Unified description of fluids and solids in Smoothed Particle Hydrodynamics

TL;DR

This paper introduces a unified SPH-like method based on SHTC equations that can simulate both fluids and solids simultaneously, enabling more comprehensive modeling of systems with mixed phases.

Contribution

It develops a novel SHTC-SPH method that discretizes symmetric hyperbolic thermodynamically compatible equations for combined fluid and solid simulation.

Findings

The method accurately models fluid-solid interactions.

It shows excellent agreement with benchmark data.

Applicable to complex systems with mixed phases.

Abstract

Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves partly as a fluid and partly as a solid, for instance, the solidification front in 3D printing, or any system involving both fluid and solid phases. We develop an SPH-like method that is suitable for both fluids and solids at the same time. Instead of the typical discretization of hydrodynamics, we discretize the Symmetric Hyperbolic Thermodynamically Compatible equations (SHTC), which describe both fluids, elastic solids, and visco-elasto-plastic solids within a single framework. The resulting SHTC-SPH method is then tested on various benchmarks from the hydrodynamics and dynamics of solids and shows remarkable agreement with the data.