Displaying similar documents to “Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint”

Accurate numerical discretizations of non-conservative hyperbolic systems

Ulrik Skre Fjordholm, Siddhartha Mishra (2012)

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

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We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments...

Accurate numerical discretizations of non-conservative hyperbolic systems

Ulrik Skre Fjordholm, Siddhartha Mishra (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments...

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.

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...

A multidimensional fluctuation splitting scheme for the three dimensional Euler equations

Jérôme Bastin, Gilbert Rogé (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The fluctuation splitting schemes were introduced by Roe in the beginning of the 80's and have been then developed since then, essentially thanks to Deconinck. In this paper, the fluctuation splitting schemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of the three dimensional Euler equations is presented. This decomposition leads to an acoustic subsystem and two scalar advection equations, one of them being the entropy advection. Thanks to this decomposition,...