Central schemes for hydrodynamical limits of discrete-velocity kinetic models

Transport Theory and Statistical Physics

Volumn 29, Issue 3-5, 2000, Pages 465-477

  Gabetta, E ^a   Pareschi, L ^b   Ronconi, M ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITY OF FERRARA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034386606     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411450008205885     Document Type: Article

References (15)

1. R.E. Caflisch, S. Jin and G. Russo, Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Num. Anal., 34, 1, pp. 246-281, (1997).
2. C. Cercignani, Theory and application of the Boltzmann equation, Springer-Verlag, New York, (1988)
3. E. Gabetta, L. Pareschi and G. Toscani, Relaxation schemes for nonlinear kinetic equations, SIAM J. Num. Anal., 34, 6, pp. 2168-2194, (1997).
4. E. Gabetta and B. Perthame, Scaling limits of the Ruijgrok-Wu model of the Boltzmann equation, Proceedings of the International Conference on Nonlinear Equations and Applications, Bangalore, 19-23 August 1996, Springer-Verlag.
5. A. Harten and S. Osher, Uniformly high order accurate non-oscillatory schemes. I, SIAM J. Num. Anal., 24, pp. 279-309, (1987).
6. S. Jin, Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms, J. Comp. Phys., 122, pp.51-67, (1995).
7. S. Jin, L. Pareschi and G. Toscani, Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations, SIAM J. Num. Anal., 35, 6, pp. 2405-2439, (1998).
8. S. Jin, L. Pareschi and G. Toscani, Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Num. Anal. to appear.
9. A. Klar, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit, SIAM J. Num. Anal., 15, pp. 1073-1094, (1998).
10. P.L. Lions and G. Toscani, Diffusive limit for finite velocities Boltzmann kinetic models, Rev. Math. Iberoamer., 13, pp. 473-513, (1997).
11. G. Naldi and L. Pareschi, Numerical schemes for kinetic equations in diffusive regimes, Appl. Math. Lett., 11, pp. 29-35, (1998).
12. G. Naldi and L. Pareschi, Numerical schemes for hyperbolic systems with stiff diffusive relaxation, SIAM J. Num. Anal. to appear.
13. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comp. Phys., 87, pp. 408-463 (1990).
14. L. Pareschi and M. Ronconi, Predictor-corrector central schemes for multiscale hyperbolic and kinetic equations, work in progress.
15. W. Ruijgrok and T.T. Wu, A completely solvable model of the nonlinear Boltzmann equation, Phys A, 113, pp. 401-416, (1982).