Interface‐preserving level‐set reinitialization for DG‐FEM. (9th December 2016)

• Record Type: Journal Article
• Authors: Utz, Thomas; Kummer, Florian; Oberlack, Martin
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 4(2017)
• Page Start: 183
• Page End: 198
• Publication Date: 2016-12-09
• Subjects: discontinuous Galerkin -- level‐set -- reinitialization -- eikonal equation; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4344
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: This paper presents a contribution to level‐set reinitialization in the context of discontinuous Galerkin finite element methods. We focus on high‐order polynomials for the discretization and level set geometries, which are comparable to the element size. In contrast to hyperbolic and geometric reinitialization techniques, our method relies on solving a nonlinear elliptic PDE iteratively. We critically compare two different variants of the algorithm experimentally in numerical studies. The results demonstrate that the method is stable for nontrivial test cases and shows high‐order accuracy. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : In contrast to common techniques, our method relies on solving a nonlinear elliptic PDE iteratively. This leads to improved stability, especially when dealing with interface geometries with high curvature compared to the element size.