A Correction Function Method for Poisson problems with interface jump conditions |
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Authors: | Alexandre Noll Marques Jean-Christophe Nave Rodolfo Ruben Rosales |
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Affiliation: | 1. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology Cambridge, MA 02139-4307, United States;2. Department of Mathematics and Statistics, McGill University Montreal, Quebec, Canada H3A 2K6;3. Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139-4307, United States |
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Abstract: | In this paper we present a method to treat interface jump conditions for constant coefficients Poisson problems that allows the use of standard “black box” solvers, without compromising accuracy. The basic idea of the new approach is similar to the Ghost Fluid Method (GFM). The GFM relies on corrections applied on nodes located across the interface for discretization stencils that straddle the interface. If the corrections are solution-independent, they can be moved to the right-hand-side (RHS) of the equations, producing a problem with the same linear system as if there were no jumps, only with a different RHS. However, achieving high accuracy is very hard (if not impossible) with the “standard” approaches used to compute the GFM correction terms. |
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Keywords: | Poisson equation Interface jump condition Ghost Fluid Method Gradient augmented level set method High accuracy Hermite cubic spline |
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