Mathematical analysis of a two-phase continuum mixture theory

Embid, Pedro; Baer, M.R.

doi:10.1007/bf01129333

Cited by 104 publications

(102 citation statements)

References 9 publications

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“…A mathematical analysis of the structure of the governing equations, including a description of the wave fields of the hyperbolic system, its Riemann invariants and simple wave solutions, was described by Embid and Baer [9]. In this paper, a degeneracy of the hyperbolic system, which occurs when the relative flow between phases becomes sonic, is identified.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent paper [15], Andrianov and Warnecke revisited the Riemann problem for the model. Using jump conditions across the solid contact, derived in [9], they explicitly construct inverse exact solutions corresponding to prescribed states on either side of the solid contact. We re-derive the jump conditions across the solid contact using a thin layer analysis, which reveals additional information that is used in the handling of the nozzling terms in our numerical method as mentioned above.…”

Section: Introductionmentioning

confidence: 99%

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The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

Schwendeman

Wahle

Kapila

2006

Journal of Computational Physics

172

188

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

Schwendeman

Wahle

Kapila

2006

Journal of Computational Physics

172

188

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“…It was first proposed in Baer & Nunziato [6] for granular energetic combustible materials embedded in gaseous combustion products. Its mathematical properties were first comprehensively studied in Embid & Baer [16]. Then, the model (and related ones, see among others Stewart & Wendroff [41], Abgrall & Saurel [37], [38]...) has gained interest for the modelling and computation of two phase flows.…”

Section: Introductionmentioning

confidence: 99%

A Godunov-type method for the seven-equation model of compressible two-phase flow

2012

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We are interested in the numerical approximation of the solutions of the compressible seven-equation two-phase flow model. We propose a numerical srategy based on the derivation of a simple, accurate and explicit approximate Riemann solver. The source terms associated with the external forces and the drag force are included in the definition of the Riemann problem, and thus receive an upwind treatment. The objective is to try to preserve, at the numerical level, the asymptotic property of the solutions of the model to behave like the solutions of a drift-flux model with an algebraic closure law when the source terms are stiff. Numerical simulations and comparisons with other strategies are proposed.

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“…The Riemann problem eigenstructure has been studied extensively in the literature [9,10,11]. The gas and solid phases couple through the solid contact wave; elsewhere, φ s remains uniform.…”

Section: Two-phase Riemann Problemmentioning

confidence: 99%

Application of a generalized multiphase Riemann solver to a finite-volume method with nozzling sources

Crochet¹,

Gonthier²,

Tohline³

2012

AIP Conference Proceedings

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Abstract. Hyperbolic model equations governing the flow of solid particles within a gas contain nonconservative nozzling sources that can introduce numerical artifacts in commonly used finite-volume methods. Modifications to these techniques have been recently proposed, involving both exact and approximate solutions to the two-phase Riemann problem with gamma-law equations of state. The present work extends this approach to solid phases characterized by general equations of state. An exact Riemann solver is formulated within the context of the second-order, semidiscrete, cell-centered Kurganov-Tadmor (KT) finite-volume method. The resulting scheme may be used to predict wave structures and energetics for 1D piston-impact of mixtures having large initial spatial variations in volume fraction, where the physical effects of nozzling are more significant. It is shown that neglecting a class of wave configurations arising in the Riemann problem, as practiced in the literature, can lead to nonphysical solutions. A framework for the analysis of Riemann problems including an arbitrary number of solid phases is also discussed.

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Mathematical analysis of a two-phase continuum mixture theory

Cited by 104 publications

References 9 publications

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

A Godunov-type method for the seven-equation model of compressible two-phase flow

Application of a generalized multiphase Riemann solver to a finite-volume method with nozzling sources

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