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Graduate Thesis of Carlos Vega

Vega, CarlosProgramPhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción
Enrollment Year2006
Senior Year2010
Thesis TitleHyperbolicity and numerical solution of certain polydisperse sedimentation models

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.

Thesis Director(s) Raimund Bürger, Pep Mulet
Thesis Project Approval Date2008, May 05
Thesis Defense Date2010, December 29
Professional MonitoringFull-time Professor Departamento de Matemáticas y Estadística, Universidad del Norte Barranquilla - Colombia
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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)

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