Shock interaction in sphere symmetry

TL;DR

This paper studies the complex interaction of two shock waves in spherical symmetry for an ideal fluid, focusing on establishing local solutions post-interaction using iterative methods.

Contribution

It extends previous work on shock interactions from plane to spherical symmetry and develops an iterative approach for local solution existence.

Findings

Successful formulation of a local in time solution after shock interaction

Extension of shock interaction analysis from plane to spherical symmetry

Development of an iterative method for free boundary problems

Abstract

We investigate the interaction of two oncoming shock waves in spherical symmetry for an ideal barotropic fluid. Our research problem is how to establish a local in time solution after the interaction point and determine the state behind the shock waves. This problem is a double free boundary problem, as the position of the shock waves in space time is unknown. Our work is based on a number of previous studies, including Lisibach's, who studied the case of plane symmetry. To solve this problem, we will use an iterative regime to establish a local in time solution.