NDLI: A kinetic scheme for the Saint-Venant system¶with a source term

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A kinetic scheme for the Saint-Venant system¶with a source term

Content Provider	Springer Nature Link
Author	Perthame, B. Simeoni, C.
Copyright Year	2001
Abstract	The aim of this paper is to present a numerical scheme to compute Saint-Venant equations with a source term, due to the bottom topography, in a one-dimensional framework, which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom. This is achieved by means of a kinetic approach to the system, which is the departing point of the method developed here. In this context, we use a natural description of the microscopic behavior of the system to define numerical fluxes at the interfaces of an unstructured mesh. We also use the concept of cell-centered conservative quantities (as usual in the finite volume method) and upwind interfacial sources as advocated by several authors. We show, analytically and also by means of numerical results, that the above properties are satisfied.
Starting Page	201
Ending Page	231
Page Count	31
File Format	PDF
ISSN	00080624
Journal	CALCOLO
Volume Number	38
Issue Number	4
e-ISSN	11265434
Language	English
Publisher	Springer-Verlag
Publisher Date	2001-12-01
Publisher Place	Milano
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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