A higher order approximate static condensation method for multi-material diffusion problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:395

Article

Zhiliakov, Alexander¹  Svyatskiy, Daniil²  Olshanskii, Maxim^1,3  Kikinzon, Evgeny²  Shashkov, Mikhail² 

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Los Alamos Natl Lab, Los Alamos, NM USA

[3] Sechenov Univ, Moscow, Russia

关键词: High contrast diffusion coefficients;    Unfitted meshes;    Approximate static condensation method;    Mimetic finite differences;    Volume-of-fluid method;   

DOI  :  10.1016/j.jcp.2019.06.044

来源: Elsevier

【 摘 要 】

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P-1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free