Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm

Gaskell, Philip; Lau, A. K. C.

doi:10.1002/fld.1650080602

Cited by 708 publications

(464 citation statements)

References 8 publications

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“…The CUBISTA scheme (Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection) has the advantage over more classical schemes, like the SMART scheme of Gaskell and Lau [10], of promoting iterative convergence when used with implicit methods. It has been found that this high-resolution scheme is accurate and very stable, thus being very adequate for the simulation of viscoelastic flows [4,8].…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Numerical simulation of viscoelastic contraction flows

ALVES¹,

OLIVEIRA²,

PINHO³

2003

Computational Fluid and Solid Mechanics 2003

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In this work we present numerical results obtained with a finite volume method for the creeping flow of viscoelastic fluids in both axisymmetric and planar 4 : 1 contractions. Two rheological equations are considered, namely the constantviscosity Oldroyd-B and the shear-thinning Phan-Thien/Tanner (PTT) models. Accurate solutions are presented over a wide range of the Deborah number (a measure of the elasticity of the flow) extending the attainable values of previous studies [1]. Vortex enhancement was observed for the axisymmetric contraction, with both rheological models, while for the planar contraction vortex enhancement is only observed for the shear-thinning PTT model. In the latter geometry, vortex reduction and the appearance of a small lip vortex is predicted for the constant-viscosity Oldroyd-B fluid.

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Numerical simulation of viscoelastic contraction flows

ALVES¹,

OLIVEIRA²,

PINHO³

2003

Computational Fluid and Solid Mechanics 2003

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“…In the current model, commercial CFD code PHOENICS was used to solve a two-phase, three-dimensional flow. A staggered grid was employed with the differencing scheme SMART 50) to solve the partial differential equations by converting it to algebraic finite volume equations. The equations are solved iteratively using the IPSA algorithms.…”

Section: Geometry and Mesh Structurementioning

confidence: 99%

Mathematical Model of Solid Flow Behavior in a Real Dimension Blast Furnace

et al. 2013

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A mathematical model based on the continuum mechanic concept has been developed to describe the profile of solid particles in an industrial scale blast furnace with respect to the in-furnace conditions and its characteristics such as the shape and size of the deadman. The Navier-Stokes differential equation for multi-phase multi-dimensional space has been used to describe the behavior of existing phases. The surface stress tensor has been defined as an extra term and added to the Navier-Stokes equation to describe the particle-particle interactions. This extra term in the Navier-Stokes equation behave as a breaking force when the particles are sliding down. It is shown that the particles change their profile from a V-shape to a W-shape due to the characteristics of the deadman. Moreover, the velocity magnitude is higher at the outer surface of the deadman for higher grid-slabs in this region than the near-wall cells. However, the situation changes as solid particles moving to even lower level of grid-slabs at the outer surface of the deadman in comparison to near-wall cells. It has also been shown that an increase in the magnitude of the effective pressure reduces the velocity magnitude of descending particles.

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“…To improve stability and resolution, we discretize the convective terms for the level set function and its reinitialization equation by employing the SMART [7] and ENO schemes [20]. The SMART scheme is in fact a second-order TVD scheme [15], although it is not included in the TVD region of Sweby [23].…”

Section: Tvd and Eno Schemes For The Convective Term Of The Interfacimentioning

confidence: 99%

A Variable-Density Projection Method for Interfacial Flows

Ni¹,

Abdou²,

Komori

2003

Numerical Heat Transfer, Part B: Fundamentals

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General second-order, variable-density, three-step and four-step projection methods are developed to simulate unsteady incompressible interfacial flows. A high-accuracy, variabledensity RKCN projection method is presented, in which the three-stage, low-storage RungeKutta technique and second-order semi-implicit Crank-Nicholson technique are employed to temporally update the convective and diffusion terms, respectively. To reduce computation cost, a simplified version of the projection method is also presented, in which the pressure Poisson equation (PPE) is solved only at the last substage. The level set approach is employed to implicitly capture the interface for falling droplet flows. Three-dimensional bubble rising flows and two-dimensional falling droplet flows in a small closed channel are studied numerically via the present method. By the definition of the effective pressure, the flow mechanisms for falling droplet flows with different density ratios, viscosity ratios, Weber numbers, and Reynolds numbers are discussed.

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Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm

Cited by 708 publications

References 8 publications

Numerical simulation of viscoelastic contraction flows

Numerical simulation of viscoelastic contraction flows

Mathematical Model of Solid Flow Behavior in a Real Dimension Blast Furnace

A Variable-Density Projection Method for Interfacial Flows

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