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

PEDROZO, H. ALEJANDRO; ROSENBERGER, MARIO R.; SCHVEZOV, CARLOS E.

Tecnología y ciencias del agua

Instituto Mexicano de Tecnología del Agua

Año: 2022 vol. 13 p. 449 - 501

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.