Sensitivity Computations of Time Relaxation Model with an Application in Cavity Computation
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 χ 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).
[1] F. Pahlevani, Sensitivity Computations of Eddy Viscosity Models with an
Application in Drag Computation, International Journal for Numerical
Methods in Fluids., 52-4:381-392, 2006.
[2] M. Anitescu and W. J. Layton, Sensitivities in Large Eddy Simulation and
Improved Estimates of Turbulent Flow Functionals J.C.P, 178: 391-426,
2001.
[3] M. Anitescu and W. J. Layton, Uncertainties in large eddy simulation and
improved of turbulent flow functionals, 2002.
[4] M. Anitescu, F. Pahlevani and W. J. Layton, Implicit for local effects
and explicit for nonlocal effects is unconditionally stable Electronic
Trnasactions of Numerical Analysis, 18: 174-187, 2004.
[5] J. Borggaard and J. Burns, A sensitivity equation approach to shape
optimization in fluid flows Flow control, 49-78, 1995.
[6] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity
equation method for flows with temperature, SIAM, 14-24, 1993.
[7] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity
equation method for flows with temperature dependent properties, in
Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplanary
Analysis and Design, 2481 1993.
[8] J. Borggaard, D. Pelletier and E. Turgeon, Sensitivity and uncertainty
analysis for variable property flows, in Proceedings of the 39th AIAA
Aerospace Sciences Meeting and Exhibit, 0140, 1993.
[9] J. Borggaard and J. Burns, A PDE sensitivity equation method for optimal
aerodynamic design, Journal of Computational Physics, 136:366-384,
1997.
[10] J. Borggaard and A. Verma, Solutions to continuous sensitivity equations
using Automatic Differentiation, SIAM Journal of Scientific Computing,
22:39-62, 2001.
[11] A. Godfrey and E. Cliff, Direct calculation of aerodynamic force
derivatives: A sensitivity equation approach, in proceedings of the 36th
AIAA Aerospace Sciences Meeting and Exhibit, 0393, 1998.
[12] J. Guermond, Stabilization of Galerkin approximations of transport
equations by subgrid modeling, M2AN, 33: 1293-1316, 1999.
[13] M. Gunzburger, Sensitivities, adjoints and flow optimization, Int. Jour.
Num. Meth. Fluids, 31:53-78, 1999.
[14] P. Sagaut and T.Lˆe, Some investigations of the sensitivity of large eddy
simulation, Tech. Rep., 1997-12, ONERA.
[15] A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution LES
model, SIAM J. Math Analysis, 2006
[16] L. Stanley and D. Stewart, Design sensitivity analysis: Computational
issues of sensitivity equation methods, Frontiers in Mathematics, SIAM,
Philadelphia, 2002.
[17] N. A. Adams and S. Stolz, Deconvolution methods for subgrid-scale
approximation in large eddy simulation Modern Simulation Strategies for
Turbulent Flow, 2001.
[18] N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for
shock capturing J.C.P, 178: 391-426, 2001.
[19] R. Guenanff, Non-stationary coupling of Navier-Stokes/Euler for the
generation and radiation of aerodynamic noises, PhD thesis, Universite
Rennes, Rennes, France, 2004.
[20] F. Hecht, O. Pironneau and K. Oshtsuka, Software Freefem++,
http://www.freefem++.org, 2003.
[21] V. J. Ervin, W. J. Layton and Monika Neda, Numerical Analysis of a
Higher Order Time Relaxation Model of Fluids, International Journal of
Numerical Analysis and Modeling, 4(3-4): 648-670.
[1] F. Pahlevani, Sensitivity Computations of Eddy Viscosity Models with an
Application in Drag Computation, International Journal for Numerical
Methods in Fluids., 52-4:381-392, 2006.
[2] M. Anitescu and W. J. Layton, Sensitivities in Large Eddy Simulation and
Improved Estimates of Turbulent Flow Functionals J.C.P, 178: 391-426,
2001.
[3] M. Anitescu and W. J. Layton, Uncertainties in large eddy simulation and
improved of turbulent flow functionals, 2002.
[4] M. Anitescu, F. Pahlevani and W. J. Layton, Implicit for local effects
and explicit for nonlocal effects is unconditionally stable Electronic
Trnasactions of Numerical Analysis, 18: 174-187, 2004.
[5] J. Borggaard and J. Burns, A sensitivity equation approach to shape
optimization in fluid flows Flow control, 49-78, 1995.
[6] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity
equation method for flows with temperature, SIAM, 14-24, 1993.
[7] J. Borggaard, D. Pelletier and E. Turgeon, A continuous sensitivity
equation method for flows with temperature dependent properties, in
Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplanary
Analysis and Design, 2481 1993.
[8] J. Borggaard, D. Pelletier and E. Turgeon, Sensitivity and uncertainty
analysis for variable property flows, in Proceedings of the 39th AIAA
Aerospace Sciences Meeting and Exhibit, 0140, 1993.
[9] J. Borggaard and J. Burns, A PDE sensitivity equation method for optimal
aerodynamic design, Journal of Computational Physics, 136:366-384,
1997.
[10] J. Borggaard and A. Verma, Solutions to continuous sensitivity equations
using Automatic Differentiation, SIAM Journal of Scientific Computing,
22:39-62, 2001.
[11] A. Godfrey and E. Cliff, Direct calculation of aerodynamic force
derivatives: A sensitivity equation approach, in proceedings of the 36th
AIAA Aerospace Sciences Meeting and Exhibit, 0393, 1998.
[12] J. Guermond, Stabilization of Galerkin approximations of transport
equations by subgrid modeling, M2AN, 33: 1293-1316, 1999.
[13] M. Gunzburger, Sensitivities, adjoints and flow optimization, Int. Jour.
Num. Meth. Fluids, 31:53-78, 1999.
[14] P. Sagaut and T.Lˆe, Some investigations of the sensitivity of large eddy
simulation, Tech. Rep., 1997-12, ONERA.
[15] A. Dunca and Y. Epshteyn, On the Stolz-Adams deconvolution LES
model, SIAM J. Math Analysis, 2006
[16] L. Stanley and D. Stewart, Design sensitivity analysis: Computational
issues of sensitivity equation methods, Frontiers in Mathematics, SIAM,
Philadelphia, 2002.
[17] N. A. Adams and S. Stolz, Deconvolution methods for subgrid-scale
approximation in large eddy simulation Modern Simulation Strategies for
Turbulent Flow, 2001.
[18] N. A. Adams and S. Stolz, A subgrid-scale deconvolution approach for
shock capturing J.C.P, 178: 391-426, 2001.
[19] R. Guenanff, Non-stationary coupling of Navier-Stokes/Euler for the
generation and radiation of aerodynamic noises, PhD thesis, Universite
Rennes, Rennes, France, 2004.
[20] F. Hecht, O. Pironneau and K. Oshtsuka, Software Freefem++,
http://www.freefem++.org, 2003.
[21] V. J. Ervin, W. J. Layton and Monika Neda, Numerical Analysis of a
Higher Order Time Relaxation Model of Fluids, International Journal of
Numerical Analysis and Modeling, 4(3-4): 648-670.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63514", author = "Monika Neda and Elena Nikonova", title = "Sensitivity Computations of Time Relaxation Model with an Application in Cavity Computation", abstract = "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 χ 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).
", keywords = "Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.", volume = "5", number = "7", pages = "1080-4", }
