Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations

SIAM Journal of Scientific Computing

Volumn 21, Issue 2, 1999, Pages 441-454

  Jin, Shi ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATION THEORY; LINEAR SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ASYMPTOTIC PRESERVING SCHEMES; BOLTZMANN EQUATION; DIFFUSION LIMIT; KINETIC EQUATIONS;

NAVIER STOKES EQUATIONS;

EID: 0033295423     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598334599     Document Type: Article

References (24)

1. R. E. CAFLISCH, S. JIN, AND G. RUSSO, Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Numer. Anal., 34 (1997), pp. 246-281.
2. T. CARLEMAN, Problèmes mathématiques dans la théorie cinétique des gaz, Publ. Sc. Inst. Mittag-Leffler, Uppsala, 1957.
3. F. CORON AND B. PERTHAME, Numerical passage from kinetic to fluid equations, SIAM J. Numer. Anal., 28 (1991), pp. 26-42.
4. E. GABETTA, L. PARESCHI, AND G. TOSCANI, Relaxation schemes for nonlinear kinetic equations, SIAM J. Numer. Anal., 34 (1997), pp. 2168-2194.
5. S. GOLDSTEIN, On diffusion by discontinuous movements, and on the telegraph equation, Quart. J Mech. Appl. Math., 4 (1951). pp. 129-156.
6. F. GOLSE, S. JIN, AND C. D. LEVERMORE, The convergence of numerical transfer schemes in diffusive regimes I: Discrete-ordinate method, SIAM J. Numer. Anal., 36 (1999), pp. 1333-1369.
7. S. JIN, Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 122 (1995), pp. 51-67.
8. S. JIN AND C. D. LEVERMORE, Numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 126 (1996), pp. 449-467.
9. S. JIN AND C. D. LEVERMORE, The discrete-ordinate method in diffusive regimes, Transport Theory Statist. Phys., 20 (1991), pp. 413-439.
10. S. JIN AND C. D. LEVERMORE, Fully discrete numerical transfer in diffusive regimes, Transport Theory Statist. Phys., 22 (1993), pp. 739-791.
11. S. JIN, L. PARESCHI, AND G. TOSCANI, Diffusive relaxation schemes for multiscale, discrete-velocity kinetic equations, SIAM J. Numer. Anal., 35 (1998), pp. 2405-2439.
12. S. JIN AND Z. XIN, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math., 48 (1995), pp. 235-277.
13. A. KLAR, A numerical method for kinetic semiconductor equations in the drift diffusion limit, SIAM J. Sci. Comput., 20 (1999), pp. 1696-1712.
14. A. KLAR, An asymptotic induced scheme for nonstationary transport equations in the diffusion limit, SIAM J. Numer. Anal., 15 (1998), pp. 1073-1094.
15. T. G. KURTZ, Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics, Trans. Amer. Math. Soc., 186 (1973), pp. 259-272.
16. E. W. LARSEN, The asymptotic diffusion limit of discretized transport problems, Nuclear Sci. Engrg., 112 (1992), pp. 336-346.
17. E. W. LARSEN, J. E. MOREL, AND W. F. MILLER, JR., Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes, J. Comput. Phys., 69 (1987), pp. 283-324.
18. P. L. LIONS AND G. TOSCANI, Diffusive limits for finite velocities Boltzmann kinetic models, Rev. Mat. Iberoamericana, 13 (1997), pp. 1-34.
19. H. P. MCKEAN, The central limit theorem for Carleman's equation, Israel J. Math., 21 (1975), pp. 54-92.
20. P. L. ROE AND M. ARORA, Characteristic-based schemes for dispersive, waves I. The method of characteristics for smooth solutions, Numer. Methods Partial Differential Equations, 9 (1993), pp. 459-505.
21. K. K. TAMMA AND R. R. NAMBURU, Hyperbolic heat-conductions problems: Numerical simulation via explicit Lax- Wendroff-based finite elements formulations, J. Termodin. Heat Transfer, 5 (1991), p. 232.
22. K. K. TAMMA AND S. B. RAILKAR, Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects, Numer. Heat Transfer Part B, 15 (1989), p. 211.
23. G. I. TAYLOR, Diffusion by continuous movements, Proc. London Math. Soc., 20 (1921), pp. 196-212.
24. B. VAN LEER, Towards the ultimate conservative difference scheme V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136.