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

Journal Article · Fri Oct 23 04:00:00 EDT 2009 · Journal of Computational Physics

OSTI ID:980773

Crockett, Robert; Graves, Daniel; Colella, Phillip

We present a method for solving Poisson and heat equations with discon- tinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materi- als, as described in Johansen& 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.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Computational Research Division; Physics Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 980773
• Report Number(s): LBNL-2929E; Journal Serial ID: 0021- 9991
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
97 MATHEMATICS AND COMPUTING
ACCURACY
APPROXIMATIONS
DIMENSIONS
REACTORS
SIMULATION
discontinuous coefficient
finite volume methods
heat equation
irregular domain
jump conditions
multigrid methods
nuclear reactor core simulation