracts/search?q=failure" title=" failure"> failure</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=fracture" title=" fracture"> fracture</a>, <a href="https://publications.waset.org/abstracts/search?q=damage" title=" damage"> damage</a> </p> <a href="https://publications.waset.org/abstracts/46261/thermomechanical-damage-modeling-of-f114-carbon-steel" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46261.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">393</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">3517</span> Numerical Solution of 1-D Shallow Water Equations at Junction for Sub-Critical and Super-Critical Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Elshobaki">Mohamed Elshobaki</a>, <a href="https://publications.waset.org/abstracts/search?q=Alessandro%20Valiani"> Alessandro Valiani</a>, <a href="https://publications.waset.org/abstracts/search?q=Valerio%20Caleffi"> Valerio Caleffi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title="numerical simulation">numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=junction%20flow" title=" junction flow"> junction flow</a>, <a href="https://publications.waset.org/abstracts/search?q=sub-critical%20flow" title=" sub-critical flow"> sub-critical flow</a>, <a href="https://publications.waset.org/abstracts/search?q=super-critical%20flow" title=" super-critical flow"> super-critical flow</a> </p> <a href="https://publications.waset.org/abstracts/44090/numerical-solution-of-1-d-shallow-water-equations-at-junction-for-sub-critical-and-super-critical-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44090.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">510</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">3516</span> Coupling Heat Transfer by Natural Convection and Thermal Radiation in a Storage Tank of LNG</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Hariti">R. Hariti</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Saighi"> M. Saighi</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Saidani-Scott"> H. Saidani-Scott</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A numerical simulation of natural convection double diffusion, coupled with thermal radiation in unsteady laminar regime in a storage tank is carried out. The storage tank contains a liquefied natural gas (LNG) in its gaseous phase. Fluent, a commercial CFD package, based on the numerical finite volume method, is used to simulate the flow. The radiative transfer equation is solved using the discrete coordinate method. This numerical simulation is used to determine the temperature profiles, stream function, velocity vectors and variation of the heat flux density for unsteady laminar natural convection. Furthermore, the influence of thermal radiation on the heat transfer has been investigated and the results obtained were compared to those found in the literature. Good agreement between the results obtained by the numerical method and those taken on site for the temperature values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tank" title="tank">tank</a>, <a href="https://publications.waset.org/abstracts/search?q=storage" title=" storage"> storage</a>, <a href="https://publications.waset.org/abstracts/search?q=liquefied%20natural%20gas" title=" liquefied natural gas"> liquefied natural gas</a>, <a href="https://publications.waset.org/abstracts/search?q=natural%20convection" title=" natural convection"> natural convection</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20radiation" title=" thermal radiation"> thermal radiation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a> </p> <a href="https://publications.waset.org/abstracts/15574/coupling-heat-transfer-by-natural-convection-and-thermal-radiation-in-a-storage-tank-of-lng" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15574.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">541</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=numerical&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&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=numerical&page=118">118</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&page=119">119</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical&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>