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Computing jump conditions for the immersed interface method using triangular meshes
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DOI：10.1016/j.jcp.2015.08.019.png)
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Abstract
En 中文
The immersed interface method (IIM) can be employed to solve many interface problems on fixed Cartesian grids by incorporating necessary interface-induced Cartesian jump conditions into numerical schemes. In this paper, we present a method to compute the necessary Cartesian jump conditions from given principal jump conditions using triangular mesh representation of an interface. The triangular mesh representation is simpler and robuster than interface parametrization for a complex or non-smooth interface. We test our method by using the computed Cartesian jump conditions in the IIM to solve a Poisson equation subject to an interface with the shape of a sphere, cube, cylinder or cone. The results demonstrate the expected second-order accuracy of the solution in the infinity norm. (C) 2015 Elsevier Inc. All rights reserved.
Keywords:
The immersed interface method
Triangular meshes
Jump conditions
Poisson solvers
Complex geometries
Non-smooth interfaces
Cartesian grid methods
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