Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 157, Issue 1, Pages 143-180Publisher
ACADEMIC PRESS INC
DOI: 10.1006/jcph.1999.6369
Keywords
finite-volume; advection-diffusion; Cartesian grid; embedded boundary; high-resolution; software
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We present a fully conservative, high-resolution, finite volume algorithm for advection-diffusion equations in irregular geometries. The algorithm uses a Cartesian grid in which some cells are cut by the embedded boundary. A novel feature is the use of a capacity function to model the fact that some cells are only partially available to the fluid. The advection portion then uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an implicit finite-volume algorithm. Results are shown for several geometries. Convergence is verified and the 1-norm order of accuracy is found to between 1.2 and 2 depending on the geometry and Peclet number. Software is available on the web. (C) 2000 Academic Press.
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