A novel regularization strategy for the local discontinuous Galerkin method for level-set reinitialization

TL;DR

This paper introduces a new regularization technique for the local discontinuous Galerkin method, enhancing its ability to solve Hamilton-Jacobi equations in level-set reinitialization, especially on unstructured meshes.

Contribution

It presents a novel regularization strategy inspired by shock-capturing schemes, combining DG with finite volume sub-cell discretization for improved accuracy in low-regularity regions.

Findings

Effective handling of low-regularity areas

Compatibility with unstructured meshes

Improved stability and accuracy

Abstract

In this paper we propose a novel regularization strategy for the local discontinuous Galerkin method to solve the Hamilton-Jacobi equation in the context of level-set reinitialization. The novel regularization idea works in analogy to shock-capturing schemes for discontinuous Galerkin methods, which are based on finite volume sub-cells. In this spirit, the local discontinuous Galerkin method is combined with an upwind/downwind finite volume sub-cell discretization, which is applied in areas of low regularity. To ensure the applicability on unstructured meshes, the finite volume discretization is based on a least squares approach.