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An introduction to the article “Reminiscences about difference schemes” by S. K. Godunov. (English) Zbl 0936.65105

The author, who is well known for his own contribution to the numerical solution of hyperbolic systems of conservation laws as the Euler equations of gas dynamics, gives some notes in addition to the paper of S. K. Godunov [ibid. 153, No. 1, 6-25 (1999; reviewed below)].
After a brief presentation of S. K. Godunov and his contributions in the branch of computational fluid dynamics, perspectives regarding the approximation of hyperbolic systems arising in physics and engineering are discussed. In particular, the influence of Godunov-type methods and the question of the wave structure are emphasized.
Reviewer: E.Emmrich (Berlin)

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
01A65 Development of contemporary mathematics
35L65 Hyperbolic conservation laws
65-03 History of numerical analysis
76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics

Software:

HLLE; SHASTA
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Full Text: DOI

References:

[1] van Leer, B., Godunov’s method for gas dynamics: Current applications and future developments, J. Comput. Phys., 132, 1 (1997)
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