An improved meshless numerical manifold method for simulating complex boundary seepage problems

Accurate seepage calculation is a prerequisite to ensuring the safety of water projects. But seepage problems face low accuracy and mesh dependence when conventional methods simulate the complex boundaries. Here, complex boundaries are reflected in the complexity of solving problems with multiple types of singularities and the complexity of the geometry of the problem domain. This paper uses the numerical manifold method based on moving least squares (MLS-NMM) interpolation to solve seepage problems with complex boundaries. The method adopts two cover systems and discrete node-based interpolation, so it owns significant advantages in dealing with complex boundaries. In order to improve the accuracy for simulating the corner singularities and jump intermittent points of essential boundaries, an improved MLS-NMM is established. Simultaneously, a background integral grid generation method based on the physical cover is introduced to improve computational accuracy and simplify the pre-processing of complex geometric problem domains, which also acquires a simple and regular background integral grid. A seepage problem with the free surface can be simulated with high accuracy by the improved MLS-NMM. The calculation results of complex boundary seepage cases with multiple types of singularities are compared with the exact or reference solutions, confirming the proposed method's validity and good applicability. As a result, the improved MLS-NMM can be used as a reference tool for analyzing complex seepage in engineering.