Abstract. This paper presents numerical solution of Richards' equation for water ow through unsaturated porous media. Di erential Quadrature Method (DQM) is employed for the rst 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 di erential equation due to strong nonlinearity between hydraulic conductivity (and di usivity) 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 1D 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.

Nonlinear nature of Richards' equation has attracted attention for providing analytical and numerical solution for this equation. In the present study, differential quadrature method (DQM) is used for presenting a numerical solution for one-dimensional Richards' equation in mixed and h-based forms, where pressure head is the dependent variable. Our results show that DQM requires less computational effort compared to finite difference technique, and can be applied for solving other similar nonlinear equations.