Solving the advection-diffusion equation in irregular geometries
by D. Calhoun and R. J. LeVeque J. Comput. Phys., 156(2000) pp. 1-38.

Abstract. 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.

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bibtex entry:
author = "D. Calhoun and R. J. LeVeque",
title = "Solving the advection-diffusion equation in irregular geometries",
journal = "J. Comput. Phys.",
year = "2000",
volume = "156",
pages = "1--38",

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