Universidad Nacional de Colombia Sede Medellín

El Coloquio de la Escuela de Matemáticas tiene el gusto de invitarlos a la conferencia

“On systems of conservation laws modelling the settling ofpolydisperse suspensions”

Que ofrecerá el profesorRaimund Bürger

de la Universidad de Concepción, Chile,el próximo martes 15 de octubre de 2013 a las 4:00 p.m.

en aula 19A 206-207

Abstract: In this talk we will revise some recent advances in the construction and (partial) analysis of numerical schemes for systems of conservation laws modelling the sedimentation of polydisperse suspensions, that is of mixtures of fine solid particles suspended in a viscous fluid. The particles are assumed to differ in size and density, so different species will segregate and form areas of different composition. A well-established mathematical model that describes this process is given by a strongly coupled system of nonlinear first-order conservation laws, whose solution are the volume fractions of the different species as a function of depth and time. The numerical solution of this model is a challenge since the eigenvalues and eigenvectors of the flux Jacobian are not available in closed form, and therefore the Riemann problem can hardly be solved explicitly.

This talk presents new results for the numerical analysis of this and related models in three different directions, namely (1) characteristic-wise high-resolution schemes that rely on a new approach to the hyperbolicity analysis of the model, (2) implicit-explicit Runge-Kutta schemes that efficiently handle an extended hyperbolic-parabolic model that accounts for the effect of sediment compressibility, and (3) a new approach to modelling polydisperse sedimentation subject to horizontal currents by a multilayer shallow water model.