Numerical solution of a heated subsidence mound problem in a porous medium

Two different numerical models are constructed to solve a two dimensional subsidence mound problem heated along the moving wet/dry interface. One numerical model is based on cartesian coordinates while the other is based on polar coordinates. In both approaches coordinate transformations are used that render the interface stationary. The problem involves a system of three coupled equations; an elliptic equation for a stream function, a parabolic equation for the temperature and a non-linear equation for the boundary location. Good agreement is found between the results of both methods. Graphic results are presented for the decay of a subsidence mound for different values of the various parameters in the model problem.