Interaction between a discontinuity wave and a shock wave: critical time for the fastest transmitted wave, example of the polytropic fluid

Abstract

In this paper we consider a homogeneous quasi-linear hyperbolic system in two independent variables, we evaluate the critical time for the fastest transmitted wave generated by the interaction between a discontinuity wave and a shock wave; We prove that in the case of propagation in a constant state the critical time is greater (smaller) than it would be in absence of interaction if the weak discontinuity of the incident wave velocity decreases (increases) through the shock. An application is made to a polytropic fluid in case of interaction with a contact shock; we prove that the critical time is smaller than it would be in absence of the shock