Influence of interfacial pressure on the hyperbolicity of the two-fluid model

Ndjinga, Michaël

doi:10.1016/j.crma.2007.02.006

Cited by 18 publications

(23 citation statements)

References 4 publications

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“…The hyperbolicity of that set of equations was investigated in Stuhmiller (1977) for non-compressible mixtures and in Ndjinga (2007) and Chang et al (2007) for compressible ones. For non-compressible mixtures Stuhmiller (1977) found the hyperbolicity condition…”

Section: Conservation Of Energymentioning

confidence: 99%

On the quest for a hyperbolic effective-field model of disperse flows

2013

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The cornerstone of multiphase flow applications in engineering practice is a scientific construct that translates the basic laws of fluid mechanics into a set of governing equations for effective interpenetrating continua, the effective-field (or two-fluid) model. Over more than half a century of development this model has taken many forms but all of them fail in a way that was known from the very beginning: mathematical ill-posedness. The aim of this paper is to refocus awareness of this problem from a unified fundamental perspective that clarifies the manner in which such failures took place and to suggest the means for a final closure.

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Section: Conservation Of Energymentioning

confidence: 99%

On the quest for a hyperbolic effective-field model of disperse flows

2013

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“…This may lead to the lack of stable mathematical and numerical solutions. Nevertheless, these models are extensively used for practical applications; and in numerical simulations they are often mitigated by specifying a regularizing interfacial pressure (see [48,1,49]). Further, estimates of fluid-mechanical sound speeds is of practical importance for the construction of efficient numerical schemes [50,44].…”

Section: The Model Hierarchymentioning

confidence: 99%

A hierarchy of non-equilibrium two-phase flow models

Linga

Flåtten

2019

ESAIM: ProcS

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We consider a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer-Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. The subcharacteristic condition is closely linked to the stability of such relaxation systems, and in the context of two-phase flow models, it implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models ] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.

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“…Both algorithms however require some informations regarding the eigenvalues location. In the multiphase flow discipline (see [2] for an introduction) the characteristic polynomial generally admits a simple expression, and such estimates are available (see for example [9] and [3]). Otherwise, estimates of the eigenvalues may be obtained through Gershgorin Disc's localisation techniques.…”

Section: Introductionmentioning

confidence: 99%

“…Recent characteristic based methods, designed for the numerical simulation of multiphase flow averaged models, also involve the computation of the matrix sign or absolute value functions (see [13,8,4]). However these models may lack hyperbolicity [9], and one has to consider the general case of real matrices with complex eigenvalues. The classical definitions of |A| and sign(A) (2) involve the left and right eigenvectors of A.…”

Section: Introductionmentioning

confidence: 99%

“…Nous proposons dans cette Note deux approches de calcul évitant une diagonalisation complète de la matrice, mais nécessitant des estimations de ses valeurs propres. Dans le cas de la simulation numérique d'écoulements diphasiques, ces estimations sont disponibles car le polynôme caractéristique de la matrice A admet une expression simple (voir par exemple [9,3]), et les deux algorithmes présentés dans cette Note peuvent donc être employés (voir [10]). …”

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