Modelamiento Numérico Espacio-Temporal 1D de la Infiltración Basado en la Ecuación de Richards y Otras Simplificadas

Abstract

The infiltration is one of the hydrological processes that receives a lot of importance in the environmental engineering and of water resources, per decades many investigators have come doing efforts to model the process of infiltration, departing from the equation of Richards (1931). The behavior of the infiltration can be treated in form three dimensional and time in its most complex, and depending on what is required even in its one-dimensional form most the temporal component. In this work Richards's equation diminishes to his expression unidimensional, more his temporary component and is solved under the method of finite differences using Crank-Nicolson's, scheme in an implicit alternate exact scheme, in the second order both in space and in time. The above mentioned scheme was codified in MATLAB, and the results fulfill satisfactorily the aim to predict the movement of the water in the subsoil, from information of physical properties of the soils and well conditions type dirichlet of water over on the soil. Likewise the model is very versatile, since it allows to establish the user, conditions as total depth of simulation, spacing between knots and intervals of calculation for the temporary variable. In case of the model of Smith-Parlange (1978), it was solved using the algorithm of Newton Raphson, the same one who also was implemented in a computational code in MATLAB, throwing satisfactory results similar to those of the previous model. Likewise, I elaborate a computational code to resolve the Model Green Ampt (1911), doing the comparison of three mentioned models.