Displaying similar documents to “Adaptive multiscale scheme based on numerical density of entropy production for conservation laws”

A numerical method for unsteady flows

Nicola Botta, Rolf Jeltsch (1995)

Applications of Mathematics

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A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is...

An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment

François Bouchut, Tomás Morales de Luna (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities...