The Riemann problem for the Baer–Nunziato two-phase flow model

Andrianov, Nikolai; Warnecke, Gerald

doi:10.1016/j.jcp.2003.10.006

Cited by 170 publications

(171 citation statements)

References 17 publications

(42 reference statements)

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“…The satisfaction of the Liu entropy condition needs to be verified for each Hugoniot locus, that is between 0 and Φ m , Φ 0 and Φ * 0 , and Φ * ∞ and Φ ∞ . In our case, the discontinuities z 1 …”

mentioning

confidence: 81%

“…We utilize here a semi-analytical approach, by which we understand an analytical solution that involves the numerical solution of ordinary differential equations and non-linear systems of equations. Semi-analytical methods have been applied to systems of conservation laws in various applications in numerous works including [1,27,28,40,42,43,49]. In [27], a general algorithm for the solution of Riemann problems is proposed and applied to three-phase flow in porous media (see also [28]).…”

Section: Related Workmentioning

confidence: 99%

“…Also, for the solution of a Riemann problem, elementary waves are connected by the intersection of the 1-wave starting at the left state with the 2-wave starting at the right state, rather than by the optimization of wave lengths, where one starts in the left state and fits the concatenated elementary waves to the prescribed right state. In [1], two sets of Euler equations describe two-phase reactive granular materials. The system is non-strictly hyperbolic and non-conservative.…”

Section: Related Workmentioning

confidence: 99%

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On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

Berres

Bürger²

2007

Z Angew Math Mech

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This paper analyses a continuum model of the sedimentation of polydisperse suspensions, where the volume concentrations of the solids species are the sought unknowns. This leads to systems of conservation laws which are non-genuinely nonlinear ("non-convex") in the sense that they are only piecewise genuinely nonlinear. The solution of a Riemann problem is represented as a concatenation of elementary waves, where the linear degeneracy requires using the Liu entropy condition. After a general description of the composition of elementary waves, an algorithm for the computational construction is given. The solution of the Riemann problem is then utilized as a problem-adapted building block of a front tracking method. For the model of bidisperse suspensions, Riemann problems are classified by the location of the left and right state in the phase space of unknown variables. The front tracking method is applied to solve the initial value problem of a first-order hyperbolic 2 × 2 system of conservation laws describing the settling of a bidisperse suspension. The solution obtained by front tracking is compared with results obtained by an experiment and a finite difference scheme.

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confidence: 81%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

Berres

Bürger²

2007

Z Angew Math Mech

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“…It was first proposed in Baer & Nunziato [4] and has since aroused more and more interest, see for instance Embid & Baer [7], Stewart & Wendroff [13], Abgrall & Saurel [11], Gallouët, Hérard & Seguin [8], Andrianov & Warnecke [3], Karni et al [9] Schwendeman, Wahle & Kapila [12], Munkejord [10], Tokareva & Toro [14], Ambroso, Chalons, Coquel & Galié [1], Ambroso, Chalons & Raviart [2], and the references therein. One of the main features of this model is that it is hyperbolic, at least in the context of subsonic flows.…”

Section: Introductionmentioning

confidence: 99%

“…This property will be used in the numerical strategy. Numerous papers are devoted to the numerical study of two-fluid two-pressure models, see again for instance [8], [3], [9], [12], [10], [14], [1], [2] and the references therein. Many of the proposed methods are based on time-explicit, exact or approximate, Godunov-type methods (Roe or Roe-like scheme, HLL or HLLC scheme...).…”

Section: Introductionmentioning

confidence: 99%

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

Chalons

Coquel

Kokh

et al. 2011

Finite Volumes for Complex Applications VI Problems &Amp; Perspectives

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A Riemann solver and upwind methods for a two-phase flow model in non-conservative form

Castro

Toro

2005

Int. J. Numer. Meth. Fluids

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SUMMARYWe present a theoretical solution for the Riemann problem for the ÿve-equation two-phase non-conservative model of Saurel and Abgrall. This solution is then utilized in the construction of upwind nonconservative methods to solve the general initial-boundary value problem for the two-phase ow model in non-conservative form. The basic upwind scheme constructed is the non-conservative analogue of the Godunov ÿrst-order upwind method. Second-order methods in space and time are then constructed via the MUSCL and ADER approaches. The methods are systematically assessed via a series of test problems with theoretical solutions.

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The Riemann problem for the Baer–Nunziato two-phase flow model

Cited by 170 publications

References 17 publications

On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

On Riemann problems and front tracking for a model of sedimentation of polydisperse suspensions

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

A Riemann solver and upwind methods for a two-phase flow model in non-conservative form

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