A Cartesian grid finite-volume method for the advection-diffusion equationin irregular geometries

We present a fully conservative, high-resolution, finite volume algorithm f or advection-diffusion equations in irregular geometries. The algorithm use s 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 so me cells are only partially available to the fluid. The advection portion t hen uses the explicit wave-propagation methods implemented in CLAWPACK, and is stable for Courant numbers up to 1. Diffusion is modelled with an impli cit finite-volume algorithm. Results are shown for several geometries. Conv ergence 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.