Author(s): Das Sanjukta; T. I. Eldho

Linked Author(s):

Keywords: Groundwater simulation; Contaminant transport; Meshless Local Petrov Galerkin; Radial Point Collocation Method; Meshless Weak strong form

Abstract: Meshless methods are proven to be efficient alternatives for the mesh/grid based Finite Difference and Finite Element methods. In the meshless methods, a set of nodes are scattered in the aquifer domain and the required unknown value is obtained at each nodal point. The dependency of the nodal arrangement, interpolation, formulation and solution on a background mesh/ grid is alleviated and in some cases, completely eliminated in the meshless methods, thereby reducing the associated instabilities, high time and cost of the remeshing process. Since the past three decades, various meshless strong and weak methods are effectively applied for the groundwater flow and transport studies. The strong form methods have a higher consistency to be differentiable up to the order of the partial derivative governing equation. These methods are truly meshless, simple and computationally efficient, but are unstable in the presence of derivative boundary conditions. Contrary to the strong form methods, a weaker consistency is sufficient in the weak form methods, which is achieved by integrating the governing equation. Though the weak form methods are highly accurate and stable even for complex problems and in the presence of the derivative boundary conditions, they are computationally expensive due to the integration process applied at each meshless node. In this context, the aim of the present study is to introduce a robust meshless method for the simulation of coupled flow and contaminant transport in a heterogeneous confined aquifer, by hybridizing the weak and the strong forms and combining their merits. The strong form Radial Point Collocation Method (RPCM) and the weak form Meshless Local Petrov Galerkin (MLPG) method are coupled to form the Meshless Weak Strong form method (RPCM-MLPG-MWS). The MLPG method is exerted only for the nodes on the derivative boundary and the nodes within the support domain of the derivative boundary nodes, while all the other nodes are simulated using RPCM. The developed model is applied on a highly heterogeneous hypothetical confined aquifer, first to obtain the head distribution and then this flow model is coupled with the transport model to understand and predict the concentration distribution. Also, the effect of heterogeneity in coupled transport studies is highlighted. The results of the RPCM-MLPG-MWS model are observed to be accurate and are obtained in a significantly less computational time, thereby demonstrating the efficient applicability of the MWS method for the groundwater flow and transport phenomena.

DOI: https://doi.org/10.3850/IAHR-39WC2521711920221203

Year: 2022