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Kinetic and Related Models (KRM)
 

Asymptotic preserving scheme for a kinetic model describing incompressible fluids
Pages: 51 - 74, Issue 1, March 2016

doi:10.3934/krm.2016.9.51      Abstract        References        Full text (693.0K)           Related Articles

Nicolas Crouseilles - Inria Rennes Bretagne Atlantique (team IPSO) and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email)
Mohammed Lemou - CNRS and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email)
SV Raghurama Rao - Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India (email)
Ankit Ruhi - National Mathematics Initiative, Indian Institute of Science, Bangalore, India (email)
Muddu Sekhar - Department of Civil Engineering, Indian Institute of Science, Bangalore, India (email)

1 M. Bennoune, M. Lemou and L. Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving compressible Navier-Stokes asymptotics, J. Comput. Phys., 227 (2008), 3781-3803.       
2 F. Bouchut and B. Perthame, The BGK model for small Prandtl number in the Navier-Stokes approximation, J. Stat. Phys., 71 (1993), 191-207.       
3 Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations, 25 (2000), 737-754.       
4 H. Chen, S. Kandasamy, S. Orzag, R. Shock, S. Succi and V. Yakhot, Extended Boltzmann kinetic equation for turbulent flows, Science Magazine, 301 (2003), 633-636.
5 F. Coron and B. Perthame, Numerical passage from kinetic to fluid equations, SIAM J. Numer. Anal., 28 (1991), 26-42.       
6 N. Crouseilles and M. Lemou, An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits, Kinetic Related Models, 4 (2011), 441-477.       
7 P. Degond and M. Lemou, Turbulence models for incompressible fluids derived from kinetic theory, J. Math. Fluid Mech., 4 (2002), 257-284.       
8 P. Degond and M. Lemou, On viscosity and termal conduction of fluids with multivalued internal energy, Eur. J. Mech. B-Fluids, 20 (2001), 303-327.       
9 P. Degond and P. F. Peyrard, Un modèle de collisions ondes-particules en physique des plasmas: Application la dynamique des gaz, C. R. Acad. Sci. Paris, Ser I, 323 (1996), 209-214.       
10 P. Degond, J. L. López and P. F. Peyrard, On the macroscopic dynamics induced by a model wave-particle collision operator, Continuum Mechanics and Thermodynamics, 10 (1998), 153-178.       
11 P. Degond, J.L. López, F. Poupaud and C. Schmeiser, Existence of solutions of a kinetic equation modeling cometary flows, J. Stat. Phys., 96 (1999), 361-376.       
12 G. Dimarco and L. Pareschi, Asymptotic preserving implicit-explicit Runge-Kutta methods for non-linear kinetic equations, SIAM Journal of Numerical Analysis, 51 (2013), 1064-1087.       
13 G. Dimarco and L. Pareschi, Exponential Runge-Kutta methods for stiff kinetic equations, SIAM Journal of Numerical Analysis, 49 (2011), 2057-2077.       
14 J. Earl, J. R. Jokipii and G. Morfill, Cosmic ray viscosity, Astrophysical Journal, 331 (1988), L91-L94.
15 F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources, J. of Comput. Phys., 229 (2010), 7625-7648.       
16 S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM Journal on Scientific Computing, 21 (1999), 441-454.       
17 A. Klar and C. Schmeiser, Numerical passage from radiative heat transfer to nonlinear diffusion models, Math. Models Methods Appl. Sci., 11 (2001), 749-767.       
18 M. Lemou, Relaxed micro-macro schemes for kinetic equations, C.R. Acad. Sci. Paris, Ser. I, 348 (2010), 455-460.       
19 M. Lemou and L. Mieussens, A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comput., 31 (2008), 334-368.       
20 L. Mieussens and H. Struchtrup, Numerical comparison of BGK-models with proper Prandtl number, Phys. Fluids, 16 (2004), 2797-2813.
21 S. Pieraccini and G. Puppo, Implicit-explicit schemes for BGK kinetic equations, Journal of Scientific Computing, 32 (2007), 1-28.       
22 S. B. Pope, Turbulent Flows, Cambridge University Press, 2000.       
23 H. Struchtrup, The BGK-model with velocity-dependent collision time, Cont. Mech. Thermodyn., 9 (1997), 23-31.       
24 D. C. Wilcox, Turbulence Modeling for CFD, D.C.W. Industries Inc., California, 1994.

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