Mohammad Vaghefi

Purpose – The 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/approach – The computational nodes are randomly distributed in domain, and the governingequationsofgroundwaterflowaresolved,relyingonthecapabilityofpresentmodelforsolvingthe partialdifferentialequations(PDEs)inirregulardomains.Toshowtheaccuracyoftheproposedmodel,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. Findings – The results indicate that the present meshless method is capable of simulating steady-state and unsteadyseepageproblems,especiallyincomplexgeometryanditprovidessufficientaccuracyandreliability, despite the low computational effort and no need for additional parameters like shape factor. Originality/value – The mainadvantage of the method is its meshless characteristic, which does not require structured grid generation and able to solve governing equation in arbitrary geometry.