{"title":"Sensitivity Computations of Time Relaxation Model with an Application in Cavity Computation","authors":"Monika Neda, Elena Nikonova","volume":55,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1077,"pagesEnd":1081,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14516","abstract":"<p>We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter &chi; on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).<\/p>\r\n","references":"[1] F. Pahlevani, Sensitivity Computations of Eddy Viscosity Models with an\r\nApplication in Drag Computation, International Journal for Numerical\r\nMethods in Fluids., 52-4:381-392, 2006.\r\n[2] M. Anitescu and W. J. Layton, Sensitivities in Large Eddy Simulation and\r\nImproved Estimates of Turbulent Flow Functionals J.C.P, 178: 391-426,\r\n2001.\r\n[3] M. Anitescu and W. J. Layton, Uncertainties in large eddy simulation and\r\nimproved of turbulent flow functionals, 2002.\r\n[4] M. Anitescu, F. Pahlevani and W. J. Layton, Implicit for local effects\r\nand explicit for nonlocal effects is unconditionally stable Electronic\r\nTrnasactions of Numerical Analysis, 18: 174-187, 2004.\r\n[5] J. Borggaard and J. Burns, A sensitivity equation approach to shape\r\noptimization in fluid flows Flow control, 49-78, 1995.\r\n[6] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity\r\nequation method for flows with temperature, SIAM, 14-24, 1993.\r\n[7] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity\r\nequation method for flows with temperature dependent properties, in\r\nProceedings of the 8th AIAA\/USAF\/NASA\/ISSMO Symposium on Multidisciplanary\r\nAnalysis and Design, 2481 1993.\r\n[8] J. Borggaard, D. Pelletier and E. Turgeon, Sensitivity and uncertainty\r\nanalysis for variable property flows, in Proceedings of the 39th AIAA\r\nAerospace Sciences Meeting and Exhibit, 0140, 1993.\r\n[9] J. Borggaard and J. Burns, A PDE sensitivity equation method for optimal\r\naerodynamic design, Journal of Computational Physics, 136:366-384,\r\n1997.\r\n[10] J. Borggaard and A. Verma, Solutions to continuous sensitivity equations\r\nusing Automatic Differentiation, SIAM Journal of Scientific Computing,\r\n22:39-62, 2001.\r\n[11] A. Godfrey and E. Cliff, Direct calculation of aerodynamic force\r\nderivatives: A sensitivity equation approach, in proceedings of the 36th\r\nAIAA Aerospace Sciences Meeting and Exhibit, 0393, 1998.\r\n[12] J. Guermond, Stabilization of Galerkin approximations of transport\r\nequations by subgrid modeling, M2AN, 33: 1293-1316, 1999.\r\n[13] M. Gunzburger, Sensitivities, adjoints and flow optimization, Int. Jour.\r\nNum. Meth. Fluids, 31:53-78, 1999.\r\n[14] P. Sagaut and T.L\u2566\u00e5e, Some investigations of the sensitivity of large eddy\r\nsimulation, Tech. Rep., 1997-12, ONERA.\r\n[15] A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution LES\r\nmodel, SIAM J. Math Analysis, 2006\r\n[16] L. Stanley and D. Stewart, Design sensitivity analysis: Computational\r\nissues of sensitivity equation methods, Frontiers in Mathematics, SIAM,\r\nPhiladelphia, 2002.\r\n[17] N. A. Adams and S. Stolz, Deconvolution methods for subgrid-scale\r\napproximation in large eddy simulation Modern Simulation Strategies for\r\nTurbulent Flow, 2001.\r\n[18] N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for\r\nshock capturing J.C.P, 178: 391-426, 2001.\r\n[19] R. Guenanff, Non-stationary coupling of Navier-Stokes\/Euler for the\r\ngeneration and radiation of aerodynamic noises, PhD thesis, Universite\r\nRennes, Rennes, France, 2004.\r\n[20] F. Hecht, O. Pironneau and K. Oshtsuka, Software Freefem++,\r\nhttp:\/\/www.freefem++.org, 2003.\r\n[21] V. J. Ervin, W. J. Layton and Monika Neda, Numerical Analysis of a\r\nHigher Order Time Relaxation Model of Fluids, International Journal of\r\nNumerical Analysis and Modeling, 4(3-4): 648-670.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 55, 2011"}