Smoothed Particle Hydrodynamics with Smoothed Pseudo-Density

TL;DR

This paper introduces SPSPH, a novel SPH formulation using a smoothed pseudo-density to effectively handle contact discontinuities and free surfaces, addressing limitations of standard SPH.

Contribution

The paper proposes a new SPH method that employs a pseudo-density with artificial diffusion, improving behavior at discontinuities compared to standard SPH.

Findings

Handles contact discontinuities effectively

Maintains physical consistency at density jumps

Improves simulation stability at free surfaces

Abstract

In this paper, we present a new formulation of smoothed particle hydrodynamics (SPH), which, unlike the standard SPH (SSPH), is well-behaved at the contact discontinuity. The SSPH scheme cannot handle discontinuities in density (e.g. the contact discontinuity and the free surface), because it requires that the density of fluid is positive and continuous everywhere. Thus there is inconsistency in the formulation of the SSPH scheme at discontinuities of the fluid density. To solve this problem, we introduce a new quantity associated with particles and "density" of that quantity. This "density" evolves through the usual continuity equation with an additional artificial diffusion term, in order to guarantee the continuity of "density". We use this "density" or pseudo density, instead of the mass density, to formulate our SPH scheme. We call our new method as SPH with smoothed pseudo-density (SPSPH). We show that our new scheme is physically consistent and can handle discontinuities quite well.