A MUSTA Scheme for a Nonconservative Two-Fluid Model

Munkejord, Svend Tollak; Evje, Steinar; Flåtten, Tore

doi:10.1137/080719273

Cited by 40 publications

(100 citation statements)

References 48 publications

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“…As was proved in [27], the equations (2.10)-(2.11) are mathematically equivalent to (2.5)-(2.6), and may be more suitable for the construction of numerical schemes. Note that the source terms are affected by this transformation, so that in general:…”

Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

“…Furthermore, the presence of the ∂ t α-terms in the energy equations presents an inconvenience for the construction of numerical methods, see for instance [27,30]. We wish to obtain a formulation of the energy equations that involves temporal derivatives only in the variable E k .…”

Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

“…We wish to obtain a formulation of the energy equations that involves temporal derivatives only in the variable E k . Such a formulation was obtained in [27]:…”

Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

“…This would generally lead to a lack of existence of stable mathematical solutions to the model, as well as loss of stability of our numerical methods. To avoid such a highly undesirable situation, we follow in the footsteps of much of the existing literature [6,7,27,30] and choose the regularization term introduced by Stuhmiller [37]: …”

Section: The Interface Pressure Termmentioning

confidence: 99%

“…Our paper is organized as follows: in Section 2, we detail the models we will be working with. In Section 2.1, we restate the formulation of the six-equation two-fluid model presented in [27]. Here a mathematical transformation allows us to express the model without non-conservative time derivatives in the energy equations.…”

Section: Introductionmentioning

confidence: 99%

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On the effect of temperature and velocity relaxation in two-phase flow models

Ferrer¹,

Flåtten²,

Munkejord³

2011

ESAIM: M2AN

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Abstract.We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This allows us to directly prove a subcharacteristic condition; each level of equilibrium assumption imposed reduces the propagation velocity of pressure waves. Furthermore, we show that each relaxation procedure reduces the mixture sound velocity with a factor that is independent of whether the other relaxation procedure has already been performed. Numerical simulations indicate that thermal relaxation in the two-fluid model has negligible impact on mass transport dynamics. However, the velocity difference of sonic propagation in the thermally relaxed and unrelaxed two-fluid models may significantly affect practical simulations.Mathematics Subject Classification. 76T10, 65M08, 35L60.

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Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

“…We wish to obtain a formulation of the energy equations that involves temporal derivatives only in the variable E k . Such a formulation was obtained in [27]:…”

Section: The Six-equation Two-fluid Modelmentioning

confidence: 99%

Section: The Interface Pressure Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the effect of temperature and velocity relaxation in two-phase flow models

Ferrer¹,

Flåtten²,

Munkejord³

2011

ESAIM: M2AN

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A well‐balanced FV scheme for compound channels with complex geometry and movable bed

Minatti

2015

Water Resources Research

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This work focuses on the implementation of a Shallow Water-Exner model for compound natural channels with complex geometry and movable bed within the finite volume framework. The model is devised for compound channels modeling: cross-section overbanks are treated with fixed bed conditions, while the main channel is left free to modify its morphology. A capacitive approach is used for bed load transport modeling, in which the solid flow rates are estimated with bed load transport formulas. The model equations pose some numerical issues in the case of natural channels, where bed load transport may occur for both subcritical and supercritical flows and geometry varies in space. An explicit path-conservative scheme, designed to overcome all these issues, is presented in the paper. The scheme solves liquid and solid phases dynamics in a coupled manner, in order to correctly model near critical currents/channel interactions and is well-balanced, that is able to properly reproduce steady states. The Roe and Osher Riemann solvers are implemented, so as to take into account the spatial geometry variations of natural channels. The scheme reaches up to second-order accuracy. Validation is performed with fixed and movable bed test cases whose analytical solution is known, and with flume experimental data. An application of the model to a real case study is also shown.

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A Roe scheme for a compressible six‐equation two‐fluid model

Morin

Flåtten

Munkejord

2012

Numerical Methods in Fluids

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SUMMARYWe derive a partially analytical Roe scheme with wave limiters for the compressible six‐equation two‐fluid model. Specifically, we derive the Roe averages for the relevant variables. First, the fluxes are split into convective and pressure parts. Then, independent Roe conditions are stated for these two parts. These conditions are successively reduced while defining acceptable Roe averages. For the convective part, all the averages are analytical. For the pressure part, most of the averages are analytical, whereas the remaining averages are dependent on the thermodynamic equation of state. This gives a large flexibility to the scheme with respect to the choice of equation of state. Furthermore, this model contains nonconservative terms. They are a challenge to handle right, and it is not the object of this paper to discuss this issue. However, the Roe averages presented in this paper are fully independent from how those terms are handled, which makes this framework compatible with any treatment of nonconservative terms. Finally, we point out that the eigenspace of this model may collapse, making the Roe scheme inapplicable. This is called resonance. We propose a fix to handle this particular case. Numerical tests show that the scheme performs well. Copyright © 2012 John Wiley & Sons, Ltd.

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A MUSTA Scheme for a Nonconservative Two-Fluid Model

Cited by 40 publications

References 48 publications

On the effect of temperature and velocity relaxation in two-phase flow models

On the effect of temperature and velocity relaxation in two-phase flow models

A well‐balanced FV scheme for compound channels with complex geometry and movable bed

A Roe scheme for a compressible six‐equation two‐fluid model

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