Thesis Summary:

In this work, a study of the strict hyperbolicity is carried out for some polydispersed sedimentation models that lead to a one-dimensional system of N nonlinear and strongly coupled conservation laws. From the fact that the flow function for the models considered can be expressed in terms of a small number (with respect to the number of N species) of scalar functions that depend only on the concentration vector, we obtain that the Jacobian matrix Of the system has a particular structure, which allows to identify its own values ​​with the roots of a rational function. In addition to obtaining qualitative information about the eigenvalues, one obtains a way of locating and approximating them numerically. In fact, all the characteristic information necessary to perform the numerical simulations with robust high-resolution methods, in particular the popular WENO method (Weighted Essentially Non-oscillatory) of the fifth order, is provided. The relevance and advantages of this method, implemented using the characteristic information intensively, is illustrated with a considerable number of numerical examples.

ISI Publications from the Thesis

Raimund BüRGER, Rosa DONAT, Pep MULET, Carlos A. VEGA: On the hyperbolicity of certain models of polydisperse sedimentation. Mathematical Methods in the Applied Sciences, vol. 35, 6, pp. 723-744, (2012).

Raimund BüRGER, Rosa DONAT, Pep MULET, Carlos A. VEGA: On the implementation of WENO schemes for a class of polydisperse sedimentation models. Journal of Computational Physics, vol. 230, 6, pp. 2322-2344, (2011).

Raimund BüRGER, Rosa DONAT, Pep MULET, Carlos A. VEGA: Hyperbolicity analysis of polydisperse sedimentation models via a secular equation for the flux Jacobian. SIAM Journal on Applied Mathematics, vol. 70, 7, pp. 2186-2213, (2010)