An artificial boundary approach for unbounded transient seepage problems

Abstract

SummaryA new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd.