A fractional step method to compute a class of compressible gas–liquid flows

Hérard, Jean-Marc; Hurisse, Olivier

doi:10.1016/j.compfluid.2011.11.001

Cited by 43 publications

(70 citation statements)

References 29 publications

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“…The numerical approximation of this complete two-fluid model can be obtained with the fractional step method that complies with the overall entropy inequality. Such recent algorithms have been introduced in [17] and [18] in order to tackle source terms.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, Riemann invariants associated with the other waves are respectively : (17) with ∂f ϕ /∂p ϕ = −1/ρ ϕ c ϕ .…”

Section: A Fractional Step Methods To Compute Baer-nunziato Modelmentioning

confidence: 99%

“…Some algorithms have been proposed in [10,17] for that purpose. The celerity of acoustic waves in the pure liquid (respectively vapour) phase is noted c l (resp.…”

Section: Governing Equations Of the Baer-nunziato Modelmentioning

confidence: 99%

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Approximate solutions of the Baer-Nunziato Model

Crouzet

Daude²,

Helluy

et al. 2013

ESAIM: Proc.

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Abstract. We examine in this paper the accuracy of some approximations of the BaerNunziato two-phase flow model. The governing equations and their main properties are recalled, and two distinct numerical schemes are investigated, including a classical secondorder extension relying on symmetrizing variables. Shock tube cases are considered, and two simple Riemann problems based on well-balanced initial data are detailed. These enable to recover the expected convergence rates. However, it is shown that these simple cases are indeed very difficult and that the accuracy of basic schemes is rather poor.Résumé. Approximation des solutions du modèle de Baer-Nunziato On examine ici la précision des approximations obtenues pour le modèle diphasique de BaerNunziato. Leséquations du modèle et ses principales propriétés sont rappellées. Deux schémas distincts sont proposés, et des extensions classiques au second-ordre sont considérées, utilisant les variables de symétrisation. Des cas tests de tubeà choc sont analysés, notamment deux cas utilisant des conditions initiales enéquilibre. Les taux de convergence attendus sont retrouvés, mais on montre que la précision des approximations de certains problèmes de Riemann est assez médiocre.

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Section: Resultsmentioning

confidence: 99%

“…Moreover, Riemann invariants associated with the other waves are respectively : (17) with ∂f ϕ /∂p ϕ = −1/ρ ϕ c ϕ .…”

Section: A Fractional Step Methods To Compute Baer-nunziato Modelmentioning

confidence: 99%

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Approximate solutions of the Baer-Nunziato Model

Crouzet

Daude²,

Helluy

et al. 2013

ESAIM: Proc.

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“…In the present work, we focus on physical configurations for which the characteristic times τ p and τ u of the relaxation terms are much larger than the simulation time T . As a consequence, we do not treat this last step (S 3 ) in the present paper, and we refer to [10] for the numerical treatment of these terms. From this point, we assume that S(U) = 0.…”

Section: The Baer-nunziato Two-phase Flow Model and Its Mathematical mentioning

confidence: 99%

“…In order to simplify the presentation, we will restrict in this paper to the barotropic version of the BN model, but the extension to the standard BN model is straightforward. Moreover, the numerical treatment of source terms will be disregarded, and we refer to relevant references for that topic [10].…”

Section: Introductionmentioning

confidence: 99%

A splitting method for the isentropic Baer-Nunziato two-phase flow model

Coquel

Hérard²,

Saleh

2012

ESAIM: Proc.

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Abstract. In the present work, we propose a fractional step method for computing approximate solutions of the isentropic Baer-Nunziato two-phase flow model. The scheme relies on an operator splitting method corresponding to a separate treatment of fast propagation phenomena due to the acoustic waves on the one hand and slow propagation phenomena due to the fluid motion on the other. The scheme is proved to preserve positive values of the statistical fractions and densities. We also provide two test-cases that assess the convergence of the method.Résumé. Nous proposons ici une méthodeà pas fractionnaires pour le calcul de solutions approchées pour la version isentropique du modèle diphasique de Baer-Nunziato. Le schéma s'appuie sur un splitting de l'opérateur temporel correspondantà la prise en compte différenciée des phéno-mènes de propagation rapide dus aux ondes acoustiques et des phénomènes de propagation lente dus aux ondes matérielles. On prouve que le schéma permet de préserver des valeurs positives pour les taux statistiques de présence des phases ainsi que pour les densités. Deux cas tests numériques permettent d'illustrer la convergence de la méthode.

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A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium

Abgrall

2022

Numerical Methods in Fluids

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Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state-stiffened gas and Peng-Robinson-were investigated.

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A fractional step method to compute a class of compressible gas–liquid flows

Cited by 43 publications

References 29 publications

Approximate solutions of the Baer-Nunziato Model

Approximate solutions of the Baer-Nunziato Model

A splitting method for the isentropic Baer-Nunziato two-phase flow model

A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium

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