Patch-recovery filters for curvature in discontinuous Galerkin-based level-set methods

TL;DR

This paper introduces a patch-recovery filtering technique to stabilize curvature evaluation in level-set methods for two-phase flow simulations, improving accuracy and computational efficiency.

Contribution

It proposes and analyzes a novel patch-recovery filter for curvature computation in discontinuous Galerkin level-set methods, enhancing stability and accuracy.

Findings

Optimal patch-recovery settings identified for accuracy and efficiency

Filtering improves stability of curvature evaluation

Numerical results demonstrate enhanced simulation quality

Abstract

In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.