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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2014

A Robust and Entropy-Satisfying Numerical Scheme for Fluid Flows in Discontinuous Nozzles

Résumé

We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is ased on a piecewise constant discretization of the cross-section and on a approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous with arbitrary large jumps. To do so, we introduce in the first step of the relaxation solver a singular dissipation measure superposed on the standing wave which enables us to control the approximate speeds of sound and thus, the time step, even for extreme initial data.
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Dates et versions

hal-00795446 , version 1 (28-02-2013)
hal-00795446 , version 2 (28-02-2013)

Identifiants

Citer

Frédéric Coquel, Khaled Saleh, Nicolas Seguin. A Robust and Entropy-Satisfying Numerical Scheme for Fluid Flows in Discontinuous Nozzles. Mathematical Models and Methods in Applied Sciences, 2014, 24 (10), pp.2043-2083. ⟨10.1142/S0218202514500158⟩. ⟨hal-00795446v2⟩
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