2003 , Volume 8, Special issue, p.67-81

Certain manipulation with the mass, momentum and energy conservation laws, written in the form of partial differential equations for an ideal non-heat- conducting medium, give a corollary saying about entropy conservation along the particle trajectory. Conservation laws on the surface of a strong shock are algebraic equations showing that entropy grows across the shock wave. This is the fundamental difference between a shock wave and a continuous solution. We will discuss only the shock wave methods that treat the strong discontinuity as a layer of a finite width (the shock is smeared within an interval of a finite length called distraction) comparable with the size of the mesh cell. Since states behind and before the shock are related, then there must exist a mechanism that ensures the growth of entropy in the shock distraction region. Only four principally different mechanisms of energy dissipation in the distraction region are known [1-4]. Consider four shock wave methods corresponding to these four mechanisms. Many difference schemes can be used to implement them. I suggest that we look only at those that were proposed by the authors of these four methods [1-4]. B.L. Rozhdestvensky and N.N. Yanenko [5] were first to try to compare these methods, focusing on approximations and stability.

*76-02 Research exposition (monographs, survey articles)

76L05 Shock waves and blast waves

76M99 None of the above, but in this section