Thesis Summary:

The purpose of this work is to get mathematical models and, subsequently, to design numerical methods that simulate polydisperse sedimentation processes, for this, a multilayer shallow water models are coupled with 1D models for polydisperse sedimentation, thus obtaining, multilayer models that not only capture the vertical movement of solid particles, but also, their horizontal movement. A multilayer approach is introduced to obtain an approximate description of polydisperse sedimentation process and sediment transport in a viscous fluid, to avoid solving complete 3D models. Here we assume that the fluid carries fine, spherical and solid particles dispersed in it, which differ in density and size. These species segregate and form areas with different composition. In addition, terms of compressibility of the sediment and mixture viscosity are considered. The horizontal components of the compression terms and the mixture viscosity have been discarded as a result of a dimensional analysis of the mass and linear momentum equations of the mixture. This results in models that are vertically consistent with classic sedimentation models. Finally, some one-dimensional, two-dimensional and three-dimensional numerical simulations are presented for different times, which illustrate the polydisperse sedimentation process coupled to a horizontal flow in several scenarios, among them, sedimentation on bottoms similar to those commonly used in the mining industry, as well as, in complete topographies that give rise to fluid recirculations. To close, we show some numerical simulations that allow us to analyze the behavior of the mixture when the compressibility of the sediment and mixture viscosity are activated and/or deactivated.

ISI Publications from the Thesis

Raimund BüRGER, Enrique D. FERNáNDEZ NIETO, Victor OSORES: A multilayer shallow water approach for polydisperse sedimentation with sediment compressibility and mixture viscosity. Journal of Scientific Computing, vol. 85, 2, article: 49 (40pp), (2020).

Raimund BüRGER, Enrique D. FERNáNDEZ NIETO, Victor OSORES: A dynamic multilayer shallow water model for polydisperse sedimentation. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 53, 4, pp. 1391-1432, (2019).