Thin Plates Spline Based Differential Quadrature for numerical solution of groundwater flow

Abstract

PurposeThe main purpose of this paper is presenting Thin Plates Spline-based Differential Quadrature (TPS-DQM) as a meshless numerical method to solve the steady and transient groundwater equation in complex geometry.Design/methodology/approachThe computational nodes are randomly distributed in domain, and the governing equations of groundwater flow are solved, relying on the capability of present model for solving the partial differential equations (PDEs) in irregular domains. To show the accuracy of the proposed model, several seepage problems in both homogenous and non-homogenous soils are solved, and the results are compared with those existing analytical solution and well-known finite element-based software SEEP/W.FindingsThe results indicate that the present meshless method is capable of simulating steady-state and unsteady seepage problems, especially in complex geometry and it provides sufficient accuracy and reliability, despite the low computational effort and no need for additional parameters like shape factor.Originality/valueThe main advantage of the method is its meshless characteristic, which does not require structured grid generation and able to solve governing equation in arbitrary geometry.