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.authorBurger, Raimund
dc.contributor.authorKozakevicius, Alice
dc.date2009
dc.date.accessioned2012-03-07T20:24:26Z
dc.date.available2012-03-07T20:24:26Z
dc.date.issued2012-03-07
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 2×2 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.es
dc.formatPDFes
dc.identifier.citationAdvances in Applied Mathematics and Mechanics, Vol.1, N°5, 581-614, 2009es
dc.identifier.doi10.4208/aamm.09-m0935es
dc.identifier.urihttps://repositoriodigital.uct.cl/handle/10925/861
dc.language.isoenes
dc.sourceAdvances in Applied Mathematics and Mechanicses
dc.subjectIngeniería matemáticaes
dc.titleNumerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemeses
dc.typeArtículo de Revistaes
uct.carreraPlan Común Ingenieríaes
uct.catalogadorrdves
uct.comunidadIngenieríaes
uct.facultadFacultad de Ingenieríaes
uct.indizacionISIes
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