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Computationally, steady seepage in arbitrary shaped aquifers reduces to a Laplacian free boundary problem. Analytic series solutions can be obtained by iteratively improving an initial estimate. Although the free water table is slowly varying in shape, accurate solutions can be extremely difficult to obtain for the long aspect ratios encountered in typical problems. In previous research, the Neumann condition along the free boundary was used as a cost function. In this paper, we present an update method that uses the Dirichlet condition as the cost function. We find that this approach is significantly more efficient and stable than the previous approach. This enables the determination of very accurate solutions for the water table at low computational cost.

A potential update method for series methods in steady seepage