Jaime Manríquez will defend his PhD thesis with the title "Modelling slow sand filtration and solving interface problems with the Transfer Path Method". Opponent is Assistant Professor Vanja Nikolić, Radboud University, The Netherlands.

Abstract: Filtration through porous media is the oldest form of drinking water treatment, and as such it constitutes a focal point of research in water engineering. Mathematical models of filtration are often used in conjunction with supplementary models of related phenomena such as free flow of fluids before entering the medium or biochemical processes occuring in the treated water. In this work, we are concerned with water filtration from two angles: first, we are interested in comprehensive modelling of Slow Sand Filters (SSFs) for drinking-water treatment, which rely on the natural development of biomass in the medium; and second, we develop further the application of the so-called Transfer Path Method (TPM) to interface problems in fluid mechanics.

The doctoral thesis is consequently divided into two parts. The first part contains a new one-dimensional model of SSFs which involves the water flow in the entire filter, consisting of the sand bed and the supernatant water sitting atop it, along with the evolution of microorganisms therein. A positivity-preserving numerical method is presented together with a documentation of the software developed for simulations. A two-dimensional model is also included; a derivation is presented as well as an invariant-region-preserving numerical method for the entire convection-reaction-Cahn–Hilliard system.

In the second part, the TPM is applied to coupled problems in fluid mechanics in the context of dissimilar meshes, that is, geometrical discretizations of two independent domains separated by an interface in which the resulting triangulations may present mismatches in the form of gaps or overlaps. The hybridizable discontinuous Galerkin method is used to discretize the corresponding systems of partial differential equations and present results for Stokes flow, Stokes/Darcy coupling and Fluid-Structure interaction.