A note on an extended clarifier-thickener model with singularsource and sink terms

Raimund Bûrger; A. García; K.H.  Karlsen; J. D.  Towers

Vol. 13 (2006): Special Issue: Proceedings of the Conferences Valparaíso Númerico II

Articles

A note on an extended clarifier-thickener model with singularsource and sink terms

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Raimund Bûrger ,
A. García,
K. H. Karlsen,
J. D. Towers

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Raimund Bûrger
Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile.

A. García
Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile.

K. H. Karlsen
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway.

J. D. Towers
MiraCosta College, 3333 Manchester Avenue, Cardiff-by-the-Sea, CA 92007-1516, USA.

Published 25-02-2025

Keywords

Conservation law,
discontinuous flux,
source term,
sink term,
entropy solution ,
jump condition ,
numerical method

...

Abstract

A one-dimensional clarifier-thickener (CT) model, which includes a singular feed source, can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable. The CT model is extended herein by a singular sink through which material is extracted. The sink gives rise to a new non-conservative transport term. The paper summarizes a recent well-posedness analysis and presents a numerical method for the extended model. A numerical example is presented.

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