Pairwise wave interactions in ideal polytropic gases

TL;DR

This paper provides a comprehensive analysis of pairwise wave interactions in 1D ideal polytropic gases, determining the types of outgoing waves and vacuum formation based on incoming wave strengths and gas properties.

Contribution

It offers a complete classification and exact outcomes of all wave interactions in ideal polytropic gases, considering various interaction types and wave strengths.

Findings

Complete breakdown of wave interaction outcomes

Dependence of reflected wave type on wave strengths and adiabatic constant

Explicit criteria for vacuum formation during interactions

Abstract

We consider the problem of resolving all pairwise interactions of shock waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal polytropic gas. Resolving an interaction means here to determine the types of the three outgoing (backward, contact, and forward) waves in the Riemann problem defined by the extreme left and right states of the two incoming waves, together with possible vacuum formation. This problem has been considered by several authors and turns out to be surprisingly involved. For each type of interaction (head-on, involving a contact, or overtaking) the outcome depends on the strengths of the incoming waves. In the case of overtaking waves the type of the reflected wave also depends on the value of the adiabatic constant. Our analysis provides a complete breakdown and gives the exact outcome of each interaction.