Front tracking for a model of immiscible gas flow with large data

Holden, Helge; Risebro, Nils Henrik; Sande, Hilde

doi:10.1007/s10543-010-0264-6

Cited by 8 publications

(4 citation statements)

References 25 publications

(47 reference statements)

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“…We refer to (6.20) for the definition of the function K; therefore, condition (2.3) is explicit. We recall that related results of global existence of solutions with large data [25,22,23,19,20] do not precise the threshold of smallness of the initial data.…”

Section: Resultsmentioning

confidence: 91%

“…A model analogous to (1.1) is also studied in [19,20], where the pressure is v −γ and the state variable λ is replaced by the adiabatic exponent γ > 1; also in this case the global existence of solutions is proved under a condition that has the same flavor of that discussed above. At last, we refer to [16] for a comprehensive discussion of the problem of the global existence of solutions for systems of conservation laws.…”

Section: Introductionmentioning

confidence: 99%

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Global weak solutions for a model of two-phase flow with a single interface

et al. 2015

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We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid and then phase transitions can be taken into consideration; moreover, phase interfaces are contact discontinuities for the system. We focus on the special case of initial data consisting of two different phases separated by an interface. We find explicit bounds on the (possibly large) initial data in order that weak entropic solutions exist for all times. The proof exploits a carefully tailored version of the front tracking scheme.

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Section: Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Global weak solutions for a model of two-phase flow with a single interface

et al. 2015

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“…The paper [39] contains an interesting analysis of the wave-pattern interactions for (4) but the proof of the global existence of solutions by the Glimm scheme seems incomplete. In the case π(v, γ) = v −γ , with γ > 1 replacing λ, the global existence of weak solutions for initial data with suitably bounded total variation have been proved in [25,26], both by the Glimm and the front-tracking scheme. We also quote [8] for a global existence result of solutions, by compensated compactness, to the analogue of (1) in Eulerian coordinates.…”

Section: Introductionmentioning

confidence: 99%

Solutions for a hyperbolic model of multi-phase flow

Amadori

Corli

2013

ESAIM: Proc.

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We discuss a model for the flow of an inviscid fluid admitting liquid and vapor phases, as well as a mixture of them. The flow is modeled in one spatial dimension; the state variables are the specific volume, the velocity and the mass density fraction λ of vapor in the fluid. The equation governing the time evolution of λ contains a source term, which enables metastable states and drives the fluid towards stable pure phases.We first discuss, for the homogeneous system, the BV stability of Riemann solutions generated by large initial data and check the validity of several sufficient conditions that are known in the literature.Then, we review some recent results about the existence of solutions, which are globally defined in time, for λ close either to 0 or to 1 (corresponding to almost pure phases). These solutions possibly contain large shocks. Finally, in the relaxation limit, solutions are proved to satisfy a reduced system and the related entropy condition.Résumé. On discute un modèle pour l'écoulement d'un fluide non visqueux admettant phases liquides et de vapeur, ainsi qu'un mélange d'entre eux. L'écoulement est modélisé dans une dimension spatiale; les variables d'état sont le volume spécifique, la vitesse et la fraction de densité de masse λ de la vapeur dans le liquide. L'équation régissant l'évolution temporelle de λ contient un terme de source, ce qui permet desétats métastables et conduit le fluide vers de phases stables pures.Nous discutons d'abord, pour le système homogène, la stabilité BV des solutions de Riemann générés par des grandes données initiales et vérifions la validité de plusieurs conditions suffisantes qui sont connues dans la littérature.Ensuite, nous passons en revue quelques résultats récents sur l'existence de solutions, qui sont definies pour tous les temps, pour λ soit près de 0 ou de 1 (correspondantà des phases presque pures). Ces solutions sont susceptibles de contenir des grands chocs. Enfin, dans la limite de la relaxation, les solutions sont prouvèes satisfaire un système réduit et la condition d'entropie.

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“…The drift-flux model has also been studied in the context of flow in networks [3]. Finally, we also would like to mention some works on a related multicomponent gas model without viscosity term where discrete algorithms are used to rigorously demonstrate convergence towards a weak solution [14,15]. A similar type of model with focus on phase transition is studied in [1,2].…”

Section: Introductionmentioning

confidence: 99%

Global weak solutions for a compressible gas-liquid model with well-formation interaction

Evje

2011

Journal of Differential Equations

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Front tracking for a model of immiscible gas flow with large data

Cited by 8 publications

References 25 publications

Global weak solutions for a model of two-phase flow with a single interface

Global weak solutions for a model of two-phase flow with a single interface

Solutions for a hyperbolic model of multi-phase flow

Global weak solutions for a compressible gas-liquid model with well-formation interaction

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