×

The relaxation schemes for systems of conservation laws in arbitrary space dimensions. (English) Zbl 0826.65078

The authors present a method for solving systems of conservation laws in several space dimensions. The method is a form of regularization using a system of equations twice the size of the original with a small parameter. They develop stable discretizations and give numerical results.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws

Software:

HLLE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] , and , Uniformly accurate schemes for hyperbolic systems with relaxation. SIAM J. Numer. Anal., submitted. · Zbl 0868.35070
[2] and , The Mathematical Theory of Nonuniform Gases, 3rd Edition, Cambridge Univ. Press, 1970.
[3] Chen, Comm. Pure Appl. Math. 47 pp 787– (1994)
[4] Colella, J. Comput. Phys. 87 pp 171– (1990)
[5] Crandall, Math. Comput. 34 pp 285– (1980)
[6] Deshpande, NASA Langley Tech. paper No. 2613 (1986)
[7] Doolen, G. D., (ed.), Lattice Gas Methods for PDE’s: Theory, Applications, and Hardware, Physica D 47 ( 1–2), 1991.
[8] Friedrichs, Proc. Nat. Acad. Sci. USA 68 pp 1686– (1971)
[9] Giga, Duke Math. J. 50 pp 505– (1983)
[10] Goodman, Math. Comp. 45 pp 15– (1985)
[11] Harten, SIAM Rev. 25 pp 35– (1983)
[12] Implicit numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., submitted. · Zbl 0860.65089
[13] and , Numerical schemes for hyperbolic systems with stiff relaxation terms, J. Comput. Phys., submitted.
[14] Lax, Comm. Pure Appl. Math. 7 pp 159– (1954)
[15] Numerical Methods for Conservation Laws, rev. ed., Birkhäuser, Basel, 1992.
[16] Liu, Comm. Math. Phys. 108 pp 153– (1987)
[17] Majda, J. Differential Equations 56 pp 229– (1985)
[18] Morawetz, Comm. Pure Appl. Math. 38 pp 797– (1985)
[19] Nessyahu, J. Comput. Phys. 87 pp 408– (1990)
[20] Perthame, SIAM J. Numer. Anal. 29 pp 1– (1992)
[21] Perthame, Comm. Math. Phys. 136 pp 501– (1991)
[22] Pullin, J. Comput. Phys. 34 pp 231– (1980)
[23] Reitz, J. Comput. Phys. 42 pp 108– (1981)
[24] Shu, J. Comput. Phys. 77 pp 439– (1988)
[25] Sod, J. Comput. Phys. 27 pp 1– (1978)
[26] Sweby, SIAM J. Numer. Anal. 21 pp 995– (1984)
[27] van Leer, J. Comput. Phys. 32 pp 101– (1979)
[28] Linear and Nonlinear Waves, Wiley, New York, 1974.
[29] Woodward, J. Comput. Phys. 54 pp 115– (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.