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.
- differential quadrature method (DQM)
- finite difference method
- finite element method (FEM)
- high-order vs low-order numerical method
- radial basis function
- Theis solution
- First received 22 July 2015.
- Accepted in revised form 26 November 2015.
- © IWA Publishing 2016