Boosting the accuracy of SPH techniques: Newtonian and special-relativistic tests

TL;DR

This paper enhances SPH techniques by introducing a matrix-inversion gradient method, a high-order Wendland kernel, improved volume elements, and adaptive dissipation triggers, significantly boosting accuracy in Newtonian and relativistic tests.

Contribution

It presents novel improvements to SPH accuracy through a new gradient prescription, kernel choice, volume elements, and dissipation triggers, outperforming standard methods.

Findings

Gradient accuracy improved by ten orders of magnitude.

Wendland kernel reduces velocity noise and improves stability.

New dissipation triggers enhance shock handling and flow stability.

Abstract

We study the impact of different discretization choices on the accuracy of SPH and we explore them in a large number of Newtonian and special-relativistic benchmark tests. As a first improvement, we explore a gradient prescription that requires the (analytical) inversion of a small matrix. For a regular particle distribution this improves gradient accuracies by approximately ten orders of magnitude and the SPH formulations with this gradient outperform the standard approach in all benchmark tests. Second, we demonstrate that a simple change of the kernel function can substantially increase the accuracy of an SPH scheme. While the "standard" cubic spline kernel generally performs poorly, the best overall performance is found for a high-order Wendland kernel which allows for only very little velocity noise and enforces a very regular particle distribution, even in highly dynamical tests. Third, we explore new SPH volume elements that enhance the treatment of fluid instabilities and, last, but not least, we design new dissipation triggers. They switch on near shocks and in regions where the flow --without dissipation-- starts to become noisy. The resulting new SPH formulation yields excellent results even in challenging tests where standard techniques fail completely.