A Direct Spectral Method for Determination of Flows over Corrugated Boundaries

Szumbarski, Jacek; Floryan, J. M.

doi:10.1006/jcph.1999.6282

Cited by 60 publications

(59 citation statements)

References 12 publications

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“…An accurate spectral approach has also been implemented by Deane et al [16] to simulate the ow inside converging-diverging channels. Szumbarski and Floryan [17] also developed a direct spectral method for the determination of ows over corrugated boundaries. They, however, treat the ow problem as an internal rather than a boundary-value problem, where the ow conditions are speciÿed along a line in the interior of a computational domain.…”

Section: Introductionmentioning

confidence: 99%

On the validity of the perturbation approach for the flow inside weakly modulated channels

Zhou

Khayat

Martinuzzi

et al. 2002

Numerical Methods in Fluids

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SUMMARYThe equations governing the ow of a viscous uid in a two-dimensional channel with weakly modulated walls have been solved using a perturbation approach, coupled to a variable-step ÿnite-di erence scheme. The solution is assumed to be a superposition of a mean and perturbed ÿeld. The perturbation results were compared to similar results from a classical ÿnite-volume approach to quantify the error. The in uence of the wall geometry and ow Reynolds number have extensively been investigated. It was found that an explicit relation exists between the critical Reynolds number, at which the wall ow separates, and the dimensionless amplitude and wavelength of the wall modulation. Comparison of the ow shows that the perturbation method requires much less computational e ort without sacriÿcing accuracy. The di erences in predicted ow is kept well around the order of the square of the dimensionless amplitude, the order to which the regular perturbation expansion of the ow variables is carried out.

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Section: Introductionmentioning

confidence: 99%

On the validity of the perturbation approach for the flow inside weakly modulated channels

Zhou

Khayat

Martinuzzi

et al. 2002

Numerical Methods in Fluids

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“…This problem is overcome here by using the IBC concept [27], which we shall explain in the next section. The present section describes discretization of the field equation.…”

Section: Discretization Of the Field Equationmentioning

confidence: 99%

“…The unknowns appearing on the left-hand side of (27) as well as the quantities appearing on the right-hand side of (27) (which are considered to be known) can be expressed in terms of the Fourier expansions in the form…”

Section: Discretization Of the Field Equationmentioning

confidence: 99%

“…These constants have also been related discretizations. A formal imposition of internal constraints suitable for spectral implementation is described in [27] and has been extended to time-dependent problems in [32] and moving boundary problems in [33,34]. The relevant methodology uses representation of flow boundaries in the spectral space and imposes constraints by nullifying the appropriate Fourier modes.…”

Section: Introductionmentioning

confidence: 99%

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Spectrally accurate method for analysis of stationary flows of second‐order fluids in rough micro‐channels

Mohammadi

Floryan

Kaloni

2011

Numerical Methods in Fluids

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SUMMARYA spectral method for the analysis of stationary flows of second-order fluids in rough micro-channels is developed. The algorithm employs a fixed computational domain with the boundaries of the flow domain being located inside the computational domain. The physical boundary conditions are enforced using the immersed boundary conditions concept. The algorithm relies on the Fourier expansions in the flow direction and the Chebyshev expansions in the transverse direction. Various tests confirm spectral accuracy of the algorithm.

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“…4. In treating the inner problem at the wall computationally, instead of mapping the wavy domain to a plane surface [38], we compute the flow and transport directly with a finite-element method. In addition to a primary inner layer along the wavy wall matching an outer layer in the core of the channel (for formal convergence of related problems see [39]), we identify a range of other asymptotic regions within and along the channel whose dimensions are functions of the effective uptake parameter and Péclet number (Sect.…”

Section: Introductionmentioning

confidence: 99%

A multi-scale model for solute transport in a wavy-walled channel

et al. 2008

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This paper concerns steady flow and solute uptake in a wavy-walled channel, where the wavelength and amplitude of the wall are comparable to each other but are much shorter than the width of the channel. The problem has two primary asymptotic regions: a core region where the walls appear flat at leading order and a wall region where there is full interaction between advection, diffusion and uptake at the wavy wall. For weak wall uptake, the effective uptake from the core is shown to increase with wall waviness in proportion to surface area, whereas for stronger wall uptake, it is found that the uptake from the core can be reduced as the wall amplitude increases. Conditions are identified under which this approximation is uniformly valid in a full channel flow, accounting for inlet conditions, and a comprehensive survey of the asymptotic distributions of solute both along and across the channel is provided. It is also shown how this multiscale approach can readily be extended to account for channel walls with multiple lengthscales of spatial variation.

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A Direct Spectral Method for Determination of Flows over Corrugated Boundaries

Cited by 60 publications

References 12 publications

On the validity of the perturbation approach for the flow inside weakly modulated channels

On the validity of the perturbation approach for the flow inside weakly modulated channels

Spectrally accurate method for analysis of stationary flows of second‐order fluids in rough micro‐channels

A multi-scale model for solute transport in a wavy-walled channel

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