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

Journal Article · Fri Apr 01 04:00:00 EDT 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.12.017· OSTI ID:21499787

Colella, P; Graves, D T ^[1]

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1. Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, MS 50A-1148, 1 Cyclotron Road, Berkeley, CA 94720 (United States)

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{sup 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.

• OSTI ID: 21499787
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 7 Vol. 230; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
APPROXIMATIONS
CALCULATION METHODS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
GEOMETRY
HEAT
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
REACTOR COMPONENTS
REACTOR CORES
SIMULATION
THREE-DIMENSIONAL CALCULATIONS