Numerical schemes for hyperbolic conservation laws with stiff relaxation terms

Journal of Computational Physics

Volumn 126, Issue 2, 1996, Pages 449-467

  Jin, Shi ^a   Levermore, C David ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; PHYSICAL PROPERTIES;

ASYMPTOTIC BEHAVIOUR; HIGH-RESOLUTION METHODS; HYPERBOLIC CONSERVATION LAWS; HYPERBOLIC SYSTEM; LONG TIME BEHAVIOR; NUMERICAL SCHEME; PARABOLICS; REDUCED SYSTEMS; RELAXATION RATES; SPATIAL GRIDS;

ASYMPTOTIC ANALYSIS;

EID: 0030194392     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0149     Document Type: Article

References (48)

1. 1. M. Ben-Artzi, J. Comput. Phys. 81, 70 (1989).
2. 2. R. Caflisch, Commun. Pure Appl. Math. 22, 521 (1979).
3. 3. R. Caflisch, S. Jin, and G. Russo, SIAM J. Numer. Anal., to appear.
4. 4. R. Caflisch and G. Papanicolaou, Commun. Pure Appl. Math. 32, 589 (1979).
5. 5. C. Cerecignani, The Boltzmann Equation and Its Applications (Springer-Verlag, New York, 1988).
6. 6. G.-Q. Chen and T.-P. Liu Commun. Pure Appl. Math. 45, 755 (1993).
7. 7. G.-Q. Chen, C. D. Levermore, and T.-P. Liu, Commun. Pure Appl. Math. 47, 787 (1994).
8. 8. J. F. Clark, Rep. Prog. Phys. 41, 807 (1978).
9. 9. P. Colella, A. Majda, and V. Roytburd, SIAM J. Sci. Statist. Comput. 7, 1059 (1986).
10. 10. P. Collela and P. R. Woodward, J. Comput. Phys. 54, 174 (1984).
11. 11. B. Engquist and B. Sjogreen, "Numerical Approximation of Hyperbolic Conservation Laws with Stiff Source Terms," in Proceedings, Third International Conf. on Hyperbolic Problems, edited by B. Engquist and B. Gustafsson (Studentlitterratur, 1991), p. 848.
12. 12. B. Engquist and B. Sjogreen, UCLA CAM Report 91-03 (unpublished).
13. 13. M. M. Gibson and B. E. Launder, J. Fluid Mech. 86, 491 (1978).
14. 14. H. M. Glaz and T.-P. Liu, Adv. Appl. Math. 29, 1244 (1992).
15. 15. J. Glimm, "The Continuous Structure of Discontinuities," Lecture Notes in Physics, Vol. 344 (Springer-Verlag, New York/Berlin, 1986), p. 177.
16. 16. S. K. Godunov, Mat. Sb. 47, 271 (1959).
17. 17. F. Golse, S. Jin, and C. D. Levermore, SIAM J. Numer. Anal., submitted.
18. 18. D. F. Griffiths, A. M. Stuart, and H. C. Yee, SIAM J. Numer. Anal. 29(5), 1244 (1992).
19. 19. E. Harabetian, SIAM J. Numer. Anal. 27, 870 (1990).
20. 20. E. Harabetian, J. Comput. Phys. 103, 350 (1992).
21. 21. A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, J. Comput. Phys. 71, 231 (1987).
22. 22. L. Hsiao and T.-P. Liu, Commun. Math. Phys. 143, 599 (1992).
23. 23. S. Jin, Ph.D. thesis, University of Arizona, 1991.
24. 24. S. Jin, J. Comput. Phys. 122, 51 (1995).
25. 25. S. Jin and D. Levermore, Transp. Theory Stat. Phys. 20, 413 (1991).
26. 26. S. Jin and C. D. Levermore, Transp. Theory Stat. Phys. 22, 739 (1993).
27. 27. D. D. Joseph, Fluid Dynamics of Viscoelastic Liquids (Springer-Verlag, New York, 1990).
28. 28. E. W. Larsen, Nucl. Sci. Eng. 112, 336 (1992).
29. 29. E. W. Larsen, J. E. Morel, and W. F. Miller Jr., J. Comput. Phys. 69 283 (1987).
30. 30. B. E. Launder and N. Shima, AIAA J. 27, 1319 (1989).
31. 31. R. J. LeVeque, Numerical Methods for Conservation Laws (Birkhauser, Basel, 1992).
32. 32. R. J. LeVeque and H. C. Yee, J. Comput. Phys. 86, 187 (1990).
33. 33. C. D. Levermore, "Fluid Dynamical Limits of the Discrete Kinetic Theories," in Macroscopic Simulations of Complex Hydrodynamic Phenomena, edited by M. Mareschal and B. L. Holian, NATO ASI Series B, Vol. 292 (Plenum Press, New York, 1992), p. 173.
34. 34. C. D. Levermore, J. Stat. Phys., to appear.
35. 35. T.-P. Liu, Commun. Math. Phys. 68, 141 (1979).
36. 36. T.-P. Liu, Commun. Math. Phys. 108, 153 (1987).
37. 37. H. Nessyahu and E. Tadmor, J. Comput. Phys. 87, 408 (1990).
38. 38. R. Pember, SIAM J. Appl. Math. 86, 1293 (1993).
39. 39. R. Pember, SIAM J. Sci. Stat. Comput. 14, 824 (1993).
40. 40. P. L. Roe, "Upwind Differencing Schemes for Hyperbolic Conservation Laws with Source Terms," Lect. Notes in Math, Vol. 1270 (Springer-Verlag, New York/Berlin, 1986), p. 41.
41. 41. P. L. Roe and M. Arora, Numer. Methods Partial Differential Equations 9, 459 (1993).
42. 42. J. Smoller, Shock Waves and Reaction-Diffusion Equation (Springer-Verlag, New York, 1983).
43. 43. J. J. Stoker, Water Waves (Interscience, New York, 1966).
44. 44. B. van Leer, J. Comput. Phys. 32, 101 (1979).
45. 45. B. van Leer, SIAM J. Sci. Stat. Comput. 5, 1 (1984).
46. 46. W. Vicenti and C. Kruger, Introduction to Physical Gas Dynamics (Kreger, Malabar, India, 1982).
47. 47. R. F. Warming and B. J. Hyett, J. Comput. Phys. 14, 159 (1973).
48. 48. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1974).