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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Oevermann, M.¹  Scharfenberg, C.²  Klein, R.² 

[1] Tech Univ Berlin, Inst Energie Tech, D-10623 Berlin, Germany

[2] Free Univ Berlin, Fachbereich Math & Informat, D-14195 Berlin, Germany

关键词: Elliptic equations;    Finite volume methods;    Embedded interface;    Variable and discontinuous coefficients;    Discontinuous solution;   

DOI  :  10.1016/j.jcp.2009.04.018

来源: Elsevier

【 摘 要 】

We present a second order sharp interface finite volume method for the solution of the three-dimensional elliptic equation del . (beta((x) over right arrow del u((x) over right arrow)) = f ((x) over right arrow) 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 21) 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 beta-ratios and non-smooth interfaces - the method achieves second order of accuracy in the L-infinity and L-2 norm. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free