A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations

Saurel, Richard; Franquet, Erwin; Daniel, Éric; Métayer, Olivier Le

doi:10.1016/j.jcp.2006.10.004

Cited by 53 publications

(74 citation statements)

References 17 publications

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“…The paper by [11] gives a relevant example where such a problem has been studied. The relaxation-projection method developed in [12,15] can be examined for the computation of such interface problems. 1 ða 1 Þ 4=3 ððða 1 Þ 2 À ða 1 Þ 2=3 þ ða 2 Þ 2 þ ða 3 Þ 2 Þ 2 þ 2ð1 À ða 1 Þ 2=3 Þ 2 þ 2ðða 2 Þ 2 þ ða 3 Þ 2 ÞÞ…”

Section: Resultsmentioning

confidence: 99%

Modelling wave dynamics of compressible elastic materials

Gavrilyuk

Favrie

Saurel

2008

Journal of Computational Physics

107

110

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Section: Resultsmentioning

confidence: 99%

Modelling wave dynamics of compressible elastic materials

Gavrilyuk

Favrie

Saurel

2008

Journal of Computational Physics

107

110

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“…The archetype five-equation model is that of Kapila et al [10]. It has already found many applications, a non-exhaustive list of excellent references is [12,3,14,2,21,17]. (Recently, Saurel et al have even derived a six-equation model from a five-equation one [22].)…”

Section: Introductionmentioning

confidence: 99%

A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment

Kreeft

Koren

2010

Journal of Computational Physics

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a b s t r a c tA new formulation of Kapila's five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The new formulation uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which exchange terms are derived from physical laws. All equations are written as a single system of equations in integral form. No equation is used to describe the topology of the two-fluid flow. Relations for the Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the exchange terms is proposed. The exchange terms have distinct contributions in the cell interior and at the cell faces. For the exchange-term evaluation at the cell faces, the same Riemann solver as used for the flux evaluation is exploited. Numerical results are presented for two-fluid shock-tube and shock-bubble-interaction problems, the former also for a two-fluid mixture case. All results show good resemblance with reference results.

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“…A pioneering work in this direction was performed by Abgrall (1996). Determination of thermodynamic flow variables in these zones is achieved on the basis of multiphase flow theory (Saurel and Abgrall, 1999;Abgrall and Saurel, 2003;Saurel et al, 2003;Murrone and Guillard, 2005;Abrall and Perrier, 2006;Saurel et al, 2007;Petitpas et al, 2007). The challenge is to derive physically, mathematically, and numerically consistent thermodynamic laws for the artificial mixture.…”

Section: Introductionmentioning

confidence: 99%