Contribution to Numerical Modeling of Water Flow in Variably Saturated, Heterogeneous Porous Media
Solutions to the Richards equation for water flow in variably saturated porous media are the focus of this paper. Working with field conditions, the extreme variability and complexity of soil, initial and boundary conditions can make the flow problem difficult to solve. This paper proposes to improve the computational efficiency of the mixed hybrid finite element (MHFE) method coupled with the variables transformation. The transform variables were introduced in order to simulate problems with convergence difficulty attributed to the presence of sharp wetting fronts. Furthermore, for better convergence behaviour, a technique that switches between the mixed-form and the pressure-head based form of the Richard’s equation was applied. Special attention was given to the top boundary conditions dealing with ponding or evaporation problems. In order to avoid non-physical oscillation problems, a mass condensation scheme was implemented in the model. Performance indicators in time and error of different options of the numerical model are defined, analyzed and classified. Thus, for each test case, a suitable numerical method that identifies which form of the Richards equation is best suited, the relevance of the switching technique as well as the utility of the transformation of the primary variable is possible. The results for the 1D Numerical test cases that have been performed matched those from the literature results. For evaporation and infiltration problem’s, the number of iterations needed to get the solution decrease when using the method of transformed pressure. Finally, knowing the soil heterogeneity, initial and boundary conditions, an agglomerative hierarchical clustering allows to analyze the need or not to transform variables and to use other options.