Solving elliptic problems with discontinuities on irregular domains - the Voronoi Interface Method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:298

Article

Guittet, Arthur¹  Lepilliez, Mathieu^3,4,5  Tanguy, Sebastien³  Gibou, Frederic^1,2 

[1] Univ Calif Santa Barbara, Dept Mech Engn, Santa Barbara, CA 93106 USA

[2] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

[3] Inst Mecan Fluides Toulouse, F-31400 Toulouse, France

[4] Ctr Natl Etud Spatiales, F-31401 Toulouse 9, France

[5] Airbus Def & Space, F-31402 Toulouse 4, France

关键词: Level-set;    Elliptic interface problems;    Discontinuous coefficients;    Irregular domains;    Voronoi;    Finite volumes;    Quad/octrees;    Adaptive mesh refinement;   

DOI  :  10.1016/j.jcp.2015.06.026

来源: Elsevier

【 摘 要 】

We introduce a simple method, dubbed the Voronoi Interface Method, to solve Elliptic problems with discontinuities across the interface of irregular domains. This method produces a linear system that is symmetric positive definite with only its right-hand-side affected by the jump conditions. The solution and the solution's gradients are second-order accurate and first-order accurate, respectively, in the L-infinity norm, even in the case of large ratios in the diffusion coefficient. This approach is also applicable to arbitrary meshes. Additional degrees of freedom are placed close to the interface and a Voronoi partition centered at each of these points is used to discretize the equations in a finite volume approach. Both the locations of the additional degrees of freedom and their Voronoi discretizations are straightforward in two and three spatial dimensions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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