Wednesday, July 7th, 2021. Time: 15h.

Online - Session link:  https://meet.google.com/wgr-kyjv-cyr

See video on Youtube

ABSTRACT

The Richards equation models phenomena of great importance in engineering. Said differential equation is a non-linear parabolic expression that describes the flow of liquids in unsaturated porous media. Except for cases for very specific geometries it is not possible to find an exact solution to this equation, with which the need arises to resort to numerical methods to approximate its solution.

Given its importance, it is possible to find very different alternatives in the literature to approximate solutions of this type of equations. One of these alternatives, naturally, are finite differences, which in classic discretization schemes, adapted to rectangular stencils, stand out for their simplicity and for the fact that there are few mathematical tools necessary for their construction. However, its use in non-regular domains has been limited for years due to the need to have regular meshes over the entire domain except eventually for a few points. To address these limitations, versions of finite differences were developed, which we refer to as generalized, which allow working with irregular meshes, and which can even be used as a non-mesh method.

This talk shows the recent advances that we have had within the work team in solving infiltration problems using adaptive integration schemes in time and generalized finite differences in space. Different alternatives implemented to control errors associated with discretization are also discussed. 

This coffee talk will be given in Spanish.

SPEAKER CV

High school professor at the Jefferson International University (Morelia, Michoacán) since 2018. Master's degree, Joint Postgraduate UNAM-UMSNH, Morelia, Michoacán, Master in mathematical sciences. Master's studies oriented to biomathematics.

See Coffee Talk’s Programme 2021