On the Inadmissibility of Non-evolutionary Shocks

Abstract

In this paper we study the general relationship between the evolutionary conditions for discontinuous solutions of hyperbolic conservation laws with a concave entropy function and the existence and uniqueness of steady dissipative shock structure. Our results confirm the classical shock theory. We also show that the appearance of intermediate shocks in numerical MHD simulations can be understood in terms of the equations planar magnetohydrodynamics for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.