Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver

Ndjinga, Michaël; Kumbaro, Anela; Vuyst, Florian De; Laurent-Gengoux, Pascal

doi:10.1016/j.nucengdes.2007.11.014

Cited by 10 publications

(3 citation statements)

References 4 publications

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“…Assuming there is a total of N fields, we define the unknown vector of the multifield model as (14) This vector is convenient for writing the system (12)- (13) in quasilinear form, and deducing its Jacobian matrix A(n ) and its spectral properties. Consider an orthonormal basis n = (n 1 , n 2 , n 3 ) of the three dimensional space » 3 , we can write the system in the following quasilinear form (15) We introduce the 3N-components velocity vector (16) the N × N matrices: and the 3N × N rectangular matrix…”

Section: The Jacobian Matrix Of the Isentropic Multifield Modelmentioning

confidence: 99%

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Influence of Interfacial Pressure Term on the Hyperbolicity of a General Multifluid Model

Kumbaro

Ndjinga

2011

The Journal of Computational Multiphase Flows

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The multifield model like its counterpart, the two-fluid model, generally fails to be hyperbolic in its basic formulation. However, interfacial forces such as the interfacial pressure term and the virtual mass force, bringing new differential terms to the system, can change the analysis and make the problem hyperbolic. The aim of this paper is to define how the interfacial pressure default force affects the hyperbolicity of a general multifield model, and consequently, its inherent numerical stability. We characterize the location of the non hyperbolic regions and propose a closure for the interfacial pressure that makes the system hyperbolic in physically relevant regions.

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Section: The Jacobian Matrix Of the Isentropic Multifield Modelmentioning

confidence: 99%

“…Two test cases are considered. All the computations are realized with OVAP code using a Roe generalized solver [14], [15]. The first test is the Ransom faucet flow problem [16] applied to the three-field model, two fields for the vapor phase, and one field for the continuous liquid.…”

Section: Numerical Illustrationmentioning

confidence: 99%

Influence of Interfacial Pressure Term on the Hyperbolicity of a General Multifluid Model

Kumbaro

Ndjinga

2011

The Journal of Computational Multiphase Flows

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“…We began the exposition by the so‐called six equations model . Despite recent progress [2, 3, 12, 15–17, 44, 77–79], this system still represents some major difficulties for the numerical solution. Namely, the advection operator may be non‐hyperbolic and contains non‐conservative terms to be defined in some sense for discontinuous solutions.…”

Section: Perspectives and Conclusionmentioning

confidence: 99%

Velocity and Energy Relaxation in Two-Phase Flows

Meyapin

Dutykh

Gisclon

2010

Studies in Applied Mathematics

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In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ish75,Rov06]. This model assumes each phase to possess its own velocity and energy variables. Despite recent advances, the six equations model remains computationally expensive for many practical applications. Moreover, its advection operator may be non-hyperbolic which poses additional theoretical difficulties to construct robust numerical schemes [GKC01]. In order to simplify this system, we complete momentum and energy conservation equations by relaxation terms. When relaxation characteristic time tends to zero, velocities and energies are constrained to tend to common values for both phases. As a result, we obtain a simple two-phase model which was recently proposed for simulation of violent aerated flows [DDG10]. The preservation of invariant regions and incompressible limit of the simplified model are also discussed. Finally, several numerical results are presented.

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Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function

Gallardo

Castro

Marquina

2021

SEMA SIMAI Springer Series

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Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver

Cited by 10 publications

References 4 publications

Influence of Interfacial Pressure Term on the Hyperbolicity of a General Multifluid Model

Influence of Interfacial Pressure Term on the Hyperbolicity of a General Multifluid Model

Velocity and Energy Relaxation in Two-Phase Flows

Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function

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