Primal mixed solution to unconfined seepage flow in porous media with numerical manifold method

The major difficulty in the analysis of unconfined flow in porous media is that the free surface is unknown a priori, where the nonlinearity is even stronger than the unsaturated seepage analysis. There is much space for both the adaptive mesh methods and the fixed mesh methods to improve. In this study, firstly two variational principles fitted to the numerical manifold method (NMM) are formulated, each of which enforces the boundary conditions and the material interface continuity conditions. In the setting of the NMM together with the moving least squares (MLS) interpolation, then the discretization models corresponding to the variational formulations are built, which are utilized to locate the free surface and scrutinize the computational results respectively. Meanwhile, a novel approach is developed to update the free surface in iteration. With high accuracy and numerical stability but no need to remesh, the proposed procedure is able to accommodate complicated dam configuration and strong non-homogeneity, where internal seepage faces may develop, a seldom touched problem in the literature.