Estimation of a Critical Spatial Discretization Limit for Solving Richards' Equation at Large Scales

摘要: Water dynamics in soil at spatial scales larger than the representative elementary volume (REV) of porous structure are typically described by Richards9 equation, which relates flux law Buckingham–Darcy to mass balance water. It is based on water retention characteristics and hydraulic conductivity function as constitutive material properties. In hydrological modeling, equation also used large up hundreds meters. Increasing scale accompanied increasing discretization for numerical solution problem. However, due underlying assumption local equilibrium between content potential, there an upper limit above expected be biased. We present a simple approach estimate this limit, depends shape functions gradient total potential. range millimeters decimeters.