A smooth transition model between kinetic and hydrodynamic equations

Journal of Computational Physics

Volumn 209, Issue 2, 2005, Pages 665-694

  Degond, Pierre ^a   Jin, Shi ^b   Mieussens, Luc ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Hydrodynamic approximation; Kinetic equation; Kinetic fluid coupling

Indexed keywords

HYDRODYNAMICS; INTEGRAL EQUATIONS; KINETIC ENERGY; KINETIC THEORY; KINETICS; NUMERICAL METHODS;

BUFFER ZONES; HYDRODYNAMIC APPROXIMATION; HYDRODYNAMICS EQUATION; INTERFACE CONDITIONS; KINETIC EQUATIONS; KINETIC-FLUID COUPLING; SMOOTH TRANSITION MODELS; SMOOTH TRANSITIONS; TRANSITION POINT; TWO EQUATION;

DOMAIN DECOMPOSITION METHODS;

EID: 21444454938     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.03.025     Document Type: Article

References (22)

1. J.-F. Bourgat P. Le Tallec M.D. Tidriri Coupling Boltzmann and Navier-Stokes equations by friction J. Comput. Phys 127 1996 227-245
2. F. Coron Derivation of slip boundary conditions for the Navier-Stokes system from the Boltzmann equation J. Stat. Phys. 54 3-4 1989 829-857
3. P. Degond S. Jin A smooth transition model between kinetic and diffusion equations SIAM J. Numer. Anal. 42 2005 2671-2687
4. F. Golse S. Jin C.D. Levermore A domain decomposition analysis for a two-scale linear transport problem M2AN Math. Model. Numer. Anal. 37 6 2003 869-892
5. A.B. Huang P.F. Hwang Test of statistical models for gases with and without internal energy states Phys. Fluids 16 4 1973 466-475
6. S. Jin Z.P. Xin The relaxation schemes for systems of conservation laws in arbitrary space dimensions Commun. Pure Appl. Math. 48 3 1995 235-276
7. A. Klar Convergence of alternating domain decomposition schemes for kinetic and aerodynamic equations Math. Meth. Appl. Sci. 18 8 1995 649-670
8. A. Klar Domain decomposition for kinetic problems with nonequilibrium states Eur. J. Mech. B 15 2 1996 203-216
9. A. Klar Asymptotic analysis and coupling conditions for kinetic and hydrodynamic equations Comput. Math. Appl. 35 1-2 1998 127-137
10. A. Klar H. Neunzert J. Struckmeier Transition from kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms Transport Theory Stat. Phys. 29 1-2 2000 93-106
11. Randall J. LeVeque Numerical methods for conservation laws Lectures in mathematics, ETH, Zürich 1990 Birkhäuser Verlag Basel
12. L. Mieussens Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics Math. Models Meth. Appl. Sci. 8 10 2000 1121-1149
13. L. Mieussens Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries J. Comput. Phys. 162 2000 429-466
14. Benôit Perthame Kinetic formulation of conservation laws Oxford lecture series in mathematics and its applications vol. 21 2002 Oxford University Press Oxford
15. Y. Qiu, Étude des équations d'Euler et de Boltzmann et de leur couplage. Application à la simulation numérique d'écoulements hypersoniques de gaz raréfiés, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, 1993, Thèse, Université Paris VI, Paris, 1993.
16. J. Schneider Direct coupling of fluid and kinetic equations Transport Theory Stat. Phys. 25 6 1996 681-698
17. P. Le Tallec F. Mallinger Coupling Boltzmann and Navier-Stokes equations by half fluxes J. Comput. Phys. 136 1 1997 51-67
18. M. Tidriri Rigorous derivation and analysis of coupling of kinetic equations and their hydrodynamic limits for a simplified Boltzmann model J. Stat. Phys. 104 1-2 2001 255-290
19. S. Tiwari Coupling of the Boltzmann and Euler equations with automatic domain decomposition J. Comput. Phys. 144 2 1998 710-726
20. A. Yamnahakki Second order boundary conditions for the drift-diffusion equations of semiconductors Math. Models Meth. Appl. Sci. 5 4 1995 429-455
21. J.Y. Yang J.C. Huang Rarefied flow computations using nonlinear model Boltzmann equations J. Comput. Phys. 120 1995 323-339
22. H.C. Yee A class of high-resolution explicit and implicit shock-capturing methods Lectures Series vol. 4 1989 von Karman Institute for Fluid Dynamics