Analyzing unconfined seepage flow with corner singularity using an enhanced second-order numerical manifold method

Due to the nonlinearities caused by free surfaces and discontinuities at turning points, analyzing unconfined seepage flow with corner singularities has always been a challenging issue in hydraulic engineering. The numerical manifold method (NMM) provides an almost perfect way to model continuous-discontinuous problems in a unified mathematical form and allows for combining analytical and numerical solutions. Using the NMM, this paper develops a high-precision and grid-independent method for unconfined flow with corner singularities involved in complex hydraulic structures. First, an iteration scheme is proposed to update the free surfaces. Second, a singular cover function for asymptotic solutions at turning points is introduced to the physical covers on singular points. This method can eliminate the necessity for remeshing when iterating seepage analysis and easily reflect strong singularity at the corner. Finally, several numerical experiments are conducted to validate the feasibility and applicability of the proposed method. The results illustrate that the enhanced NMM is efficient and accurate in homogeneous and heterogeneous models for free-surface locating. It also achieves precise results for challenging examples with various singular points, thus laying a solid foundation for further analyzing the coupled effects of seepage and corner singularity on complex structures.