Repository: Freie Universität Berlin, Math Department

A sharp interface finite volume method for elliptic equations on Cartesian grids

Oevermann, M. and Scharfenberg , C. and Klein, R. (2009) A sharp interface finite volume method for elliptic equations on Cartesian grids. Journal of Computational Physics, 228 (14). pp. 5184-5206.

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We present a second order sharp interface finite volume method for the solution of the three-dimensional elliptic equation inlMMLBox with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewise trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M. Oevermann, R. Klein, A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, Journal of Computational Physics 219 (2006) 749–769] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases – including large β -ratios and non-smooth interfaces – the method achieves second order of accuracy in the L ∞ and L 2 norm.

Item Type:Article
Uncontrolled Keywords:Elliptic equations; Finite volume methods; Embedded interface; Variable and discontinuous coefficients; Discontinuous solution
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:531
Deposited By: Ulrike Eickers
Deposited On:10 Jul 2009 14:08
Last Modified:21 Jul 2009 12:22

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