Rigorous derivation and analysis of coupling of kinetic equations and their hydrodynamic limits for a simplified boltzmann model

Journal of Statistical Physics

Volumn 104, Issue 1-2, 2001, Pages 255-290

  Tidriri, M ^a  

^a ISU   (United States)

Author keywords

Asymptotic behaviour; Carleman equations; Coupling of kinetic equations and their hydrodynamic limits; Transmission time marching algorithm

Indexed keywords

EID: 0035535145     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010313828663     Document Type: Article

References (28)

1. C. Bardos, F. Golse, and D. Levermore, Fluid dynamics limits of kinetic equations I: Formal derivation, J. Stat. Phys. 63:323-344 (1991).
2. C. Bardos, F. Golse, and D. Levermore, Fluid dynamics limits of kinetic equations II, Commun. Pure Appl. Math. 46:667-753 (1993).
3. J.-F. Bourgat, P. Le Tallec, F. Mallinger, Y. Qiu, and M. D. Tidriri, Numerical coupling of Boltzmann and Navier Stokes, I.U.T.A.M. (International Union of Theoretical and Applied Mechanics) Conference, Marseille, France, Sept. 1-4, 1992.
4. J.-F. Bourgat, P. Le Tallec, and M. D. Tidriri, Coupling Boltzmann and Navier-Stokes equations by friction, J. Comp. Phys. 127:227-245 (1996).
5. J.-F. Bourgat, P. Le Tallec, B. Perthame, and Y. Qiu, Coupling Boltzmann and Euler equations without overlapping, in Domain Decomposition Methods in Science and Engineering, A. Quarteroni et al., ed., pp. 377-388, CM 157, AMS (1994).
6. R. Brun, Transport et relaxation dans les écoulements gazeux (Masson, Paris, 1986).
7. R. Caflish, The fluid dynamical limit of the nonlinear Boltzmann equation, Commun. Pure Appl. Math. 33:651-666 (1980).
8. T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz (Publ. Sc. Inst. Mittag-Leffler, Upsala, 1957).
9. C. Cercignani, Theory and Application of the Boltzmann Equation (Springer, 1988).
10. K. A. Comeaux, D. R. Chapman, and R. W. MacCormack, An analysis of the Burnett equations based on second law of Thermodynamics, AIAA Paper 95-0415 (January 1995).
11. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 4th ed. (Cambridge University Press, 1990).
12. H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math. 2:331 407 (1947).
13. M. Kogan, Rarefied Gas Dynamics (Plenum, 1969).
14. P. Le Tallec and M. D. Tidriri, Kinetic upgrade of Navier-Stokes equations for transitional flows, Rapport de contrat 6465/91 ATP DPH (October 1992).
15. P. Le Tallec and M. D. Tidriri, Kinetic upgrade of Navier-Stokes equations for Transitional Flows, Rapport de contrat HERMES R/Q 6465/91, INRIA (février 1993).
16. P. Le Tallec and M. D. Tidriri, Analysis of the Time Marching Algorithm, INRIA Research Report RR-2435 (Oct. 1994).
17. P. Le Tallec and M. D. Tidriri, Convergence Analysis of Domain Decomposition algorithms with full overlapping for the advection-diffusion problems, ICASE-TR No. 96-37, June 1996. Math. Comput. 68(226):585-606 (1999).
18. P. Le Tallec and M. D. Tidriri, Analysis of the explicit Time Marching Algorithm, ICASE Report No. 96-45 (August 1996).
19. P. Le Tallec and M. D. Tidriri, Application of maximum principles to the analysis of a coupling time marching algorithm. J. Math. Anal. Appl. 229:158-169 (1999).
20. T. Nishida, Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the incompressible Euler equation, Commun. Math. Phys. 61:119-148 (1978).
21. A. Palczewski, Exact and Chapman Enskog Solutions for the Carleman Model, Math. Meth. Appl. Sci. 6:417-432 (1984).
22. T. Sideris, Formation of singularities in three dimensional compressible fluids, Commun. Math. Phys. 101:475-485 (1985).
23. M. D. Tidriri, Couplage d'approximations et de modèles de types différents dans le calcul d'écoulements externes, Ph.D. thesis, Université de Paris Dauphine (1992).
24. M. D. Tidriri, Domain Decomposition for Incompatible nonlinear models, INRIA Research Report RR-2378 (October 1994).
25. M. D. Tidriri, Domain decompositions for compressible Navier-Stokes equations with different discretizations and formulations, J. Comp. Phys. 119:271-282 (1995).
26. M. D. Tidriri, Asymptotic analysis of a coupled system of kinetic equations, C. R. Acad. Sci. Paris, t. 328, Série I Math. 637-642 (1999).
27. M. D. Tidriri, Numerical analysis of coupling for a kinetic equation. Mathematical Modelling and Numerical Analysis M2 AN, Vol. 33, No. 6, pp. 1121-1134 (1999).
28. X. Zhong, R. W. MacCormack, and D. R. Chapman, AIAA J. 31:6 (1993).