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Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for onedimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one-dimensional radial flow problem and then tentatively applied to more general two-dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary.

We propose a general method for constructing the semi-analytical solution of the inverse Laplace transform, realized through the powerful exponential approximation invented by Wang et al. in 1993. Bearing their credits, this method inherits all the merits such as analytical expression, avoiding free parameters, simple calculation with high accuracy, and the availability of error estimation. Illustrating calculations indicate the potential applications to the vast problems in the fields of mathematical physics as well as engineering and medicine.