On a Model for Continuous Sedimentation in Vessels with Discontinuous Cross-sectional Area

R. Bürger (), K. H. Karlsen (), N. H. Risebro () and J. D. Towers ()
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R. Bürger: University of Stuttgart, Institute of Applied Analysis and Numerical Simulation
K. H. Karlsen: University of Bergen, Department of Mathematics
N. H. Risebro: University of Oslo, Department of Mathematics
J. D. Towers: MiraCosta College

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 397-406 from Springer

Abstract: Abstract We study a clarifier-thickener unit considering that its cross-sectional area is not constant in both the clarification and the thickening zones. A mathematical model of sedimentation in such a vessel can be formulated as an initial value problem for a scalar conservation law with a nonconvex spatially varying flux and several types of discontinuities with respect to the space variable. Weak solutions of this non-standard conservation law are approximated by an extension of the well-known Engquist-Osher scheme. The key new ingredient is the discretization of the discontinuous flux parameters on a grid staggered against that of the conserved (sought) variable. The mathematical model and the numerical scheme are illustrated by a number of simulations.

Keywords: Weak Solution; Traffic Flow; Thickening Zone; Kinematic Wave; Continuous Sedimentation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_36

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DOI: 10.1007/978-3-642-55711-8_36

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