A high-resolution multidimensional finite volume scheme coupled to a nonlinear two-point flux approximation method for the numerical simulation of groundwater contaminant transport using unstructured 2D meshes

Abstract

In this paper, we propose a novel full finite volume method to solve the advection–dispersion transport equation, where the pressure and concentration equations are solved implicitly and explicitly, respectively. The advective term is discretized using a high-order MUSCL-type finite volume method (Monotonic Upstream-centered Scheme for Conservation Laws) and to avoid numerical oscillations, we use a Multidimensional Limiting Process (MLP). An improved least squares method is used for the gradient reconstruction to increase robustness. The dispersion term and the Darcy’s diffusive flux are discretized by a nonlinear two-point flux approximation method (NL-TPFA). This method is very robust and able to reproduce piecewise linear solutions exactly and ensures the preservation of positivity. The proposed formulation combines numerical methods specifically designed to achieve good accuracy and robustness of the numerical solution for the governing equation. To verify the accuracy and robustness of our formulation, we solve some benchmark problems found in the literature. Numerical experiments show that our formulations can provide accurate solutions when simulating groundwater processes, especially in aquifer systems with complex physical and geological properties.