A simple, entropy-based dissipation trigger for SPH

Abstract: Smoothed Particle Hydrodynamics (SPH) schemes need to be enhanced by dissipation mechanisms to handle shocks. Most SPH formulations rely on artificial viscosity and while this is working well in pure shocks, attention has to be payed to avoid dissipation where it is not wanted. Commonly used approaches include limiters and time-dependent dissipation parameters. The former try to distinguish shocks from other types of flows that do not require dissipation while in the latter approach the dissipation parameters are steered by some source term ("trigger") and, if not triggered, they decay to a pre-described floor value. The commonly used source terms trigger on either compression, $-\nabla\cdot\vec{v}$, or its time derive. Here we explore a novel way to trigger SPH-dissipation: based on the entropy growth rate between two time steps we identify "troubled particles" that need to have dissipation added because they are either passing through a shock wave or become noisy. Our new scheme is implemented into the Lagrangian hydrodynamics code MAGMA2 and scrutinized in a number of shock and fluid instability tests. We find excellent results in shocks and only a moderate (and desired) switch-on in instability tests, despite our conservatively chosen trigger parameters. The new scheme is robust, trivial to implement into existing SPH codes and does not add any computational overhead.