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

The physical processes involved in the advective-acoustic instability are investigated with two-dimensional numerical simulations. Simple toy models, developed 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 one-dimensional simulations. We demonstrate that the numerical accuracy of the quantities that 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 standing accretion shock instability 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.