An Upwind Numerical Method for Two-Fluid Two-Phase Flow Models

Toumi, I.

doi:10.13182/nse96-a24180

Cited by 80 publications

(84 citation statements)

References 17 publications

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“…This motivates our choice of terminology. We also remark that there is some reason to expect that the main conclusions of this paper may carry over to the more general case where v g = v , a question that may possibly be further investigated through an asymptotic analysis following for instance the approach of [15,40].…”

Section: The Five-equation Drift-flux Modelmentioning

confidence: 91%

On the effect of temperature and velocity relaxation in two-phase flow models

Ferrer¹,

Flåtten²,

Munkejord³

2011

ESAIM: M2AN

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Abstract.We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This allows us to directly prove a subcharacteristic condition; each level of equilibrium assumption imposed reduces the propagation velocity of pressure waves. Furthermore, we show that each relaxation procedure reduces the mixture sound velocity with a factor that is independent of whether the other relaxation procedure has already been performed. Numerical simulations indicate that thermal relaxation in the two-fluid model has negligible impact on mass transport dynamics. However, the velocity difference of sonic propagation in the thermally relaxed and unrelaxed two-fluid models may significantly affect practical simulations.Mathematics Subject Classification. 76T10, 65M08, 35L60.

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Section: The Five-equation Drift-flux Modelmentioning

confidence: 91%

On the effect of temperature and velocity relaxation in two-phase flow models

Ferrer¹,

Flåtten²,

Munkejord³

2011

ESAIM: M2AN

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“…The authors in the references (Toumi, 1996, Cortes et al, 1998, Evje and Fjelde, 2003 used a perturbation method in order to obtain the approximate eigenvalues of the system. It is important to highlight that, if p 0 Δ = , the model becomes non-hyperbolic due to the existence of complex eigenvalues.…”

Section: The Two-fluid Modelmentioning

confidence: 99%

“…The water faucet problem (Ransom, 1987) became a benchmark and has been extensively used by many authors in order to test numerical schemes in tracking volume fraction fronts (Toumi, 1996, Coquel et al, 1997, Paillère et al, 2003, Evje and Flatten, 2003, De Vuyst, 2004. This problem is a study of the gravity effects on a vertical downward water jet flow.…”

Section: Water Faucetmentioning

confidence: 99%

“…The generalization of the FDS scheme is difficult because it is not always possible to analytically obtain the necessary expressions for the average state in which the Jacobian matrix must be evaluated. This class of methods was adopted by several authors (Sainsaulieu, 1995;Toumi, 1996, Toumi andKumbaro 1996;Tiselj and Petelin, 1997;Fjelde and Karlsen, 2002;Cortes et al, 1998;Romate, 1998;Faille, 1999;Saurel and Abgrall, 1999).…”

Section: Introductionmentioning

confidence: 99%

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A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

Coelho

Lage

Telles

2010

Braz. J. Chem. Eng.

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-Riemann-solver based schemes are difficult and sometimes impossible to be applied for complex flows due to the required average state. Other methods that do not use Riemann-solvers are best suited for such cases. Among them, AUSM+, AUSMDV and the recently proposed Hybrid Lax-Friedrichs-Lax-Wendroff (HLFW) have been extended to two-phase flows. The eigenstructure of the two-fluid model is complex due to the phase interactions, leading to numerous numerical difficulties. One of them is the well-posedness of the equation system because it may lose hyperbolicity. Therefore, the methods that are not based on the wave structure and that are not TVNI could lead to strong oscillations. The common strategy to handle this problem is the adoption of a pressure correction due to interfacial effects. In this work, this procedure was applied to HLFW and AUSM-type methods and their results analyzed. The AUSM+ and AUSMDV were extended to achieve second-order using the MUSCL strategy for which a conservative and a non-conservative formulation were tested. Additionally, several AUSMDV weighting functions were compared. The first and second-order AUSM-type and HLFW methods were compared for the solution of the water faucet and the shock tube benchmark problems. The pressure correction strategy was efficient to ensure hyperbolicity, but numerical diffusion increased. The MUSCL AUSMDV and HLFW methods with pressure correction strategy were, on average, the best of the analyzed methods for these test problems. The HLFW was more stable than the other methods when the pressure correction was considered.

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“…Toumi and Kumbaro [31] presented a Roe scheme for such a model including a virtual mass force term. A generalization allowing for a pressure-modification term at the gas-liquid interface was presented in [29]. An alternative Roe scheme for this model was presented by Evje and Flåtten [9].…”

Section: Introductionmentioning

confidence: 99%

The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

Flåtten¹,

Munkejord²

2006

ESAIM: M2AN

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Abstract.We construct a Roe-type numerical scheme for approximating the solutions of a driftflux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber-Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples.Mathematics Subject Classification. 35L65, 76M12, 76T10.

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An Upwind Numerical Method for Two-Fluid Two-Phase Flow Models

Cited by 80 publications

References 17 publications

On the effect of temperature and velocity relaxation in two-phase flow models

On the effect of temperature and velocity relaxation in two-phase flow models

A comparison of hyperbolic solvers II: ausm-type and Hybrid Lax-Wendroff-Lax-Friedrichs methods for two-phase flows

The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

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