A simple toy model of the advective-acoustic instability. II. Numerical simulations

TL;DR

This paper uses 2D numerical simulations with two different Eulerian codes to study the advective-acoustic instability, confirming theoretical predictions and analyzing numerical convergence issues related to shock physics accuracy.

Contribution

It validates the perturbative analysis of advective-acoustic instability using numerical simulations and discusses the limitations of current numerical schemes in shock physics accuracy.

Findings

Numerical convergence is linear for shock-dependent quantities.

Current schemes have limited accuracy in shock physics, affecting SASI simulations.

A strategy for mesh size selection improves simulation accuracy.

Abstract

The physical processes involved in the advective-acoustic instability are investigated with 2D numerical simulations. Simple toy models, developped in a companion paper, are used to describe the coupling between acoustic and entropy/vorticity waves, produced either by a stationary shock or by the deceleration of the flow. Using two Eulerian codes based on different second order upwind schemes, we confirm the results of the perturbative analysis. The numerical convergence with respect to the computation mesh size is studied with 1D simulations. We demonstrate that the numerical accuracy of the quantities which depend on the physics of the shock is limited to a linear convergence. We argue that this property is likely to be true for most current numerical schemes dealing with SASI in the core-collapse problem, and could be solved by the use of advanced techniques for the numerical treatment of the shock. We propose a strategy to choose the mesh size for an accurate treatment of the advective-acoustic coupling in future numerical simulations.