Differential quadrature method for two-dimensional unsaturated water flow

Abstract

This paper presents numerical solution of Richards' equation for water flow through unsaturated porous media. Differential Quadrature Method (DQM) is employed for the first time to solve the governing equations in two-dimensional space. The moisture content-based Richards' equation is considered. This equation is known as a highly nonlinear partial differential equation due to strong nonlinearity between hydraulic conductivity (and diffusivity) and moisture content. In order to investigate the robustness of DQM in dealing with such strong nonlinearities, two popular constitutive models, i.e. White and Broadbrige (1988) and Van Genuchten (1980), are investigated for the 2D case. The analytical solution based on Brooks and Coley model in a special ID case is used to compare the results with those of DQM. For the 2D case, the study also demonstrates that DQM with considerably smaller number of grid points gives excellent results which are in close agreement with other numerical techniques such as multi-grid approach reported in the literature.