A local discontinuous Galerkin level set reinitialization with subcell stabilization on unstructured meshes[Formula presented]


Karakus A., Chalmers N., Warburton T.

Computers and Mathematics with Applications, vol.123, pp.160-170, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 123
  • Publication Date: 2022
  • Doi Number: 10.1016/j.camwa.2022.08.010
  • Journal Name: Computers and Mathematics with Applications
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.160-170
  • Keywords: Discontinuous Galerkin, Hamilton-Jacobi, Level set, Reinitialization, Stabilization, Subcell

Abstract

© 2022 Elsevier LtdIn 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.