TY - GEN A1 - Oevermann, Michael A1 - Scharfenberg, Carsten A1 - Klein, Rupert T1 - A sharp interface finite volume method for elliptic equations on Cartesian grids N2 - We present a second order sharp interface finite volume method for the solution of the three-dimensional poisson equation 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 piecewiese 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, J.~Comp.~Phys.~219 (2006)] 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 coefficient ratios and non-smooth interfaces -- the method achieves second order of accuracy in the L_inf and L_2 norm. T3 - ZIB-Report - 08-38 KW - elliptische Gleichungen KW - Finite Volumen KW - eingebettete Ränder KW - variable und diskontinuierliche Koeffizienten KW - diskontinuierliche Lösung KW - Elliptic equations KW - finite volume methods KW - embedded interface KW - variable and discontinuous coefficients KW - discontinuous solution Y1 - 2008 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1090 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-10900 SN - 1438-0064 ER -