Numerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemes

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dc.contributor.authorBerres, Stefan
dc.contributor.authorBuerger, Raimund
dc.contributor.authorKozakevicius, Alice
dc.date2009
dc.date.accessioned2021-04-30T16:58:22Z
dc.date.available2021-04-30T16:58:22Z
dc.description.abstractThe generic structure of solutions of initial value problems of hyperbolic-elliptic systems, also called mixed systems, of conservation laws is not yet fully understood. One reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity approach. There is, however, theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations, so-called oscillatory waves, which are (in general, measure-valued) solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic region. To capture these solutions, usually a fine computational grid is required. In this work, a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave type. The hyperbolic-elliptic 2 x 2 systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse suspension. In the latter case, varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space, giving rise to different kinds of oscillation waves.
dc.identifier.citationADVANCES IN APPLIED MATHEMATICS AND MECHANICS,Vol.1,581-614,2009
dc.identifier.doi10.4208/aamm.09-m0935
dc.identifier.urihttp://repositoriodigital.uct.cl/handle/10925/3612
dc.language.isoen
dc.publisherGLOBAL SCIENCE PRESS
dc.sourceADVANCES IN APPLIED MATHEMATICS AND MECHANICS
dc.subject.englishHyperbolic-elliptic system
dc.subject.englishconservation law
dc.subject.englishoscillation wave
dc.subject.englishnumerical simulation
dc.subject.englishmultiresolution method
dc.subject.englishsedimentation model
dc.titleNumerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemes
dc.typeArticle
uct.catalogadorWOS
uct.indizacionSCI
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