Performance assessment of low-order versus high-order numerical schemes in the numerical simulation of aquifer flow

Abstract

Numerical methods have been widely used to simulate transient groundwater flow induced by pumping wells in geometrically and mathematically complex systems. However, flow and transport simulation using low-order numerical methods can be computationally expensive with a low rate of convergence in multi-scale problems where fine spatial discretization is required to ensure stability and desirable accuracy (for instance, close to a pumping well). Numerical approaches based on high-order test functions may better emulate the global behavior of parabolic and/or elliptic groundwater governing equations with and without the presence of pumping well(s). Here, we assess the appropriateness of high-order differential quadrature method (DQM) and radial basis function (RBF)-DQM approaches compared to low-order finite difference and finite element methods. This assessment is carried out using the exact analytical solution by Theis and observed head data as benchmarks. Numerical results show that high-order DQM and RBF-DQM are more efficient schemes compared to low-order numerical methods in the simulation of 1-D axisymmetric transient flow induced by a pumping well. Mesh-less RBF-DQM, with the ability to implement arbitrary (e.g., adaptive) node distribution, properly simulates 2-D transient flow induced by pumping wells in confined/unconfined aquifers with regular and irregular geometries, compared to the other high-order and low-order approaches presented in this paper.