A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Crockett, R. K.¹  Colella, P.¹  Graves, D. T.¹ 

[1] Univ Calif Berkeley, Lawrence Berkeley Lab, Appl Numer Algorithms Grp, Berkeley, CA 94720 USA

关键词: Heat equation;    Jump conditions;    Discontinuous coefficient;    Irregular domain;    Finite volume methods;    Multigrid methods;   

DOI  :  10.1016/j.jcp.2010.12.017

来源: Elsevier

【 摘 要 】

We present a method for solving Poisson and heat equations with discontinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in Johansen and Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 106, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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