Stability regions for an explicit numerical solution of the one-dimensional Richards equation applied to water soil infiltration

Richards equation describes the infiltration and movement of water in porous media, such as soils. This equation, added to the complex constitutive equations which characterize the soil, produces a nonlinear system of partial differential equations. In this work, the Richards equation formulated as a function of the saturation degree was solved by an explicit finite difference method. The matric potential was obtained as a function of the saturation degree, and the convergence of the solutions was analyzed by a modified von Neumann procedure and compared with numerical calculations. As a result, an analytical expression was obtained to determine a priori if a simulation was stable for given time and spatial steps. From those simulation parameters and soils properties, dimensionless numbers were defined to generalize the proposed method.