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A Cartesian Grid Embedded Boundary Method for the Heat Equation on Irregular Domains

โœ Scribed by Peter McCorquodale; Phillip Colella; Hans Johansen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
667 KB
Volume
173
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

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 (1998, J. Comput. Phys. 147, 60) 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 in which 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 0 -stable implicit Runge-Kutta method of Twizell, Gumel,

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