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Numerical schemes for kinematic flows with discontinuous flux
Author(s) -
Bürger Raimund,
García Antonio,
Karlsen Kenneth H.,
Towers John D.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700494
Subject(s) - kinematics , kinematic wave , nonlinear system , simple (philosophy) , flux (metallurgy) , flow (mathematics) , conservation law , sedimentation , series (stratigraphy) , mechanics , variable (mathematics) , mathematics , physics , classical mechanics , geology , mathematical analysis , materials science , sediment , ecology , philosophy , paleontology , epistemology , quantum mechanics , surface runoff , metallurgy , biology
Spatially one‐dimensional kinematic flows arise in a series of applications including traffic flow and sedimentation. They lead to nonlinear systems of conservation law whose flux has an explicit “concentration times velocity” structure. A new family of simple numerical schemes which are adapted to this structure, and which handle fluxes that are discontinuous with respect to the space variable, is presented and in part analyzed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)