A high-order discontinuous Galerkin method for level set problems on polygonal meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:397

Article

Lipnikov, Konstantin¹  Morgan, Nathaniel² 

[1] Los Alamos Natl Lab, Theoret Div, Appl Math & Plasma Phys Grp, Mail Stop B284, Los Alamos, NM 87545 USA

[2] Los Alamos Natl Lab, X Computat Phys Div, Methods & Algorithms Grp, Mail Stop F663, Los Alamos, NM 87545 USA

关键词: Discontinuous Galerkin;    High-order;    Level set;    Polygonal mesh;    Virtual element projectors;   

DOI  :  10.1016/j.jcp.2019.07.033

来源: Elsevier

【 摘 要 】

We propose and analyze discontinuous Galerkin schemes for solving level set equations on polygonal meshes. For linear equations, we assume that the velocity is given only on the cell surface. Velocity inside mesh cells is approximated using virtual element projectors on polynomial spaces. For nonlinear equations, we use the Taylor expansion to approximate the normalized solution gradient. We analyze the new schemes for a set of typical level set problems using square and polygonal meshes. The numerical results indicate great potential for using polygonal meshes in applications. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free