A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation

Journal of Computational Physics

Volumn 199, Issue 2, 2004, Pages 776-808

  Crouseilles, N ^a,b   Degond, P ^a   Lemou, M ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b CEA CESTA   (France)

Author keywords

BGK equation; Entropy minimization principle; Euler equations; Kinetic hydrodynamic coupling; Numerical schemes

Indexed keywords

BOLTZMANN EQUATION; ENTROPY; GAS DYNAMICS; INTEGRAL EQUATIONS;

BGK EQUATION; BOLTZMANN; ENTROPY MINIMIZATION; ENTROPY MINIMIZATION PRINCIPLE; EULER'S EQUATION; FAST PARTICLE; FLUID MODELING; HYDRODYNAMIC COUPLING; KINETIC-HYDRODYNAMIC COUPLING; NUMERICAL SCHEME;

KINETICS;

EID: 4544253987     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.03.007     Document Type: Article

References (31)

1. Anile A.M. Romano V. Russo G. Extended hydrodynamical model of carrier transport in semiconductors SIAM J. Appl. Math. 61 1 2000 74-101
2. Aoki K. Kanba K. Takata S. Numerical analysis of a supersonic rarefied gas flow past a flat plate Phys. Fluids 9 4 1997 1144-1161
3. Bathnagar P.L. Gross E.P. Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems Phys. Rev. 94 1954 511-525
4. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Glows 1994 Oxford Science Publications
5. J.F. Bourgat, P. Le Tallec, B. Perthame, Y. Qiu, Coupling Boltzmann and Euler Equations without Overlapping, Domain Decomposition Methods in Science and Engineering (COMO, 1992), American Mathematical Society, pp. 377-398
6. Brunner S. Valeo E. Krommes J.A. Linear delta-f simulations of nonlocal electron heat transport Phys. Plasmas 7 7 2000
7. Buet C. A discrete-velocity scheme for the Boltzmann operator of rarefied gas dynamics Transp. Th. Stat. Phys. 25 1 1996 33-60
8. Cercignani C. The Boltzmann Equation and its Applications Lectures Series in Mathematics vol. 68 1988 Springer Berlin
9. Chapman S. Cowling T.G. The Mathematical Theory of Non-Uniform Gases 1970 Cambridge University Press Cambridge
10. Crouseilles N. Dérivation de modèles couplés dérive-diffusion/cinétique par une méthode de décomposition en vitesse C. R. Acad. Sci. Paris I 334 2002 827-832
11. Crouseilles N. Degond P. Lemou M. Hybrid kinetic/fluid models for nonequilibrium systems C. R. Acad. Sci. Paris I 336 2003
12. Degond P. Lemou M. Turbulence models for incompressible fluids derived from kinetic theory J. Math. Fluid Mech. 4 2002 257-284
13. Degond P. Peyrard P.F. Russo G. Villedieu Ph. Polynomial upwind schemes for hyperbolic systems C. R. Acad. Sci. Paris 1 328 1999 479-483
14. Dubroca B. Klar A. Prise en compte d'un fort déséquilibre cinétique par un modèle aux demi-moments C. R. Math. Acad. Sci. Paris 335 8 2002 699-704
15. Goldstein D. Sturtevant B. Broadwell J.E. Investigations of the motion of discrete-velocity gases Rarefied Gas Dyn. 1989
16. Grad H. On the kinetic theory of rarefied gases Commun. Pure Appl. Math 2 1949
17. Grad H. Principles of the kinetic theory of gases, In: Flugge S. (Ed.). Handbuch der Physik vol. XII 1958 Springer Berlin
18. Gropengiesser F. Neunzert H. Struckmeier J. Wiesen B. Rarefied gas flow around a disc with different angles of attack Rarefied Gas Dynamics 1991 VCH Weinheim pp. 546-553
19. Groth C. Gombosi T.I. Roe P. Brown S. Gaussian-based Moment-method Closures for the Solution of the Boltzmann Equation Hyperbolic Problems: Theory, Numerics, Applications (Stony Brook, NY, 1994) 1996 World Scientific Publishing pp. 339-346
20. Junk M. Maximum entropy for reduced moment problem Math. Models Meth. Appl. Sci. 10 7 2000 1001-1025
21. Levermore C.D. Moment closure hierarchies for kinetic theories J. Stat. Phys. 83 1996 1021-1065
22. Mieussens L. Discrete velocities model and implicit scheme for the BGK equation of rarefied gas dynamics Math. Models Meth. Appl. Sci. 10 8 2000 1121-1149
23. Le Tallec P. Mallinger F. Coupling Boltzmann and Navier - Stokes equations by half fluxes J. Comput. Phys. 136 1 1997 51-67
24. Le Tallec P. Perlat J.P. Coupling kinetic models with Navier - Stokes equations CFD Rev. II 1998 833-855
25. Muller I. Ruggeri T. Rational Extended Thermodynamics second ed. Springer Tracts in Natural Philosophy vol. 37 1998
26. Nanbu K. Direct simulation scheme derived from the Boltzmann equation J. Phys. Soc. Jpn. 45 1980 2042-2049
27. Parker S.E. Lee W.W. A fully nonlinear characteristic method for gyrokinetic simulation Phys. Fluids 5 1993 77-86
28. J.P. Perlat, Modélisation et calcul parallèle d'une couche limite cinétique, Ph.D. Thesis, Université Pierre et Marie Curie, Paris, 1997, p. 6
29. Rogier F. Schneider J. A direct method for solving the Boltzmann equation Transp. Th. Stat. Phys. 23 1-3 1994 313-338
30. Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws J. Comput. Phys. 27 1 1978 1-31
31. H.C. Yee, A class of high-resolution explicit and implicit shock-capturing methods, Von Karman Institute for Fluid Dynamics, Lecture Series, vol. 4, 1989