A cartesian grid embedded boundary method for the heat equationand poisson's equation in three dimensions

Journal Article · Tue Nov 02 04:00:00 EST 2004 · Journal of Computational Physics

OSTI ID:878684

Schwartz, Peter; Barad, Michael; Colella, Phillip; Ligocki, Terry

We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60-85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60-85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.

• Research Organization: Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Office of AdvancedScientific Computing Research. Mathematical Information and ComputationalSciences Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 878684
• Report Number(s): LBNL--56607; BnR: KJ0101010
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 211; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DIMENSIONS
POISSON EQUATION