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.
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页数：13
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