ABSTRACT: The Richards equation describes the infiltration of a fluid in a porous media, such as water in soil, under partially saturated conditions. This equation is a strongly nonlinear parabolic PDE, which PDE also becomes doubly degenerate when regions of the porous media are completely desaturated (or dry) and others fully saturated. Appropriate formulations and numerical methods are required to efficiently handle the strong nonlinearities and degeneracies present in Richards equation. The talk will cover few aspects of this problem, illustrated by numerical test cases. This work is joint with Abdelaziz Beljadid, Abderrahmane Benfanich, Sana Keita, Nour-Eddine Toutlini and Azzeddine Soulaı̈mani.

BIO: Yves Bourgault obtained his PhD in mathematics from Laval University in 1996, under the supervision of Professor Michel Fortin. In 1995, he joined the Computational Fluid Dynamics Laboratory of Concordia University, initially as a research associate and then as a research assistant professor. He was the technical coordinator of a university-industry consortium on the numerical simulation of in-flight icing, still a major concern for aircraft safety. As part of this project, his main contributions are the development of an Eulerian model of icing droplet impingement and a thermodynamical model of ice accretion. DROP3D, the Eulerian droplet impingement model, is now commonly used in the aerospace industries all over Canada, the United States and Europe. In July 1999, he was appointed as assistant professor at the Department of Mathematics and Statistics of the University of Ottawa. He was a visiting professor at the Swiss Polytechnic Institute of Lausanne in 2006-2007 and at the INRIA (Bordeaux) in 2013. He works on the development of numerical methods, in particular finite element methods, for solving partial differential equations (PDE).