Author(s): D. E. Caviedes-Voullieme; P. Garcia-Navarro; J. Murillo
Linked Author(s): Daniel Caviedes-Voullieme
Keywords: Richards’ equation; Unsaturated soil; Finite-differences; Stability
Abstract: Flow in variably saturated soils is described by Richards' equation. This PDE is commonly found in three physically equivalent forms which lead to different discretization techniques. Such techniques show different properties and range for variably saturated soil simulations. Furthermore, the properties of the soil constitutive model interact with the numerical techniques and affect their response in several ways. Our goal is to evaluate the numerical solution of the three PDE's using well-known numerical methods from the point of view of mass conservation, convergence and computational efficiency to set a framework for a 3D variably saturated soil model with surface interactions. The interrelated effects of the PDE's, numerical schemes and saturated/unsaturated conditions are explored. Additionally, the effects of non-linearity of the soil constitutive model functions, as well as those of hydraulic conductivity averaging on intercell boundaries are also studied. A validation case is presented and the response to different configurations and parameters is examined. From them, it is concluded that the explicit and the implicit schemes based on the mixed form of Richards' equation are better suited for unsaturated problems. For variably saturated problems, the implicit scheme based on the mixed form is the best choice, since the explicit model cannot solve saturation conditions. Conditional stability of the explicit model affects negatively its performance in certain cases, which also leads to the conclusion that the implicit scheme is more efficient and reliable.
Year: 2011