A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

Petitpas, Fabien; Franquet, Erwin; Saurel, Richard; Métayer, Olivier Le

doi:10.1016/j.jcp.2007.03.014

Cited by 71 publications

(86 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a corollary of our Theorem 5.2, the MTT-equilibrium system defined in [10] or the Euler system provided with the EOS defined in [4,29,31,34,40,47,55] are strictly hyperbolic.…”

Section: Theorem 52 (Hyperbolicity) For Smooth Solutions the Comprmentioning

confidence: 84%

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

2012

View full text Add to dashboard Cite

Abstract.In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own equation of state (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption provides an implicit definition of an equilibrium EOS for the two-phase medium. Within this framework, mass transfer is the result of local and instantaneous equilibria between both phases. The overall model is strictly hyperbolic. We examine properties of the equilibrium EOS and we propose a discretization strategy based on a finite-volume relaxation method. This method allows to cope with the implicit definition of the equilibrium EOS, even when the model involves complex EOS's for the pure phases. We present two-dimensional numerical simulations that shows that the model is able to reproduce mechanism such as phase disappearance and nucleation.Mathematics Subject Classification. 76T10, 76N10, 65M08.

show abstract

“…As a corollary of our Theorem 5.2, the MTT-equilibrium system defined in [10] or the Euler system provided with the EOS defined in [4,29,31,34,40,47,55] are strictly hyperbolic.…”

Section: Theorem 52 (Hyperbolicity) For Smooth Solutions the Comprmentioning

confidence: 84%

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

2012

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…Models that allow describing the diffusion regions are divided into nonequilibrium (there is no equality of phase pressures and phase velocities) [1] and equilibrium (phases are in mechanical equilibrium) [2]. Numerical approximation for equilibrium models proves to be simpler, but in this case a number of problems arises [3]: 1) the nonmonotonic behavior of a two-phase mixture sound velocity as a function of the volume fraction, that can lead to errors in the calculation of the passage of waves across the interface; 2) non-conservative form of the equation for the volume fraction. Even using of specially obtained relations on the front of the shock wave [4], it is not always possible to achieve a coincidence between the numerical and analytical solutions, since the averaging of non-conservative variables has no physical meaning.…”

Section: Introductionmentioning

confidence: 99%

“…Even using of specially obtained relations on the front of the shock wave [4], it is not always possible to achieve a coincidence between the numerical and analytical solutions, since the averaging of non-conservative variables has no physical meaning. This problem was overcome in [3], using the relaxation algorithm instead of the averaging procedure. A more robust approach involves the model that is nonequilibrium only by pressure [5].…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of two-phase gas dynamic flows with phase transition for water and for liquid sodium

et al. 2017

View full text Add to dashboard Cite

show abstract

A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

Cited by 71 publications

References 29 publications

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium

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

Direct numerical simulation of two-phase gas dynamic flows with phase transition for water and for liquid sodium

Contact Info

Product

Resources

About