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

• Published in: Journal of computational physics Vol. 230; no. 7; pp. 2451 - 2469
• Main Authors: Crockett, R.K., Colella, P., Graves, D.T.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.04.2011; Elsevier
• Subjects: Accuracy; Approximation; APPROXIMATIONS; Arrays; Boundaries; CALCULATION METHODS; Cartesian; Computational techniques; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; Discontinuous coefficient; ENERGY; EQUATIONS; Exact sciences and technology; Finite volume methods; GEOMETRY; HEAT; Heat equation; Heat equations; Irregular domain; Jump conditions; MATHEMATICAL METHODS AND COMPUTING; Mathematical methods in physics; MATHEMATICS; Multigrid methods; PARTIAL DIFFERENTIAL EQUATIONS; Physics; POISSON EQUATION; REACTOR COMPONENTS; REACTOR CORES; SIMULATION; Solvers; Three dimensional; THREE-DIMENSIONAL CALCULATIONS; Discontinuous coefficient; Heat equation; Multigrid methods; Jump conditions; Irregular domain; Finite volume methods; Second order; Poisson equation; Calculation methods; Multigrid; Physical parameter; Nuclear cores; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.12.017

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 10 6, 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.