Finite-difference approximation of the Hugoniot conditions on a shock front propagating with variable velocity (Q1571219)

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.