The method of fundamental solutions and domain decomposition method for degenerate seepage flownet problems

Abstract

This paper proposes an innovative method of fundamental solutions (MFS) which is used along with the domain decomposition method (DDM) to solve degenerate boundary problems in ground water flows governed by the Laplace equations. The method is utilized to study flownets generated in the presence of sheet piles, by decomposing regions into sub‐domains along the degenerate sheet‐pile boundary. After validating two degenerate seepage flownet problems, the method is then applied to solve three practical flownet problems with sheet piles: (1) impermeable dam, (2) semi‐circular soil stratum and (3) sloping soil stratum. The predicted flownets show good agreement with available literature. Moreover, the proposed meshless scheme is easier to implement to measure degenerate seepage flownets as compared to other numerical schemes.