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A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. (English) Zbl 0387.76063


MSC:

76L05 Shock waves and blast waves in fluid mechanics
35L65 Hyperbolic conservation laws
65N06 Finite difference methods for boundary value problems involving PDEs
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References:

[1] Boris, J. P.; Book, D. L., J. Computational Phys., 11, 38 (1973)
[2] Boris, J. P.; Book, D. L.; Hain, K. J., J. Computational Phys., 18, 248 (1975)
[3] Chorin, A. J., J. Computational Phys., 22, 517 (1976)
[4] Chorin, A. J., J. Computational Phys., 25, 253 (1977)
[5] Godunov, S. K., Mat. Sbornik, 47, 271 (1959)
[6] Godunov, S. K.; Zabrodin, A. V.; Prokopov, G. P., J. Comp. Math. Math. Phys. USSR, 1, 1187 (1962)
[7] Glimm, J., Comm. Pure Appl. Math., 18, 697 (1965)
[8] Harten, A., The Method of Artificial Compression, (AEC Research and Development Report C00-3077-50 (1974), New York University)
[9] Harten, A., Comm. Pure Appl. Math., 30, 611 (1977)
[10] A. Harten; A. Harten · Zbl 0409.76057
[11] A. Harten and G. Sod; A. Harten and G. Sod
[12] Harten, A.; Zwas, G., J. Computational Phys., 6, 568 (1972)
[13] J. M. Hyman; J. M. Hyman
[14] Lapidus, A., J. Computational Phys., 2, 154 (1967)
[15] Lax, P. D., Comm. Pure Appl. Math., 7, 159 (1954)
[16] Lax, P. D., Comm. Pure Appl. Math., 10, 537 (1957)
[17] Van Leer, B., J. Computational Phys., 3, 473 (1969)
[18] Maccormack, R., (Holt, M., Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics. Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, Vol. 8 (1971), Springer-Verlag: Springer-Verlag New York)
[19] Richtmyer, R., A Survey of Difference Methods for Non-Steady Fluid Dynamics, (NCAR Technical Note 63-2 (1962), National Center for Atmospheric Research: National Center for Atmospheric Research Boulder, Colo)
[20] Richtmyer, R.; Morton, K., Difference Methods for Initial-Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[21] Rusanov, V. V., J. Comp. Math. Math. Phys. USSR, No. 2 (1962)
[22] Son, G. A., The Computer Implementation of Glimm’s Method, (UCID-17252 (1976), Lawrence Livermore Laboratory, University of California)
[23] Sod, G. A., J. Fluid Mech., 83, 785 (1977)
[24] G. A. Son, A numerical model of unsteady combustion phenomena, to appear.; G. A. Son, A numerical model of unsteady combustion phenomena, to appear.
[25] G. A. Soo, “Numerical Analysis with Application to Fluid Dynamics,” Courant Institute Lecture Notes, to appear.; G. A. Soo, “Numerical Analysis with Application to Fluid Dynamics,” Courant Institute Lecture Notes, to appear.
[26] Von Neumann, J.; Richtmyer, R. D., J. Appl. Phys., 21, 232 (1950)
[27] Buckley, S. E.; Leverett, M. C., Trans. AIME, 146, 107 (1942)
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