I work with professor Björn Birnir on erosion modeling of fluvial landscapes. The model involves numerically solving the Smith and Bretherton model which consists of two partial differential equations; one for the flow of water and one for the movement of the sediment.
This research has great assistance from the UCSB Center for Scientific Computing (CSC). Solving the model is done using parallelized C++ code running on the Knot Cluster at the CSC. Even with this great resource, solving these differential equations numerically still takes multiple months.
Current work involves using a technique referred to as fractal interpolation to generate a possible fluvial surface without solving the differential equations. The hope is to quickly generate a mountainous landscape and then fill in the small scale details using fractal interpolation.
You can download my C++ code for numerically solving the Smith and Bretherton model, along with some MatLab code to graph the surfaces by clicking here.
If you have any questions about this code, please send me an email and I will address your concerns as soon as possible.