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HIGH-ORDER NUMERICAL SCHEMES FOR ONE-DIMENSIONAL NONLOCAL CONSERVATION LAWS

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dc.creatorLUIS MIGUEL VILLADA OSORIO
dc.date2018
dc.date.accessioned2025-01-10T14:57:53Z
dc.date.available2025-01-10T14:57:53Z
dc.date.issued2018
dc.description.abstractTHIS PAPER FOCUSES ON THE NUMERICAL APPROXIMATION OF THE SOLUTIONS OF NONLOCAL CONSERVATION LAWS IN ONE SPACE DIMENSION. THESE EQUATIONS ARE MOTIVATED BY TWO DISTINCT APPLICATIONS, NAMELY, A TRAFFIC FLOW MODEL IN WHICH THE MEAN VELOCITY DEPENDS ON A WEIGHTED MEAN OF THE DOWNSTREAM TRAFFIC DENSITY, AND A SEDIMENTATION MODEL WHERE EITHER THE SOLID PHASE VELOCITY OR THE SOLID-FLUID RELATIVE VELOCITY DEPENDS ON THE CONCENTRATION IN A NEIGHBORHOOD. IN BOTH MODELS, THE VELOCITY IS A FUNCTION OF A CONVOLUTION PRODUCT BETWEEN THE UNKNOWN AND A KERNEL FUNCTION WITH COMPACT SUPPORT. IT TURNS OUT THAT THE SOLUTIONS OF SUCH EQUATIONS MAY EXHIBIT OSCILLATIONS THAT ARE VERY DIFFICULT TO APPROXIMATE USING CLASSICAL FIRST-ORDER NUMERICAL SCHEMES. WE PROPOSE TO DESIGN DISCONTINUOUS GALERKIN (DG) SCHEMES AND FINITE VOLUME WENO (FV-WENO) SCHEMES TO OBTAIN HIGH-ORDER APPROXIMATIONS. AS WE WILL SEE, THE DG SCHEMES GIVE THE BEST NUMERICAL RESULTS BUT THEIR CFL CONDITION IS VERY RESTRICTIVE. ON THE CONTRARY, FV-WENO SCHEMES CAN BE USED WITH LARGER TIME STEPS. WE WILL SEE THAT THE EVALUATION OF THE CONVOLUTION TERMS NECESSITATES THE USE OF QUADRATIC POLYNOMIALS RECONSTRUCTIONS IN EACH CELL IN ORDER TO OBTAIN HIGH-ORDER ACCURACY WITH THE FV-WENO APPROACH. SIMULATIONS USING DG AND FV-WENO SCHEMES ARE PRESENTED FOR BOTH APPLICATIONS.
dc.formatapplication/pdf
dc.identifier.doi10.1137/16M110825X
dc.identifier.issn1095-7197
dc.identifier.issn1064-8275
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/9770
dc.languagespa
dc.publisherSIAM JOURNAL ON SCIENTIFIC COMPUTING
dc.relation.uri10.1137/16M110825X
dc.rightsPUBLICADA
dc.titleHIGH-ORDER NUMERICAL SCHEMES FOR ONE-DIMENSIONAL NONLOCAL CONSERVATION LAWS
dc.title.alternativeESQUEMAS NUMÉRICOS DE ALTO ORDEN PARA LEYES DE CONSERVACIÓN NO LOCAL UNIDIMENSIONALES
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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