Séminaire d'AnalyseNumerical approximation of growing sandpiles
Maurizio Falcone (Dipartimento di Matematica, SAPIENZA - Università di Roma)
mercredi 13 juin 2012 15:00 - Tours - Salle 1180 (Bât E2)
The mathematical modelling of granular materials is a source of challenging problems with many interesting applications ranging from the microscopic to the macroscopic scale. We study from a numerical point of view some differential models in this area. The starting model describes the growth of a sandpile on a flat bounded table under the action of a vertical source and is based on a two-layer formulation. The model is made by a nonlinear system of pdes where an eikonal equation for the standing layer of the pile is coupled with an advection equation for the rolling layer. We will discuss some properties of the solution and present two approximation schemes for that system showing that the finite difference scheme mimics the physics of the problem. We will also compare, through experiments in one and two dimensions, the asymptotic behavior and the equilibria of the models.