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Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Authors:
Buerger, Raimund [Departamento de Ingenieria Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)]. E-mail: rburger@ing-mat.udec.cl
Kozakevicius, Alice [Departamento de Matematica-CCNE, Universidade Federal de Santa Maria, Faixa de Camobi, km 9, Campus Universitario, Santa Maria, RS, CEP 97105-900 (Brazil)]. E-mail: alicek@smail.ufsm.br
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| Abstract: Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model and a model for the sedimentation of polydisperse suspensions. Their solutions typically involve kinematic shocks separating areas of constancy, and should be approximated by high resolution schemes. A fifth-order weighted essentially non-oscillatory (WENO) scheme is combined with a multiresolution technique that adaptively generates a sparse point representation (SPR) of the evolving numerical solution. Thus, computational effort is concentrated on zones of strong variation near shocks. Numerical examples from the traffic and sedimentation models demonstrate the effectiveness of the resulting WENO multiresolution (WENO-MRS) scheme. |
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| Publication Date: |
10 Jun 2007
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| Resource Type: |
Journal Article
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| Resource Relation: |
Journal: Journal of Computational Physics; Journal Volume: 224; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2006.11.010; PII: S0021-9991(06)00572-9; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Cou
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| Country of Publication: |
United States
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| Language: |
English
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