A study on the numerical stability of the two-fluid model near ill-posedness

Liao, Jun; Mei, Renwei; Klausner, James F.

doi:10.1016/j.ijmultiphaseflow.2008.02.010

Cited by 37 publications

(40 citation statements)

References 20 publications

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“…The model is similar to the models used by Liao et al [6] and Fullmer et al [8] . A difference worth noting is the hydrostatic pressure term p av, β in the momentum Eq.…”

Section: Two-fluid Modelmentioning

confidence: 99%

“…The two-fluid model, however, is not unconditionally stable. When the slip velocity, the velocity difference between the two phases, becomes too large the model becomes ill-posed [6] . This is a known problem of the two-fluid model.…”

Section: Definition 3 (Dispersion)mentioning

confidence: 99%

“…The artificial diffusion introduced by first order methods effectively regularizes the differential equations through damping non-physical instabilities associated with ill-posedness [9] . However, a major disadvantage of first order methods is that any physical instabilities will also be damped due to excessive numerical diffusion [6] . As a result, very fine meshes are required (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Fullmer et al [9] show improved accuracy of a second order method over a first order method, although the second order method leads to non-monotone results. In all cases, these high-order upwind schemes can have unfavourable stability properties [6] , giving a numerical growth rate which is quite different from the physical growth rate of instabilities. Consequently, high-order methods are not yet commonly applied for solving the two-fluid model equations.…”

Section: Introductionmentioning

confidence: 99%

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Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

et al. 2017

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a b s t r a c tOne-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time Discontinuous Galerkin (DG) Finite Element method with h -adaptivity to improve the efficiency of one-dimensional multiphase flow simulations. For smooth initial boundary value problems we show that the DG method converges with the theoretical rate and that the growth rate and phase shift of small, harmonic perturbations exhibit superconvergence. We employ two techniques to accurately and efficiently represent discontinuities. Firstly artificial diffusion in the neighbourhood of a discontinuity suppresses spurious oscillations. Secondly local mesh refinement allows for a sharper representation of the discontinuity while keeping the amount of work required to obtain a solution relatively low. The proposed DG method is shown to be superior to FV.

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“…The model is similar to the models used by Liao et al [6] and Fullmer et al [8] . A difference worth noting is the hydrostatic pressure term p av, β in the momentum Eq.…”

Section: Two-fluid Modelmentioning

confidence: 99%

Section: Definition 3 (Dispersion)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

et al. 2017

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“…However, due to the importance and influence of the mesh size and the discretization schemes for the numerical solution of the 1D Two-Fluid Model, a more rigorous approach is to perform a linear stability analysis in the discretized equations of the model. This methodology, labeled von Neumann analysis, has been recently used in literature (Liao et al, 2008;Issa & Galleni, 2015;Sanderse et al, 2017). Nevertheless, due to nonlinear effects and to the intricacies of the numerical methodologies that are often used, the ultimate test of hyperbolicity (and, of course, well-posedness) is to perform the classical mesh convergence test for key parameters of the solution of the 1D Two-…”

Section: The Stability-hyperbolicity Problem Of the 1d Two-fluid Modelmentioning

confidence: 99%

Optimization of the Interfacial Shear Stress and Assessment of Closure Relations for Horizontal Viscous Oil-Gas Flows in the Stratified and Slug Regimes

PASQUALETTE¹

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Marcelo de Alencastro PasqualetteThe author graduated in Mechanical Engineering from the Federal University of Rio de Janeiro in 2015 with the cum laude honor. In the former, the author received a PIBIC-CNPq scholarship for two years and an ANP PRH-37 scholarship for other two years. He has been working at the SINTEF Institute of Brazil for four years in the areas of multiphase flow, thermodynamics and flow assurance. He has eight complete papers published at conferences and two peer-reviewed articles published at journals.

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Energy‐consistent formulation of the pressure‐free two‐fluid model

Buist

Sanderse

Dubinkina

et al. 2023

Numerical Methods in Fluids

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The pressure‐free two‐fluid model (PFTFM) is a recent reformulation of the one‐dimensional two‐fluid model (TFM) for stratified incompressible flow in ducts (including pipes and channels), in which the pressure is eliminated through intricate use of the volume constraint. The disadvantage of the PFTFM was that the volumetric flow rate had to be specified as an input, even though it is an unknown quantity in case of periodic boundary conditions. In this work, we derive an expression for the volumetric flow rate that is based on the demand for energy (and momentum) conservation. This leads to PFTFM solutions that match those of the TFM, justifying the validity and necessity of the derived choice of volumetric flow rate. Furthermore, we extend an energy‐conserving spatial discretization of the TFM, in the form of a finite volume scheme, to the PFTFM. We propose a discretization of the volumetric flow rate that yields discrete momentum and energy conservation. The discretization is extended with an energy‐conserving discretization of the source terms related to gravity acting in the streamwise direction. Our numerical experiments confirm that the discrete energy is conserved for different problem settings, including sloshing in an inclined closed tank, and a traveling wave in a periodic domain. The PFTFM solutions and the volumetric flow rates match the TFM solutions, with reduced computation time, and with exact momentum and energy conservation.

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A study on the numerical stability of the two-fluid model near ill-posedness

Cited by 37 publications

References 20 publications

Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

Efficient simulation of one-dimensional two-phase flow with a high-order h-adaptive space-time Discontinuous Galerkin method

Optimization of the Interfacial Shear Stress and Assessment of Closure Relations for Horizontal Viscous Oil-Gas Flows in the Stratified and Slug Regimes

Energy‐consistent formulation of the pressure‐free two‐fluid model

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