**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.

**Preprint:**
jcp00.ps.gz ...
jcp00.pdf ...

**Code:**

- README
- advdiff.tar.gz tar file of codes (including necessary routines from clawpack) 54KB.
- irr.tar.gz Data for the flow through irregular objects (stream function, etc.) 921KB

**bibtex entry:**

@Article{dc-rjl:advdiff,

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",

}