A variable speed of sound formulation for weakly compressible smoothed particle hydrodynamics

TL;DR

This paper introduces a novel WCSPH formulation with a temporally variable speed of sound, enhancing accuracy and efficiency over traditional constant sound speed methods in simulating fluid flows.

Contribution

It proposes a new variable sound speed approach in WCSPH, improving performance and accuracy, and demonstrates its effectiveness through multiple test cases.

Findings

Improved computational performance over traditional WCSPH.

Maintained or enhanced accuracy in test simulations.

Robustness demonstrated across diverse flow scenarios.

Abstract

We present a Weakly Compressible SPH (WCSPH) formulation with a temporally variable speed of sound. The benefits of a time-varying sound speed formulation and the weaknesses of a constant sound speed formulation are worked out. It is shown how a variable sound speed can improve the performance, accuracy, and applicability of the WCSPH method. In our novel Uniform Compressible SPH (UCSPH) method, the required artificial speed of sound is calculated at each time step based on the current flow field. The method's robustness, performance, and accuracy are demonstrated with three test cases: a Taylor-Green vortex flow, a falling droplet impact, and a dam break. For all showcases, we observe at least similar accuracy as computed with WCSPH at strongly improved computational performance.