Mathematical programming approach for unconfined seepage flow problem
In this paper, a mathematical programming technique for numerical simulation of unconfined flow through porous media is presented. Considering the original free boundary problem as a shape optimization problem, we perform boundary elements discretization. Taking the state variable and free boundary variable as independent variables, we treat the discretized problem as nonlinear mathematical program and apply interior point algorithm to solve it. This simple, accurate and computationaly efficient technique can be easily applied to 2D real size problems and extended to 3D problems. Numerical results for an illustrative 2D test problem of an earth dam are discussed.
mathematical programming free boundary problem shape optimization boundary elements method dam problem