Singularity Treatments in Transient Confined Seepage Using Numerical Manifold Method

Abstract

The numerical manifold method (NMM) with the mathematical cover and the physical cover is proposed for analysis the two-dimensional transient confined seepage flow problems with singular corner points. To deal with the singularity of corner points, a special local approximation obtained from the asymptotic expansion of the analytical solution in the neighborhood of corner points is introduced by NMM in this study. Firstly, the special local approximation is applied to the patches affected by the singularity point, and the constant local approximation is assigned to the other star patches. Secondly, based on the governing equations, the initial condition, and the boundary conditions, the NMM discrete formulations are deduced. For time integration, the backward time integration scheme is adopted. The accuracy and effectiveness of the proposed method are proved by four engineering examples in homogeneous, heterogeneous, and anisotropic material. Comparing with finite element method, the proposed method can better reflect the strong singularity of corner points.

Keywords: Numerical manifold method, transient confined seepage, the asymptotic expansion, time discretization