Two Dimensional Riemann Problems for the Nonlinear Wave System: Rarefaction Wave Interactions

TL;DR

This paper investigates rarefaction wave interactions in 2D gas dynamics Riemann problems, establishing existence of solutions and analyzing boundary degeneracies related to transonic flow transitions.

Contribution

It provides the first existence proof for supersonic solutions in 2D Riemann problems with detailed analysis of sonic boundary formation and degeneracies.

Findings

Existence of supersonic solutions for sectorial Riemann data.

Characterization of sonic boundary formation and degeneracies.

Analysis of transition from sonic boundary to shock boundary.

Abstract

We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for the two dimensional Riemann problems. We establish the existence result of the supersonic solution to the prototype nonlinear wave system for the sectorial Riemann data, and study the formation of the sonic boundary and the transonic shock. The transition from the sonic boundary to the shock boundary inherits at least two types of degeneracies (1) the system is sonic, and in addition (2) the angular derivative of the solution becomes zero where the sonic and shock boundaries meet.