A Cartesian grid embedded boundary method for the heat equation on irregular domains

Journal Article · Wed Mar 14 04:00:00 EST 2001 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.2001.6900· OSTI ID:835804

McCorquodale, Peter ^[1]; Colella, Phillip; Johansen, Hans

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1. LBNL Library

We present an algorithm for solving the heat equation on irregular time-dependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (J. Comput. Phys. 147(2):60--85) for discretizing Poisson's equation, combined with a second-order accurate discretization of the time derivative. This leads to a method that is second-order accurate in space and time. For the case where the boundary is moving, we convert the moving-boundary problem to a sequence of fixed-boundary problems, combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves. We find that, in the moving boundary case, the use of Crank--Nicolson time discretization is unstable, requiring us to use the L{sub 0}-stable implicit Runge--Kutta method of Twizell, Gumel, and Arigu.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathematical Information and Computing Sciences Division. Grants DE-FG03-94ER25205 and DE-FG03-92ER25140 and DE-AC03-76SF00098; National Science Foundation Graduate Fellowship Program (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 835804
• Report Number(s): LBNL--47459
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 173
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
EXTRAPOLATION
INITIAL VALUE PROBLEMS FOR SECOND-ORDER PARABOLIC EQUATIONS EMBEDDED BOUNDARY MOVING BOUNDARIES
LAWRENCE BERKELEY LABORATORY