A Local Discontinuous Galerkin Level Set Reinitialization with Subcell Stabilization on Unstructured Meshes

TL;DR

This paper introduces a high-order local discontinuous Galerkin method with subcell stabilization for level set reinitialization on unstructured meshes, improving stability, efficiency, and convergence by discretizing the Eikonal equation.

Contribution

It presents a novel level set reinitialization technique using a DG method with subcell stabilization and Eikonal equation discretization, eliminating regularization parameters and enhancing performance.

Findings

Achieves design order accuracy in numerical experiments.

Improves stability and convergence speed.

Effective for both smooth and non-smooth interfaces.

Abstract

In this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear stability of the method. Instead of the standard hyperbolic level set reinitialization, the flow of time Eikonal equation is discretized to construct an approximate signed distance function. Using the Eikonal equation removes the regularization parameter in the standard approach which allows more predictable behavior and faster convergence speeds around the interface. This makes our approach very efficient especially for banded level set formulations. A set of numerical experiments including both smooth and non-smooth interfaces indicate that the method experimentally achieves design order accuracy.