Coiflet Wavelet-Homotopy Solution of Channel Flow due to Orthogonally Moving Porous Walls Governed by the Navier–Stokes Equations

Chen, Qing-Bo; Xu, Hang

doi:10.1155/2020/5739648

Cited by 3 publications

(2 citation statements)

References 40 publications

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“…Yu and Xu [25][26][27] established a generalized boundary modification approach based on the Coiflet wavelet which is suitable for both ordinary and partial differential equations subjected to non-homogenous boundary conditions. Their idea was further adopted by Wang et al [28] for a electrohydro-dynamic flow problem and Chen [29] for a channel flow problem, respectively.…”

Section: Introductionmentioning

confidence: 99%

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Ahmed¹,

Xu²,

Wang³

et al. 2021

Preprint

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The magnetised Jeffery-Hamel flow due to a point sink or source in convergent and divergent channels is studied. The simplified governing equation ruled by the Reynolds number, the Hartmann number and the divergent-convergent angle with appropriate boundary conditions are solved by the newly proposed Coiflet wavelet-homotopy method. Highly accurate solutions are obtained, whose accuracy is rigidly checked. As compared with the traditional homotopy analysis method, our proposed technique has higher computational efficiency and larger applicable range of physical parameters. Results show that our proposed technique is very convenient to handle strong nonlinear problems without special treatment. It is expected that this technique can be further applied to study complex nonlinear problems in science and engineering involving into extreme physical parameters. Besides, the influence of physically important quantities on the flow is discussed. It is found that wall stretching and shrinking exhibits totally different roles on the flow development. The enhanced Lorenz force affects the flow behaviours significantly for both convergent and divergent cases.

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Section: Introductionmentioning

confidence: 99%

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Ahmed¹,

Xu²,

Wang³

et al. 2021

Preprint

Self Cite

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“…Later, a wavelet-homotopy method was developed by Chen and Xu [15] to give solutions to this problem. For a porous tube with an expanding or contracting sidewall, analytical solutions for both large and small Reynolds number with small-to-moderate α were obtained by Saad and Majdalani [16] recently.…”

Section: Introductionmentioning

confidence: 99%

Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

2021

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In this paper, the temporal stability of multiple similarity solutions (flow patterns) for the incompressible laminar fluid flow along a uniformly porous channel with expanding or contracting walls is analyzed. This work extends the recent results of similarity perturbations of [1] by examining the temporal stability with perturbations of general form (including similarity and non-similarity forms). Based on the linear stability theory, two-dimensional eigenvalue problems associated with the flow equations are formulated and numerically solved by a finite difference method on staggered grids. The linear stability analysis reveals

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Highly accurate Coiflet wavelet-homotopy solution of Jeffery–Hamel problem at extreme parameters

Ahmed

Wang

et al. 2022

Int. J. Wavelets Multiresolut Inf. Process.

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The magnetized Jeffery–Hamel flow due to a point sink or source in convergent and divergent channels is studied. Such viscous flow plays an important role in understanding rivers and canals, human anatomy, and the connection between capillaries and arteries. The simplified governing equation ruled by the Reynolds number, the Hartmann number and the divergent–convergent angle with appropriate boundary conditions is solved by the newly proposed Coiflet wavelet-homotopy analysis method (CWHAM). A highly accurate solution is obtained, whose accuracy is rigidly checked. Our proposed method combines the advantages of the homotopy analysis method for strong nonlinearity and the Coiflet wavelet method for excellent local expression capability so that it holds higher computational efficiency, larger applicable range of physical parameters, and better nonlinear processing capability. Different from the previously published research on the CWHAM, we focus on establishing the solution process of nonlinear flow problems with extreme physical parameters, which is not considered before.

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Coiflet Wavelet-Homotopy Solution of Channel Flow due to Orthogonally Moving Porous Walls Governed by the Navier–Stokes Equations

Cited by 3 publications

References 40 publications

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Temporal stability of multiple similarity solutions for porous channel flows with expanding or contracting walls

Highly accurate Coiflet wavelet-homotopy solution of Jeffery–Hamel problem at extreme parameters

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