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The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...
The numerical solution of the elliptic Monge-Ampère Partial Differential
Equation has been a subject of increasing interest recently [Glowinski,
in 6th International
Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192;
Oliker and Prussner,
Numer. Math.54 (1988) 271–293; Oberman,
Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski,
in Partial differential equations, Comput.
Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al.,
Japan...
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