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van Leer, Bram

Towards the ultimative conservative difference scheme. V: A second-order sequel to Godunov’s method. (English) Zbl 0939.76063

J. Comput. Phys. 135, No. 2, 229-248 (1997).
Reprinted from ibid. 32, No. 1, 101–136 (1979; Zbl 1364.65223); for parts II, III and IV see the author, ibid. 14, 361–370 (1974; Zbl 0276.65055); ibid. 23, 263–275 (1977; Zbl 0339.76039) and ibid. 23, 276–299 (1977; Zbl 0339.76056), respectively.

Cited in 4 Reviews
Cited in 54 Documents

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)

Keywords:

ideal compressible flow; integral conservation laws; one-dimensional Lagrangian scheme; second-order accuracy; positivity; monotonicity; nonlinear stability

Citations:

Zbl 0276.65055; Zbl 0339.76039; Zbl 0339.76056; Zbl 1364.65223
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\textit{B. van Leer}, J. Comput. Phys. 135, No. 2, 229--248 (1997; Zbl 0939.76063)
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References:

[1] Godunov, S. K., Mat. Sb., 47, 271 (1959)
[2] van Leer, B., J. Comput. Phys., 23, 276 (1977)
[3] Boris, J. P., Memorandum Report, 2542 (Dec. 1972)
[4] Godunov, S. K.; Zabrodyn, A. W.; Prokopov, G. P., Z. Vyčisl. Mat. i Mat. Fiz., 1, 1020 (1961)
[5] van Leer, V., J. Comput. Phys., 23, 263 (1977)
[6] Strang, W. G., SIAM J. Numer. Anal., 5, 506 (1968)
[7] Noh, W. F.; Woodward, P. R., Lecture Notes in Physics, 59 (1977), Springer-Verlag: Springer-Verlag Berlin, p. 330-
[9] Weber, W. J.; Boris, J. P.; Gardner, J., ALFVEN, a two-dimensional SHASTA code solving the radiative, diffusive MHD equations, Comput. Phys. Comm., 16, 243 (1979)
[10] Boris, J. P., Memorandum Report, 3237 (March 1976)
[11] Fromm, J. E., J. Comput. Phys., 3, 176 (1968)
[12] van Leer, B., Lecture Notes in Physics, 18 (1973), Springer-Verlag: Springer-Verlag Berlin, p. 163-
[13] van Leer, B., J. Comput. Phys., 14, 361 (1974)
[14] Courant, R.; Isaacson, E.; Rees, M., Comm. Pure Appl. Math., 5, 243 (1952)
[15] Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves (1948), Interscience: Interscience New York · Zbl 0041.11302
[18] Sod, G. A., J. Comput. Phys., 27, 1 (1978)
[19] Richtmyer, R. D.; Morton, D. W., Difference Methods for Initial-Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[20] Fromm, J. E., Research Report, RJ 780 (1970)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.