Spectral Computation of Triple-Deck Flows

Burggraf, O. R.; Duck, Peter W.

doi:10.1007/978-3-662-12610-3_9

Cited by 26 publications

(24 citation statements)

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“…Spectral methods have the important advantage of treating reversed-flow regions correctly, without the need for any kind of approximation or cumbersome adaptation required in conventional schemes. The original version of this method introduced by Burggraf & Duck (1981) can be applied only if the transformed variable T(w, y ) = rrn [T(x, y ) -11 e-'us dx + 0 for w +. o (31 a ) sufficiently fast so that the contribution for the discretized inverse Fourier integral in the interval around w = 0 vanishes, F(w, y) ei* dx = 0, E2 and the point OJ = 0 must be excluded from the computational domain.…”

Section: Numerical Confirmation and Application Of The Resultsmentioning

confidence: 99%

On similarity solutions occurring in the theory of interactive laminar boundary layers

Gittler

1992

J. Fluid Mech.

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A theoretical investigation of similarity solutions for interactive laminar boundary layers is presented. The questions of uniqueness and of the appearance of homogeneous eigensolutions are discussed. The similarity solutions yielding the asymptotic behaviour of the nonlinear triple-deck equations in the far field can be used either to improve the development of computational schemes or to check the accuracy of numerical results. A special similarity solution governed by a modified Falkner-Skan boundary-value problem determines the shape of a wall generating the largest possible deflection of a laminar boundary layer in supersonic flow if separation is to be avoided. Increasing the controlling parameter of this special pressure distribution (for both supersonic and subsonic flows) beyond a cutoff value leads to a global breakdown of the interacting laminar-boundary-layer approach which cannot be removed or avoided.

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Section: Numerical Confirmation and Application Of The Resultsmentioning

confidence: 99%

On similarity solutions occurring in the theory of interactive laminar boundary layers

Gittler

1992

J. Fluid Mech.

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“…Daniels 1974) involves introducing a small amplitude eigensolution far upstream of any flow perturbation, and adjusting the magnitude of this (iteratively) so that far downstream, the flow asymptotes to some reasonable conditions and also finitelocation breakdowns are avoided. A second approach, proposed by Burggraf & Duck (1982) involves Fourier transforming the problem (in the streamwise direction), a technique which automatically handles upstream/downstream issues (implicitly assuming reasonable downstream conditions). A third approach, which has some similarity with the treatment of § 5 was proposed by Rizzetta, Burggraf & Jenson (1978), treating the (interaction) problem in a quasi-elliptic manner, thereby again suppressing exponentially growing eigenstates.…”

Section: Discussionmentioning

confidence: 99%

On the growth (and suppression) of very short-scale disturbances in mixed forced–free convection boundary layers

Denier

Duck

2005

J. Fluid Mech.

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The two-dimensional boundary-layer flow over a cooled/heated flat plate is investigated. A cooled plate (with a free-stream flow and wall temperature distribution which admit similarity solutions) is shown to support non-modal disturbances, which grow algebraically with distance downstream from the leading edge of the plate. In a number of flow regimes, these modes have diminishingly small wavelength, which may be studied in detail using asymptotic analysis.Corresponding non-self-similar solutions are also investigated. It is found that there are important regimes in which if the temperature of the plate varies (in such a way as to break self-similarity), then standard numerical schemes exhibit a breakdown at a finite distance downstream. This breakdown is analysed, and shown to be related to very short-scale disturbance modes, which manifest themselves in the spontaneous formation of an essential singularity at a finite downstream location. We show how these difficulties can be overcome by treating the problem in a quasi-elliptic manner, in particular by prescribing suitable downstream (in addition to upstream) boundary conditions.

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“…This technique is based on Chebyshev polynomials, the accuracy of which becomes superior to the finite-difference or Runga-Kutta numerical integration as the number of collocation points to be employed is increased. The current trend seems to be in the use of Cheyshev collocation method for the solution of boundary-layer equations of fluid dynamics, see for instance, [6], [7], [8] and [9] amongst many others. An analytic nature method based on homotopy analysis was also presented for some boundary layer flows [10].…”

Section: Introductionmentioning

confidence: 99%

A combined analytic-numeric approach for some boundary-value problems

Türkyılmazoğlu¹

2016

Communications in Numerical Analysis

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A combined analytic-numeric approach is undertaken in the present work for the solution of boundary-value problems in the finite or semi-infinite domains. Equations to be treated arise specifically from the boundary layer analysis of some two and three-dimensional flows in fluid mechanics. The purpose is to find quick but accurate enough solutions. Taylor expansions at either boundary conditions are computed which are next matched to the other asymptotic or exact boundary conditions. The technique is applied to the well-known Blasius as well as Karman flows. Solutions obtained in terms of series compare favorably with the existing ones in the literature.

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Spectral Computation of Triple-Deck Flows

Cited by 26 publications

References 0 publications

On similarity solutions occurring in the theory of interactive laminar boundary layers

On similarity solutions occurring in the theory of interactive laminar boundary layers

On the growth (and suppression) of very short-scale disturbances in mixed forced–free convection boundary layers

A combined analytic-numeric approach for some boundary-value problems

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