Analytic solution of the free boundary problem for porous media flow using a conformal map validated by the boundary element method

This paper presents an analytic approach to solving the classical problem of free boundary porous media flow. The solution is found by constructing an operator, derived from a conformal map, which is then reduced to a matrix and inverted. This matrix is then used to solve a system of linear equations with all terms in the matrix calculated exactly. To confirm the solution, we made a comparison with an iterative boundary element solution, which shows good agreement. Visual representations of the flow are also provided.