Simulation of a free-surface and seepage face using boundary-fitted coordinate system method

The boundary-fitted coordinate (BFC) system method is applied to simulate steady groundwater seepage with a free-surface and seepage face using the finite-difference method. The BFC system method eliminates the difficulty of fitting finite-difference grids to a changeable free-surface which is not known a priori but will be obtained as part of a solution.

Also, grid generation with this approach is simpler than with the finite-element method. At each iterative sweep, the changeable free-surface becomes a part of the boundary-fitted grid lines, making boundary condition implementation easy and accurate. An example problem demonstrating the simulation procedure and numerical results compares very well with the analytical solution.