Generalized formulations for the Rhie–Chow interpolation

Zhang, Sijun; Zhao, Xiang; Bayyuk, Sami

doi:10.1016/j.jcp.2013.11.006

Cited by 67 publications

(43 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To the best of the authors' knowledge, the first study that systematically addressed this issue was that of Rhie and Chow in [39], where the first interpolation scheme tailored to collocated grids was proposed. Since this pioneering work, various authors have enhanced or modified the original scheme; see, for example, the very recent article of [40], as well as the older works of [41][42][43]. These interpolation schemes are collectively referred to as ''Rhie-Chow interpolations''.…”

Section: Convective and Viscous Fluxesmentioning

confidence: 99%

“…In our case, an interpolation scheme can be searched from Eqs. (32) and (40). Indeed, conservation of momentum dictates that (32) and (40) are valid both at the cell centers and interfaces.…”

Section: Convective and Viscous Fluxesmentioning

confidence: 99%

“…(32) and (40) requires the computation of the gradients of the phasial pressures ∇p and ∇p ′ f . As regards the fluid phase, a conservative scheme based on the divergence theorem is sufficiently robust for our purposes.…”

Section: Projection Stepsmentioning

confidence: 99%

“…As regards the fluid phase, a conservative scheme based on the divergence theorem is sufficiently robust for our purposes. Then, (40) reads,…”

Section: Projection Stepsmentioning

confidence: 99%

See 3 more Smart Citations

Projection methods for two velocity–two pressure models for flows of heterogeneous mixtures

Varsakelis

Monsorno

Papalexandris

2015

Computers & Mathematics with Applications

View full text Add to dashboard Cite

a b s t r a c tIn this paper, a numerical analysis of two velocity-two pressure models for flows of solid particles and fluids is presented. First, a formal exploitation of the weak formulation of such models asserts that they are amenable to integration via projection methods. The challenging issues in the algorithm development for these models are then documented and suitable numerical methodologies for their remedy are devised. Subsequently, an algorithm for the integration of the models of interest is proposed. This is a two-phase projection method on collocated grids that utilizes a fractional-step time-marching scheme. It is further endowed with an interface detection-and-treatment methodology to properly account for the stiffness induced by the presence of moving and deforming material interfaces. The efficiency and robustness of the proposed numerical method are assessed in a series of numerical experiments that are delineated in the last part of this paper.

show abstract

Section: Convective and Viscous Fluxesmentioning

confidence: 99%

Section: Convective and Viscous Fluxesmentioning

confidence: 99%

Section: Projection Stepsmentioning

confidence: 99%

“…As regards the fluid phase, a conservative scheme based on the divergence theorem is sufficiently robust for our purposes. Then, (40) reads,…”

Section: Projection Stepsmentioning

confidence: 99%

See 2 more Smart Citations

Projection methods for two velocity–two pressure models for flows of heterogeneous mixtures

Varsakelis

Monsorno

Papalexandris

2015

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…Many variations, corrections and extensions of this term have been published so far, e.g. [5][6][7][8][9][10][11][12] to arbitrarily cite a few. Since work on the stabilization term typically takes place in the context of SIMPLE, it has led to the entanglement of the solution method and the stabilization method.…”

Section: Introductionmentioning

confidence: 99%

On the stabilization of finite volume methods with co-located variables for incompressible flow

Klaij

2015

Journal of Computational Physics

View full text Add to dashboard Cite

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

Marchisio

Hasse

et al. 2019

AIChE Journal

View full text Add to dashboard Cite

The spatial gas distribution of poly-disperse bubbly flows depends greatly on the bubble size. To reflect the resulting polycelerity, more than two momentum balance equations (typically for the gas and liquid phases) have to be considered, as done in the multifluid approach. The inhomogeneous multiple-size group model follows this approach, also combined with a population balance model. As an alternative, in a previous work, an Eulerian quadrature-based moments method (E-QBMM) was implemented in OpenFOAM; however, only the drag force was included. In this work, different nondrag forces (lift, wall lubrication, and turbulent dispersion) are added to enable more complex test cases to be simulated. Simulation results obtained using E-QBMM are compared with the classical E-E method and validated against experimental data for different test cases. The results show that there is good agreement between E-QBMM and E-E methods for mono-disperse cases, but E-QBMM can better simulate the separation and segregation of small and large bubbles.

show abstract

Generalized formulations for the Rhie–Chow interpolation

Cited by 67 publications

References 13 publications

Projection methods for two velocity–two pressure models for flows of heterogeneous mixtures

Projection methods for two velocity–two pressure models for flows of heterogeneous mixtures

On the stabilization of finite volume methods with co-located variables for incompressible flow

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

Contact Info

Product

Resources

About