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

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

doi:10.1002/fld.3752

Cited by 13 publications

(14 citation statements)

References 35 publications

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“…Readers who are interested in other possible approaches for closure models are referred to the following journal papers, Section 3.11 of [3], Sections 6.2 and 6.3 of [33] and [34,6,7,[35][36][37][38][39][40][41][42][43]. Also of note is [36], where the author considers a thermodynamic and dynamic subgrid closure model for a two-material cell, and the recent paper by B. Rider and co-authors, which discusses the use of limiters to combine a Tipton-like model and the equal compressibility model, [44].…”

Section: Results Of Comprehensive Testing Of the New Model For One-anmentioning

confidence: 99%

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics

Barlow¹,

Hill

Shashkov

2014

Journal of Computational Physics

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A systematic description of the new interface-aware sub-scale-dynamics (IA-SSD) closure model for the Lagrangian stage of multimaterial arbitrary Lagrangian-Eulerian methods is presented. The IA-SSD closure model consists of two stages. During the first, bulk, stage, the well known equal compressibility model is used. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is utilized, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and is limited using physically justified constraints: positivity of volume, positivity of internal energy and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. The algorithm guarantees the positivity of the material volume and internal energy as well as the smooth relaxation of the pressure-this allows a significant increase in the robustness of the overall algorithm. The results of comprehensive testing of the new model have been presented for one-and two-dimensional multimaterial Lagrangian hydrodynamics along with representative results for 2D multimaterial arbitrary Lagrangian-Eulerian (ALE) calculations. The numerical tests have shown that in most cases the new IA-SSD closure model produces better results compared to the well known Tipton's closure model.

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Section: Results Of Comprehensive Testing Of the New Model For One-anmentioning

confidence: 99%

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics

Barlow¹,

Hill

Shashkov

2014

Journal of Computational Physics

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“…Section 5). The inaccuracies visible between the two middle waves on the velocity plots can be related to the inaccuracies visible in the shock-tube plots of [29]. They are believed to be caused by the non-conservative terms.…”

Section: Shock Tubementioning

confidence: 98%

“…These waves are entropy and volume-fraction waves (cf. [29] for the six-equation model, [8] for the five-equation model and [9] for the four-equation model).…”

Section: Characteristic Wave-structure Of the Modelsmentioning

confidence: 99%

A method for simulating two-phase pipe flow with real equations of state

Hammer

Morin

2014

Computers & Fluids

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Common two-fluid models for pipe flow assume local non-equilibrium regarding phase transfer. To solve the two-fluid models together with accurate equations of state for real fluids will in most cases require mechanical, thermal and chemical equilibrium between the phases. The reason is that reference equations of state for real substances typically describe full thermodynamic equilibrium. In this paper, we present a method for numerically solving an equilibrium model analysed by Morin and Flåtten in the paper A two-fluid four-equation model with instantaneous thermodynamical equilibrium, 2013.The four-equation two-fluid model with instantaneous thermodynamical equilibrium is derived from a five-equation two-fluid model with instantaneous thermal equilibrium. The four-equation model has one mass equation common for both phases, but allows for separate phasic velocities. For comparison, the five-equation two-fluid model is numerically solved, using source terms to impose thermodynamical equilibrium. These source terms are solved using a fractional-step method.We employ the highly accurate Span-Wagner equation of state for CO 2 , and use the simple and robust FORCE scheme with MUSCL slope limiting. We demonstrate that second-order accuracy may be achieved for smooth solutions, whereas the first-order version of the scheme even allows for a robust transition to single-phase flow, also in the presence of instantaneous phase equilibrium.

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“…In complicated conditions in which the second phase changes the hydrodynamic behavior of the flow, such as gas bubbles rising in a liquid, the multiphase nature of the flow cannot be ignored. Therefore, recent studies often consider the domains of both phases together (Štrubelj and Tiselj, 2011; Shang et al , 2013; Jasak, 1996; Morin et al , 2013; Yu et al , 2015).…”

Section: Introductionmentioning

confidence: 99%

FGA-MMF method for the simulation of two-phase flows

Behrangi

Banihashemi

Namin

et al. 2018

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Purpose This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model. Design/methodology/approach The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used. Findings This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results. Research limitations/implications The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow. Originality/value The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

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

Cited by 13 publications

References 35 publications

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics

A method for simulating two-phase pipe flow with real equations of state

FGA-MMF method for the simulation of two-phase flows

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