An exact Riemann solver for compressible two-phase flow models containing non-conservative products

Deledicque, Vincent; Papalexandris, Miltiadis

doi:10.1016/j.jcp.2006.07.025

Cited by 76 publications

(83 citation statements)

References 27 publications

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“…This means that source and non-conservative product are evaluated point-wise at each node, see [17]. We then insert (15) and (16) into (14) and obtain the following final fixed-point iteration scheme in order to evolve the reconstruction polynomials w h in time within the predictor step of our one-step scheme:…”

Section: The Local Space-time Galerkin Predictormentioning

confidence: 99%

See 1 more Smart Citation

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Dumbser

Hidalgo

Castro

et al. 2010

Computer Methods in Applied Mechanics and Engineering

143

144

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Section: The Local Space-time Galerkin Predictormentioning

confidence: 99%

“…For these shock tube problems, exact reference solutions are available in the literature [3,34,15]. To our knowledge, the first exact Riemann solver for the compressible Baer-Nunziato equations was published by Andrianov and Warnecke [3].…”

Section: Shock Tube Problems In Multiple Space Dimensionsmentioning

confidence: 99%

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Dumbser

Hidalgo

Castro

et al. 2010

Computer Methods in Applied Mechanics and Engineering

143

144

View full text Add to dashboard Cite

“…On the contrary, a direct iterative approach is used in [40] leading to exact solutions of the Riemann problem for any initial left and right states. See also the recent work of Deledicque & Papalexandris [15]. Another direct approach to construct theoretical solutions is proposed in Castro & Toro [9].…”

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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An exact Riemann solver for compressible two-phase flow models containing non-conservative products

Cited by 76 publications

References 27 publications

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

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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