NUMERICAL STUDY OF THE EROSION PROCESS

摘要

The erosion is a complex process determined by different physical and biological factors. It is difficult to find a mathematical model that captures all the details of the sediment transport through water flow in the presence of vegetation. Consequently, we build a model that captures the essence of the phenomenon by coupling Saint-Venant type equations for water dynamics with a HairsineRose type model for soil erosion, both taking into account the presence of the plants on the soil surface. For numerical purposes, we discretize the PDE system using a finite volume method for the space variables. To advance in time, we use a two-step fractionary method. Finally, several numerical results are presented.