Repository: Freie Universit├Ąt Berlin, Math Department

A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces

Oevermann, M. and Klein, R. (2006) A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces. Journal of Computational Physics, 219 (2). 749-769 .

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Abstract

We present a finite volume method for the solution of the two-dimensional elliptic equation @?.(@b(x)@?u(x))=f(x) with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution u(x) resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. 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:547
Deposited By: Ulrike Eickers
Deposited On:16 Jul 2009 14:02
Last Modified:29 Jul 2010 11:24

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