Simulation du ruissellement d'eau de pluie sur des surfaces agricoles

In this work, we aim at developping both a model and a numerical method adapted to the simulation of rainfall runoff on agricultural fields. The model used is a system of partial differential equations for shallow water flows : namely the system of Saint Venant. Rain and infiltration are treated as source terms and with a coupled model of infiltration. Because of the hyperbolicity and conservativity properties, we are using a finite volume scheme with the hydrostatic reconstruction. This reconstruction allows us to deal with stationary equilibria and wet/dry transitions due to rainfall events. First, a systematic comparison on analytic solutions is achieved between various numerical fluxes, two second order reconstructions (a MUSCL and a modified ENO reconstructions) and different numerical treatment of the friction term. This allows us to choose a numerical method adapted to runoff simulation. Moreover it is able to catch roll waves phenomenons. Then we are interested in the rain and infiltration treatment. Infiltration is modeled thanks to the Green Ampt model. This method is thereafter generalized to two dimensions and validated on experimental results obtained by the INRA of Orléans and the IRD. The chosen numerical method has been implemented in an C++ open-source software for rainfall runoff on agricultural fields simulations : FullSWOF_2D.