Symmetrization of conservation laws with entropy for high-temperature hypersonic computations

Chalot, F.; Hughes, Thomas J.R.; Shakib, Farzin

doi:10.1016/0956-0521(90)90032-g

Cited by 60 publications

(25 citation statements)

References 12 publications

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“…We finally discuss in Section 7 the numerical simulation of multicomponent flows with complex chemistry and detailed transport [54,55,56,57,58,59,60,61,62,63,64]. We notably address the mathematical structure of the transport linear systems and fast accurate evaluation of the transport coefficients [65,66,67,68,69,70,71].…”

Section: Introductionmentioning

confidence: 99%

Multicomponent flow modeling

Giovangigli

2011

Sci. China Math.

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We first present multicomponent flow models derived from the kinetic theory of gases. We then investigate the symmetric hyperbolic-parabolic structure of the resulting system of partial differential equations and discuss the Cauchy problem for smooth solutions. We also address the existence of deflagration waves also termed anchored waves. We further indicate related models which have a similar hyperbolic-parabolic structure, notably the Saint-Venant system with a temperature equation as well as the equations governing chemical equilibrium flows. We next investigate multicomponent ionized and magnetized flow models with anisotropic transport fluxes which have a different mathematical structure. We finally discuss numerical algorithms specifically devoted to complex chemistry flows, in particular the evaluation of multicomponent transport properties, as well as the impact of multicomponent transport.

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Section: Introductionmentioning

confidence: 99%

Multicomponent flow modeling

Giovangigli

2011

Sci. China Math.

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“…The result, derived in Reference [29] for a perfect gas and extended in Reference [45] for a general divariant uid is the following:…”

Section: Generalized Entropy (In)equalitymentioning

confidence: 90%

“…Therefore, the change of variables is well deÿned and the function H(U) is a convex function of U. Likewise, the matrices A i is symmetric and K = [ K ij ] is symmetric positive-semideÿnite (see Reference [45]). …”

Section: Generalized Entropy Function and The Symmetric Formmentioning

confidence: 99%

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A segregated method for compressible flow computation. Part II: general divariant compressible flows

Hauke

Landaberea²,

Garmendia³

et al. 2005

Int. J. Numer. Meth. Fluids

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SUMMARYTypically, segregated methods have been used for the computation of incompressible ows whereas coupled solvers, for compressible ows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible ows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, in this paper a segregated method for non-isothermal compressible ows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods.

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“…The isothermal compressibility coe cient is in this case ÿ T → 0 (45) limit that can be obtained from the isothermal perfect gas model with…”

Section: Incompressible Uidmentioning

confidence: 99%

A segregated method for compressible flow computation Part I: isothermal compressible flows

Hauke

Landaberea²,

Garmendia³

et al. 2004

Numerical Methods in Fluids

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SUMMARYTraditionally, coupled methods have been employed for the computation of compressible ows, whereas segregated methods have been preferred for the computation of incompressible ows. Compared to coupled methods, segregated solvers present the advantage of reduced computer memory and CPU time requirements, although at the cost of an inferior robustness. Therefore, in a series of papers we present uniÿed computational techniques to compute compressible and incompressible ows with segregated stabilized methods. The proposed algorithms have an increased robustness compared to existing techniques, while possessing additional beneÿts such as employing standard pressure boundary conditions. In this ÿrst part, the thermodynamics of isothermal, thermally perfect compressible ows is set up in the framework of symmetric systems and the corresponding segregated algorithms are introduced.

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Symmetrization of conservation laws with entropy for high-temperature hypersonic computations

Cited by 60 publications

References 12 publications

Multicomponent flow modeling

Multicomponent flow modeling

A segregated method for compressible flow computation. Part II: general divariant compressible flows

A segregated method for compressible flow computation Part I: isothermal compressible flows

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