A boundary element method for steady viscous fluid flow using penalty function formulation

Grigoriev, M. M.; Fafurin, A. V.

doi:10.1002/(sici)1097-0363(19971030)25:8<907::aid-fld592>3.0.co;2-t

Cited by 24 publications

(17 citation statements)

References 16 publications

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Section: 2mentioning

confidence: 89%

“…This makes comparison between different works for this problem more difficult than for the lid-driven cavity problem. Therefore, instead of comprehensive comparison of computation of series of corner eddies for this problem, we just compute the backward-facing step flow for one choice of parameters and compare our results with one of the works available in the literature (namely, with [23]). …”

Section: 2mentioning

confidence: 99%

“…We chose the parameters of the problem in accordance with the first computational example of [23]. The domain sizes and Reynolds number in the computed example are chosen as follows: L = 20, L e = 3, H = 1, h = 0.5, Re = 1000.…”

Section: 2mentioning

confidence: 99%

“…There were two insignificant differences in choice of parameters between our work and [23]. First, the value of Reynolds number in [23] was 500 due to the different way of defining it.…”

Section: 2mentioning

confidence: 99%

“…First, the value of Reynolds number in [23] was 500 due to the different way of defining it. And second, the outlet boundary conditions in [23] were such that the normal derivatives of velocity were zero at the outlet. However, as was stated in [23], with the chosen outlet boundary conditions and the channel length L, their results were "channel-length-independent".…”

Section: 2mentioning

confidence: 99%

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An Asymptotic Fitting Finite Element Method with Exponential Mesh Refinement for Accurate Computation of Corner Eddies in Viscous Flows

Shapeev¹,

Lin²

2009

SIAM J. Sci. Comput.

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General rights Copyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain.• You may freely distribute the URL identifying the publication in the public portal. Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract.It is well known that any viscous fluid flow near a corner consists of infinite series of eddies with decreasing size and intensity, unless the angle is larger than a certain critical angle [H. K. Moffat, J. Fluid Mech., 18 (1964), pp. 1-18]. The objective of the current work is to simulate such infinite series of eddies occurring in steady flows in domains with corners. The problem is approached by high-order finite element method with exponential mesh refinement near the corners, coupled with analytical asymptotics of the flow near the corners. Such approach allows one to compute position and intensity of the eddies near the corners in addition to the other main features of the flow. The method was tested on the problem of the lid-driven cavity flow as well as on the problem of the backward-facing step flow. The results of computations of the lid-driven cavity problem show that the proposed method computes the central eddy with accuracy comparable to the best of existing methods and is more accurate for computing the corner eddies than the existing methods. The results also indicate that the relative error of finding the eddies' intensity and position decreases uniformly for all the eddies as the mesh is refined (i.e., the relative error in computation of different eddies does not depend on their size). 1. Introduction. The two-dimensional flow of a viscous fluid near the corner between two steady rigid planes was first examined by Moffatt [28]. He established that when the angle between planes is less than a certain critical angle, any flow near the corner consists of infinite series of eddies with decreasing size and intensity as the corner point is approached.One of the most famous examples of flow in domain with corners is a flow in the lid-driven cavity. The lid-driven cavity problem has become a benchmark problem for researchers to test the performance of numerical methods designed for computation of viscous fluid flow. Particularly, among other criteria, the researchers examine the accuracy of their methods based on how accurately they can compute the corner eddies. However, in the previous works only a few eddies were computed (maximum four corner eddies [4,18] for certain Reynolds numbers). In ad...

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Section: 2mentioning

confidence: 89%

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

“…There were two insignificant differences in choice of parameters between our work and [23]. First, the value of Reynolds number in [23] was 500 due to the different way of defining it.…”

Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

See 3 more Smart Citations

An Asymptotic Fitting Finite Element Method with Exponential Mesh Refinement for Accurate Computation of Corner Eddies in Viscous Flows

Shapeev¹,

Lin²

2009

SIAM J. Sci. Comput.

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A poly-region boundary element method for incompressible viscous fluid flows

Grigoriev

Dargush

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA boundary element method (BEM) for steady viscous #uid #ow at high Reynolds numbers is presented. The new integral formulation with a poly-region approach involves the use of the convective kernel with slight compressibility that was previously employed by Grigoriev and Fafurin [1] for driven cavity #ows with Reynolds numbers up to 1000. In order to avoid the overdeterminancy of the global set of equations when using eight-noded rectangular volume cells from that previous work, 12-noded hexagonal volume regions are introduced. As a result, the number of linearly independent integral equations for each node becomes equal to the degrees of freedom of the node. The numerical results for square-driven cavity #ow having Reynolds numbers up to 5000 are compared to those obtained by Ghia et al.[2] and demonstrate a high level of accuracy even in resolving the secondary vortices at the corners of the cavity. Next, a comprehensive study is done for backward-facing step #ows at Re"500 and 800 using the BEM, along with a standard Galerkin-based "nite element methods (FEM). The numerical methods are in excellent agreement with the benchmark solution published by Gartling [3]. However, several additional aspects of the problem are also considered, including the e!ect of the in#ow boundary location and the traction singularity at the step corner. Furthermore, a preliminary comparative study of the poly-region BEM versus the standard FEM indicates that the new method is more than competitive in terms of accuracy and e$ciency.

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Efficiency of boundary element methods for time‐dependent convective heat diffusion at high Peclet numbers

Grigoriev

Dargush

2004

Commun. Numer. Meth. Engng.

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SUMMARYA higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192:4281-4298; 4299-4312; 4313-4335) for time-dependent convective heat di usion in two-dimensions appears to be a very attractive tool for e cient simulations of transient linear ows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. t 6 4Ä=V2 ) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and e ciency of BEM formulations for Peclet numbers in the range from 10 3 to 10 5 .

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A boundary element method for steady viscous fluid flow using penalty function formulation

Cited by 24 publications

References 16 publications

An Asymptotic Fitting Finite Element Method with Exponential Mesh Refinement for Accurate Computation of Corner Eddies in Viscous Flows

An Asymptotic Fitting Finite Element Method with Exponential Mesh Refinement for Accurate Computation of Corner Eddies in Viscous Flows

A poly-region boundary element method for incompressible viscous fluid flows

Efficiency of boundary element methods for time‐dependent convective heat diffusion at high Peclet numbers

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