An Approximate Linearized Riemann Solver for a Two-Fluid Model

Toumi, I.; Kumbaro, Anela

doi:10.1006/jcph.1996.0060

Cited by 133 publications

(82 citation statements)

References 10 publications

(15 reference statements)

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“…This ill-posedness is not only an intriguing outcome, but also a major obstacle in the design of numerical methods. Hyperbolicity is also lost in two-pressure models if one of the phases is assumed incompressible [14,15,19,22]. 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 000000000000000000000000000 The inevitable nonconservative form of the average model poses a theoretical difficulty since many problems of interest involve shock waves, whose definition assumes conservation.…”

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confidence: 99%

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Compressible two-phase flows by central and upwind schemes

et al. 2004

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Abstract. This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed.Mathematics Subject Classification. 35L65, 65M06, 76N15, 76T99.

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confidence: 99%

“…Asymptotic shock jump conditions valid for weak shocks were given in [19]. Numerical methods were derived in [19,22]. However, these results cannot be extended to general nonconservative models.…”

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confidence: 99%

Compressible two-phase flows by central and upwind schemes

et al. 2004

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“…Nevertheless considerable improvements in the application of finite volumes to two phase flows have been achieved ( [50], [56], [25], [15] [41]). For example in [59], the authors consider the case of a small difference between the liquid and gas velocities, and in [18], the case of a small ratio of gas to liquid densities, and in both cases these hypothesis are used to introduce some interesting simplifications. But only few works have been presented in the case of multidimensional twofluid problems in high non-equilibrium configurations ( [26], [1]).…”

Section: Introductionmentioning

confidence: 99%

A sign matrix based scheme for non-homogeneous PDE’s with an analysis of the convergence stagnation phenomenon

Sahmim¹,

Benkhaldoun

Alcrudo

2007

Journal of Computational Physics

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To cite this version:Slah Sahmim, Fayssal Benkhaldoun, Francisco Alcrudo. A sign matrix based scheme for nonhomogeneous PDE's with an analysis of the convergence stagnation phenomenon. Journal of Computational Physics, Elsevier, 2007, 226 (2) AbstractThis work is devoted to the analysis of a finite volume method recently proposed for the numerical computation of a class of non homogenous systems of partial differencial equations of interest in fluid dynamics. The stability analysis of the proposed scheme leads to the introduction of the sign matrix of the flux jacobian. It appears that this formulation is equivalent to the VFRoe scheme introduced in the homogeneous case and has a natural extension here to non homogeneous systems. Comparative numerical experiments for the Shallow Water and Euler equations with source terms, and a model problem of two phase flow (Ransom faucet) are presented to validate the scheme. The numerical results present a convergence stagnation phenomenon for certain forms of the source term, notably when it is singular. Convergence stagnation has been also shown in the past for other numerical schemes. This issue is addressed in a specific section where an explanation is given with the help of a linear model equation, and a cure is demonstrated.

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“…Toumi and Kumbaro [31] presented a Roe scheme for such a model including a virtual mass force term. A generalization allowing for a pressure-modification term at the gas-liquid interface was presented in [29].…”

Section: Introductionmentioning

confidence: 99%

The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

Flåtten¹,

Munkejord²

2006

ESAIM: M2AN

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Abstract.We construct a Roe-type numerical scheme for approximating the solutions of a driftflux two-phase flow model. The model incorporates a set of highly complex closure laws, and the fluxes are generally not algebraic functions of the conserved variables. Hence, the classical approach of constructing a Roe solver by means of parameter vectors is unfeasible. Alternative approaches for analytically constructing the Roe solver are discussed, and a formulation of the Roe solver valid for general closure laws is derived. In particular, a fully analytical Roe matrix is obtained for the special case of the Zuber-Findlay law describing bubbly flows. First and second-order accurate versions of the scheme are demonstrated by numerical examples.Mathematics Subject Classification. 35L65, 76M12, 76T10.

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An Approximate Linearized Riemann Solver for a Two-Fluid Model

Cited by 133 publications

References 10 publications

Compressible two-phase flows by central and upwind schemes

Compressible two-phase flows by central and upwind schemes

A sign matrix based scheme for non-homogeneous PDE’s with an analysis of the convergence stagnation phenomenon

The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model

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