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Approximate Riemann solvers, parameter vectors, and difference schemes. (English) Zbl 0474.65066


MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L60 First-order nonlinear hyperbolic equations
76N15 Gas dynamics (general theory)
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References:

[1] Roe, P. L., (Proceedings, Seventh Int. Conf. Num. Meth. Fluid Dyn. (1981), Springer-Verlag: Springer-Verlag New York/Berlin)
[2] Oleinik, O. A., Trans. Amer. Math. Soc. Sect. 2, 33, 285 (1963) · Zbl 0132.33303
[3] Lax, P. D., Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (1972), SIAM: SIAM Philadelphia
[4] Godunov, S. K., Mat. Sb., 47, 271 (1959), also as US JPRS translation 7226 (1960)
[5] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial-Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[6] Holt, M., Numerical Methods in Fluid Dynamics (1977), Springer-Verlag: Springer-Verlag New York/Berlin · Zbl 0357.76009
[7] Van Leer, B., J. Comput. Phys., 32, 101 (1979) · Zbl 1364.65223
[8] Glimm, J., Comm. Pure Appl. Math., 18, 697 (1965) · Zbl 0141.28902
[9] Chorin, A. J., J. Comput. Phys., 22, 517 (1976) · Zbl 0354.65047
[10] Harten, A.; Lax, P. D., SIAM J. Numer. Anal., 18, 289 (1981) · Zbl 0467.65038
[11] Sells, C. C.L., RAE TR 80065 (1980)
[13] Viviand, H., (Proceedings, Seventh Int. Conf. Num. Meth. Fluid Dyn. (1981), Springer-Verlag: Springer-Verlag New York/Berlin)
[14] Sod, G. A., J. Comput. Phys., 27, 1 (1978) · Zbl 0387.76063
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