Moving boundary problems in earth-surface dynamics

This paper illustrates a novel two-dimensional moving boundary problem describing the evolution of a sediment fan in a closed depositional basin. This problem is analogous to a point source melting problem with zero latent heat and a space dependent melting temperature. A simple time explicit numerical solution scheme is developed. The performance of the solution is checked against measurements taken from a sediment fan build in a laboratory scale experiment. Results indicate that the proposed model has promise but further work is required to characterize the nature of the sediment diffusion.