On shock capturing in smoothed particle hydrodynamics

TL;DR

This paper introduces a novel shock capturing method for smoothed particle hydrodynamics that improves dissipation control while maintaining shock fidelity, building on the Riemann solver philosophy.

Contribution

A new shock capturing approach in SPH that enhances dissipation management and shock accuracy compared to existing methods.

Findings

Improved dissipation control away from shocks.

Enhanced shock fidelity.

Outperforms traditional artificial viscosity methods.

Abstract

For the past 20 years, our approach to shock capturing in smoothed particle hydrodynamics (SPH) has been to use artificial viscosity and conductivity terms supplemented by switches to control excess dissipation away from shocks (Monaghan 1997; Morris & Monaghan 1997). This approach has been demonstrated to be superior to approximate Riemann solvers in a recent comparison (Puri & Ramachandran 2014). The Cullen & Dehnen (2010) switch is regarded as the state of the art. But are we missing something? I will present a novel approach to shock capturing in SPH that utilises the philosophy of approximate Riemann solvers but provides a direct improvement on the ability to reduce excess dissipation away from shocks while preserving the fidelity of the shock itself.