Convergence of Second-Order Schemes for Isentropic Gas Dynamics

Liu, Jianguo

doi:10.2307/2153243

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…One can ease these difficulties with some stepsize-dependent limiters. For example, the works of Coquel and LeFloch [5], Johnson, Szepessy and Hansbo [12], Cockburn, Coquel and LeFloch [3], Cockburn and Gremaud [4], and Chen and Liu [2] all use stepsize-dependent limiters. These results are usually more general (multispace dimensions, nonconvex fluxes, systems, etc.).…”

Section: U H) ≡ F(u) (14)mentioning

confidence: 99%

On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

Yang

1996

Math. Comp.

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Abstract. We develop a new approach, the method of wavewise entropy inequalities for the numerical analysis of hyperbolic conservation laws. The method is based on a new extremum tracking theory and Vol pert's theory of BV solutions. The method yields a sharp convergence criterion which is used to prove the convergence of generalized MUSCL schemes and a class of schemes using flux limiters previously discussed in 1984 by Sweby.

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Section: U H) ≡ F(u) (14)mentioning

confidence: 99%

On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

Yang

1996

Math. Comp.

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“…where u 0 (x) and ρ 0 (x) ≥ 0 ( ≡ 0) is studied in [4]. The authors established the convergence of a second-order shock-capturing scheme.…”

Section: Introductionmentioning

confidence: 99%

Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach

Boureni

Georgiev²,

Kheloufı³

et al. 2022

Appl. Gen. Topol.

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Entropy flux‐splittings for hyperbolic conservation laws part I: General framework

LeFloch

1995

Comm Pure Appl Math

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A general framework is proposed for the derivation and analysis of flux-splittings and the corresponding flux-splitting schemes for systems of conservation laws endowed with a strictly convex entropy. The approach leads to several new properties of the existing flux-splittings and to a method for the construction of entropy flux-splittings for general situations. A large family of genuine entropy flux-splittings is derived for several significant examples: the scalar conservation laws, the p-system, and the Euler system of isentropic gas dynamics. In particular, for the isentropic Euler system, we obtain a family of splittings that satisfy the entropy inequality associated with the mechanical energy. For this system, it is proved that there exists a unique genuine entropy flux-splitting that satisfies all of the entropy inequalities, which is also the unique diagonatizable splitting. This splitting can be also derived by the so-called kinetic formulation. Simple and useful difference schemes are derived from the flux-splittings for hyperbolic systems. Such entropy flux-splitting schemes are shown to satisfy a discrete cell entropy inequality. For the diagonalizable splitting schemes, an a priori L" estimate is provided by applying the principle of bounded invariant regions. The convergence of entropy fluxsplitting schemes is proved for the 2 x 2 systems of conservation laws and the isentropic Euler system.

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Convergence of Second-Order Schemes for Isentropic Gas Dynamics

Cited by 4 publications

References 12 publications

On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case

Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach

Entropy flux‐splittings for hyperbolic conservation laws part I: General framework

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