Solving elliptic interface problems with jump conditions on Cartesian grids

被引：29

作者：

Bochkov, Daniil ^{[1
]}

Gibou, Frederic ^{[1
,2
]}

机构：

[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

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 407卷

关键词：

Poisson equation; Immersed interface; Level-set method; EMBEDDED BOUNDARY METHOD; FINITE-ELEMENT-METHOD; IRREGULAR DOMAINS; POISSONS-EQUATION; ARBITRARY DISCONTINUITIES; IMMERSED BOUNDARY; MULTIGRID METHODS; HEAT-EQUATIONS; DISCRETIZATION; ALGORITHMS;

D O I：

10.1016/j.jcp.2020.109269

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate solutions and first-order accurate gradients in the L-infinity-norm on Cartesian grids. The condition number is bounded, regardless of the ratio of the diffusion constant and scales like that of the standard 5-point stencil approximation on a rectangular grid with no interface. Numerical examples are given in two and three spatial dimensions. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：13

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