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Solving elliptic problems with discontinuities on irregular domains – the Voronoi Interface Method

Guittet, Arthur and Lepilliez, Mathieu and Tanguy, Sébastien and Gibou, Frédéric Solving elliptic problems with discontinuities on irregular domains – the Voronoi Interface Method. (2015) Journal of Computational Physics, 298. 747-765. ISSN 0021-9991

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Official URL: http://dx.doi.org/10.1016/j.jcp.2015.06.026

Abstract

We introduce a simple method, dubbed the Voronoi Interface Method, to solve Elliptic problems with discontinuities across the interface of irregular domains. This method produces a linear system that is symmetric positive definite with only its right-hand-side affected by the jump conditions. The solution and the solution's gradients are second-order accurate and first-order accurate, respectively, in the L∞L∞ norm, even in the case of large ratios in the diffusion coefficient. This approach is also applicable to arbitrary meshes. Additional degrees of freedom are placed close to the interface and a Voronoi partition centered at each of these points is used to discretize the equations in a finite volume approach. Both the locations of the additional degrees of freedom and their Voronoi discretizations are straightforward in two and three spatial dimensions.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at http://www.sciencedirect.com/science/article/pii/S0021999115004234
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Airbus (FRANCE)
French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > University of California - UC Santa Barbara (USA)
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Deposited By: Sebastien TANGUY
Deposited On:17 May 2016 13:58

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