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Tytuł artykułu

Kinetic-induced moment systems for the Saint-Venant equations

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Języki publikacji
EN
Abstrakty
EN
Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog-like asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.
Rocznik
Strony
63--90
Opis fizyczny
Bibliogr. 7 poz., rys., tab.
Twórcy
  • Faculty of Applied Physics and Mathematics, Gdansk University of Technology
  • Department of Mathematics, University of Hamburg
  • Department of Mathematics, University of Hamburg
Bibliografia
  • [1] Leveque R J 2002 Finite Volume Methods for Hyperbolic Problems, Applied Mathematics, Cambridge
  • [2] Stoker J J 1958 Water Waves. The Mathematical Theory with Applications, Wiley
  • [3] Lions P L, Perthame B and Tadmor E 1994 Commun. Math. Phys. 163 115
  • [4] Perthame B 2002 Kinetic Formulation of Conservation Laws, Oxford University Press, NY
  • [5] Struchtrup H 2005 Macroscopic Transport Equations for Rarefied Gas Flows, Springer-Verlag, Berlin
  • [6] Gil Montoya D C. Struchtrup H and Struckmeier J 2013 A Kinetic-Induced Moment System for Burgers Equation. Hamburg (in preparation)
  • [7] Leveque R J. Berger M J, Langseth J O, Calhoun D, Mitran S, Blossey P, George D, Mandli K. Swierczewski C and Ketcheson D 2012 Clawpark Software 4.6, www.clawpack.org
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0e23e7ed-f580-4a3f-b6b9-3b9f966816fd
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