Shock Transmission Across a Low-Impedance Contact Surface

The classical problem of a shock wave incident upon a contact surface between two materials manifests a variety of flow patterns. These patterns are typically characterized through comparison of the shock impedance of the adjacent materials. For the case where a shock in a high-impedance material transmits into a low-impedance material, the wave reflected from the contact surface is a rarefaction wave. This work treats this classical problem using modern techniques of infinitesimal analysis rooted in nonstandard analysis. In this construction the time-dependent shock wave and contact surface trajectories are readily captured using idealized infinitesimal intervals defined on generalized number systems containing infinitely small numbers; within this representation the nonstandard jump functions in the flow and state variables may vary continuously. The reflected wave is characterized using this same technique, so that the notion of continuity in the infinitesimal sense must be reconciled with that in the global sense, as is expected for rarefaction wave structures.