Kinetic-induced moment systems for the Saint-Venant equations

• Autorzy: Gil Montoya D. C. , Struckmeier J.
• 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.

Słowa kluczowe

EN

Saint-Venant equations; shallow water equations; Boltzmann equation; hyperbolic conservation laws; kinetic models; kinetic representations; relaxion systems; shock waves; rarefaction waves

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2013
• Tom: Vol.17, No 1-2
• Strony: 63--90
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Gil Montoya D. C.

• Faculty of Applied Physics and Mathematics, Gdansk University of Technology
• Department of Mathematics, University of Hamburg

autor

Struckmeier J.

• 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