Solving elliptic interface problems with jump conditions on Cartesian grids

•A finite-volume numerical method for elliptic problems with discontinuous parameters and solutions.•Uniform Cartesian grids with implicitly described (the Level-Set Method) irregular interfaces.•Second-order accurate numerical solutions with first-order accurate gradients (in the L∞-norm).•Conditio...

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Vydáno v:Journal of computational physics Ročník 407; s. 109269
Hlavní autoři: Bochkov, Daniil, Gibou, Frederic
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge Elsevier Inc 15.04.2020
Elsevier Science Ltd
Témata:
Algorithms
Cartesian coordinates
Computational physics
Diffusion coefficient
Elliptic functions
Immersed interface
Level-set method
Numerical analysis
Poisson equation
Poisson equation
Immersed interface
Level-set method
ISSN:0021-9991, 1090-2716
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Shrnutí:•A finite-volume numerical method for elliptic problems with discontinuous parameters and solutions.•Uniform Cartesian grids with implicitly described (the Level-Set Method) irregular interfaces.•Second-order accurate numerical solutions with first-order accurate gradients (in the L∞-norm).•Condition number remains finite as the ratio of diffusion coefficients across the discontinuity approaches 0 or ∞.•Numerical examples in two and three spatial dimensions. 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∞-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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109269