Accelerating Surface Tension Calculation in SPH via Particle Classification & Monte Carlo Integration

TL;DR

This paper introduces a novel method for efficiently calculating surface tension forces in SPH simulations by classifying particles and using Monte Carlo integration to estimate local normals and curvatures, resulting in faster and stable computations.

Contribution

The proposed approach distinguishes surface from non-surface particles and employs Monte Carlo integration, improving speed and stability over previous methods in SPH surface tension calculations.

Findings

Reduces computation time per time step

Maintains stability and avoids artifacts

Applicable to both 2D and 3D simulations

Abstract

Surface tension has a strong influence on the shape of fluid interfaces. We propose a method to calculate the corresponding forces efficiently. In contrast to several previous approaches, we discriminate to this end between surface and non-surface SPH particles. Our method effectively smooths the fluid interface, minimizing its curvature. We make use of an approach inspired by Monte Carlo integration to estimate local normals as well as curvatures, based on which the force can be calculated. The technique is applicable, but not limited to 2D and 3D simulations, and can be coupled with any common SPH formulation. It outperforms prior approaches with regard to total computation time per time step, while being stable and avoiding artifacts.