Ray theory of gas dynamic discontinuities

Abstract

A geometric theory of the motion of surfaces of discontinuity is based on the quasilinear algebraic system of generalized Rankine-Hugoniot jump conditions for an ideal gas. Vanishing of a characteristic determinant is necessary for the existence of a nontrivial jump. Geometrical, dynamical, and persistence conditions are applied to the discontinuity of an arbitrary strength, resulting in a set of Hamiltonian equations for the position coordinates and for the space-time normal to the surface. The rays are defined as the integral curves of the Hamiltonian system and generate the singular surface that satisfies the imposed jump conditions.