An exact Riemann solver based solution for regular shock refraction

TL;DR

This paper introduces an exact Riemann solver approach to analyze shock refraction at density discontinuities, accounting for magnetic fields and predicting wave pattern transitions, with validation through experiments and simulations.

Contribution

It presents a novel exact Riemann solver-based method to model initial shock refraction and vorticity deposition, including magnetic field effects, validated by experiments and simulations.

Findings

Exact solution describes initial refraction phase and vorticity deposition.

Magnetic field slightly increases vorticity deposition.

Predicted wave pattern transitions align with experiments and theory.

Abstract

We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest. When the shock impinges on the density discontinuity, it refracts and in the hydrodynamical case 3 signals arise. Regular refraction means that these signals meet at a single point, called the triple point. After reflection from the top wall, the contact discontinuity becomes unstable due to local Kelvin-Helmholtz instability, causing the contact surface to roll up and develop the Richtmyer-Meshkov instability. We present an exact Riemann solver based solution strategy to describe the initial self similar refraction phase, by which we can quantify the vorticity deposited on the contact interface. We investigate the effect of a perpendicular magnetic field and quantify how addition of a perpendicular magnetic field increases the deposition of vorticity on the contact interface slightly under constant Atwood number. We predict wave pattern transitions, in agreement with experiments, von Neumann shock refraction theory, and numerical simulations performed with the grid-adaptive code AMRVAC. These simulations also describe the later phase of the Richtmyer-Meshkov instability.