Singularity treatments in transient confined seepage using numerical manifold method

The numerical manifold method (NMM) is proposed for analysis of the two-dimensional transient confined seepage flow problems with singular corner points. To deal with the singularity of corner points, the asymptotic expansion of the solution in the vicinity of corner points is incorporated into the local approximations of the relevant physical patches of the NMM, while the constant local approximation is assigned to the other patches far from the singularity points. Then, the NMM discrete formulation for the initial – boundary value problem for transient seepage flow is deduced based on the Galerkin approximation. For time integration, the backward time integration scheme is adopted. The accuracy and effectiveness of the proposed method are demonstrated in typical examples involving homogeneous, heterogeneous, and anisotropic material. Comparing with constant local approximations to all the patches, the proposed method can better reflect the strong singularity of corner points.