The MLS-based numerical manifold method for Darcy flow in heterogeneous porous media

The moving least squares (MLS) interpolation gets rid of the shackles of meshes, while the numerical manifold method (NMM) can solve both continuity and discontinuity problems in a unified way. The MLS-based NMM (abbreviated as MLS-NMM) inherits the individual merits of MLS and NMM. In the present work, the MLS-NMM is extended to solve groundwater flow problems in heterogeneous porous media. To accurately simulate the flow velocity field at and in the vicinity of the material interfaces, the refraction law is introduced into the proposed model as a posteriori condition. Several examples are employed to verify the correctness and accuracy of the proposed model. The results indicate that the MLS-NMM can model the Darcy flow in heterogeneous porous media with high accuracy, as well as satisfy the refraction law rigorously. In addition, the smooth flow velocity field can be obtained directly without the need for extra post-processing.