Displaying similar documents to “Entropy consistent, TVD methods with high accuracy for conservation laws.”

Adaptive multiscale scheme based on numerical density of entropy production for conservation laws

Mehmet Ersoy, Frédéric Golay, Lyudmyla Yushchenko (2013)

Open Mathematics

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We propose a 1D adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). This density is used as an a posteriori error which provides information if the mesh should be refined in the regions where discontinuities occur or coarsened in the regions where the solution remains smooth. As due to the Courant-Friedrich-Levy stability condition the time step is restricted and...

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients

Kenneth Hvistendahl Karlsen, Nils Henrik Risebro (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a “rough” coefficient function k ( x ) . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k ' is in B V , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion...

Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function

Sébastien Martin, Julien Vovelle (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the problem of numerical approximation in the Cauchy-Dirichlet problem for a scalar conservation law with a flux function having finitely many discontinuities. The well-posedness of this problem was proved by Carrillo [  (2003) 687–705]. Classical numerical methods do not allow us to compute a numerical solution (due to the lack of regularity of the flux). Therefore, we propose an implicit Finite Volume method based on an equivalent formulation of the initial problem....

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...