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Finite-difference approximation of the Hugoniot conditions on a shock front propagating with variable velocity. (English. Russian original) Zbl 1086.76552
Comput. Math. Math. Phys. 38, No. 8, 1299-1311 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 8, 1355-1367 (1998).
This paper is devoted to the analysis of accuracy with which explicit two-layer conservative difference schemes approximate Hugoniot conditions on unsteady shock fronts. The author introduces Hugoniot \(\epsilon\)-conditions as relations between the values of a generalized solution on the boundaries in an \(\epsilon\)-neighborhood of a line of discontinuity. It shown that explicit two-layer conservative difference schemes, that are high-order accurate as applied to smooth solutions, approximate Hugoniot \(\epsilon\)-conditions for unsteady shock waves with sufficiently smooth wavefronts.

76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics