Are heuristic switches necessary to control dissipation in modern smoothed particle hydrodynamics ?

TL;DR

This paper introduces a new shock capture scheme for smoothed particle hydrodynamics that eliminates the need for complex artificial viscosity switches, improving accuracy and reducing noise.

Contribution

A velocity-reconstruction technique combined with Balsara correction that provides effective dissipation control without relying on switches.

Findings

Improved accuracy over traditional switch-based methods.

Lower spurious dissipation in various flow regimes.

Effective across shocks, shear flows, and subsonic instabilities.

Abstract

Artificial viscosity is commonly employed in smoothed particle hydrodynamics (SPH) to model dissipation in hydrodynamic simulations. However, its practical implementation today relies, in many cases, on complex numerical switches to restrict its application to regions where dissipation is physically warranted, such as shocks. These switches, while essential, are imperfect and can introduce additional numerical noise. In this work we develop and validate a more efficient shock capture scheme for SPH that does not rely on artificial viscosity switches. Recent studies have proposed that subtracting the linear component of the velocity field can suppress spurious dissipation in shear-dominated regions. Building on this idea, we implement a velocity-reconstruction technique that removes the bulk linear motion from the local velocity field and uses the Balsara correction to modulate the dissipation. The presented methodology yields a balanced dissipation scheme that performs well across a range of regimes, including subsonic instabilities, shear flows, and strong shocks. We demonstrate that this approach yields improved accuracy and lower spurious dissipation, compared to the reference viscosity switch used in this work.