Numerical Resolution of CO<sub>2</sub>Transport Dynamics

Morin, Alexandre; Aursand, Peder; Flåtten, Tore; Munkejord, Svend Tollak

doi:10.1137/1.9781611973303.13

Cited by 8 publications

(14 citation statements)

References 8 publications

(21 reference statements)

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“…In the LTS Roe scheme for the homogeneous equilibrium model (10), we use the Roe matrix described by Morin et al [18]. The Roe matrix is diagonalized numerically.…”

Section: Two-phase Flow Modelmentioning

confidence: 99%

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Lindqvist¹,

Lund²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. We consider a large time step (LTS) Roe scheme, originally suggested by LeVeque [Comm. Pure Appl. Math., 37 (1984), pp. 463-477] which has attained increased popularity in recent years. The scheme is based on a wave formulation of the ordinary Roe scheme, and the assumption that waves interact linearly. This assumption lets us propagate waves over more than one cell, thereby violating the ordinary CFL condition requiring the Courant number to be less than one. The LTS Roe scheme is applied to a two-phase flow model with phase transfer, modelled using the stiffened-gas equation of state. Results from various test cases show that the LTS Roe scheme with moderate Courant numbers is significantly more efficient than the ordinary Roe scheme, measured by an error-to-runtime ratio. The optimal Courant number is mainly a trade-off between reduced runtime due to fewer time steps, and increased error due to the assumption of linear wave interactions.

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“…In the LTS Roe scheme for the homogeneous equilibrium model (10), we use the Roe matrix described by Morin et al [18]. The Roe matrix is diagonalized numerically.…”

Section: Two-phase Flow Modelmentioning

confidence: 99%

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Lindqvist¹,

Lund²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…A Roe solver is often more suitable for cases where discontinuities are dominant. Morin et al (2009) Table 2 shows the computational time spent for a range of different grid sizes, to give an impression of how the computational cost for the two methods are related. As seen in this table, the time spent is rather similar for the same grid size, although the ASY1 scheme seems to have slightly better performance.…”

Section: Numerical Resultsmentioning

confidence: 99%

Splitting methods for relaxation two-phase flow models

Lund

Aursand

2013

IJMATEI

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A model for two-phase pipeline flow is presented, with evaporation and condensation modelled using a relaxation source term based on statistical rate theory. The model is solved numerically using a Godunov splitting scheme, making it possible to solve the hyperbolic fluid-mechanic equation system and the relaxation term separately. The hyperbolic equation system is solved using the multi-stage (MUSTA) finite volume scheme. The stiff relaxation term is solved using two approaches: One based on the Backward Euler method, and one using a time-asymptotic scheme. The results from these two methods are presented and compared for a CO 2 pipeline depressurization case.

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“…We again consider a mixture of N immiscible fluids, each following its separate stiffened-gas equation of state (9).…”

Section: Thermal and Mechanical Equilibriummentioning

confidence: 99%

“…This problem is considered in [2,9]. Analogously to section 3, we define a hierarchy of classes of solutions below.…”

Section: Thermal and Mechanical Equilibriummentioning

confidence: 99%

See 1 more Smart Citation

On Solutions to Equilibrium Problems for Systems of Stiffened Gases

Flåtten¹,

Morin²,

Munkejord³

2011

SIAM J. Appl. Math.

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Abstract.We consider an isolated system of N immiscible fluids, each following a stiffened-gas equation of state. We consider the problem of calculating equilibrium states from the conserved fluid-mechanical properties, i.e., the partial densities and internal energies. We consider two cases; in each case mechanical equilibrium is assumed, but the fluids may or may not be in thermal equilibrium. For both cases, we address the issues of existence, uniqueness, and physical validity of equilibrium solutions. We derive necessary and sufficient conditions for physically valid solutions to exist, and prove that such solutions are unique. We show that for both cases, physically valid solutions can be expressed as the root of a monotonic function in one variable. We then formulate efficient algorithms which unconditionally guarantee global and quadratic convergence toward the physically valid solution.

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Numerical Resolution of CO₂Transport Dynamics

Cited by 8 publications

References 8 publications

A Large Time Step Roe Scheme Applied to Two-Phase Flow

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Splitting methods for relaxation two-phase flow models

On Solutions to Equilibrium Problems for Systems of Stiffened Gases

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Numerical Resolution of CO2Transport Dynamics

Cited by 8 publications

References 8 publications

A Large Time Step Roe Scheme Applied to Two-Phase Flow

A Large Time Step Roe Scheme Applied to Two-Phase Flow

Splitting methods for relaxation two-phase flow models

On Solutions to Equilibrium Problems for Systems of Stiffened Gases

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Numerical Resolution of CO₂Transport Dynamics