Calculation of separation bubbles using boundary-layer-type equations

Halim, A.; Hafez, Mohammed M.

doi:10.2514/3.9311

Cited by 10 publications

(7 citation statements)

References 11 publications

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“…The backward-facing step is a less challenging test problem since certain characteristics, i.e. the reattachment length, scale with the Reynolds number (see Reference [29]). As Gunzburger [2, p. 236] states, the forwardfacing step and the full step are better test problems for computational studies since they are geometrically simple and do not scale with the Reynolds number.…”

Section: The Test Problemsmentioning

confidence: 99%

Time‐dependent flow across a step: the slip with friction boundary condition

John

Liakos

2005

Numerical Methods in Fluids

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SUMMARYThe paper studies numerically the slip with friction boundary condition in the time-dependent incompressible Navier-Stokes equations. Numerical tests on two-and three-dimensional channel ows across a step using this boundary condition on the bottom wall are performed. The in uence of the friction parameter on the ow ÿeld is studied and the results are explained according to the physics of the ow. Due to the stretching and tilting of vortices, the three-dimensional results di er in many respects from the two-dimensional ones.

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Section: The Test Problemsmentioning

confidence: 99%

Time‐dependent flow across a step: the slip with friction boundary condition

John

Liakos

2005

Numerical Methods in Fluids

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“…The convergence of this solution technique can be accelerated by the introduction of a relaxation parameter j3 for the streamfunction equation. 4 AIAA JOURNAL VOL. 27, NO.…”

Section: Methods Imentioning

confidence: 98%

Comparison of iterative and direct solution methods for viscous flowproblems

Dam

Hafez

1989

AIAA Journal

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IntroductionT HE purpose of this study is to compare quantitatively several numerical solution techniques for solving twodimensional viscous flow problems, including separated flows, at moderate to high Reynolds numbers. These solution techniques have various degrees of implicitness, and they are compared on the basis of convergence, CPU time, storage requirements, and solution accuracy. The stream-function (\l/) vorticity (co) approach is used to formulate the partially parabolized Navier-Stokes (PPNS) equations that describe the two-dimensional incompressible flow. The PPNS equations are quite similar to the Navier-Stokes (NS) equations; streamwise diffusion is the only physical process neglected, and terms representing this diffusion are dropped from the NS equations. The governing equations arewhere the term otu t represents an artificial time-dependent term, and the velocity u = \l/ y and v --\l/ x . At the solid wall, the no-slip boundary condition requires u = 0 and v = 0. For external flows co = 0 and u = U(x) at the upper boundary. For internal flows the boundary conditions at the centerline of, e.g., a channel, are co = 0 and \l/ = \l/(x Q9 y c ). At the inflow boundary \l/ and co are prescribed, whereas at the outflow boundary the PPNS equations are reduced to the boundarylayer equations by neglecting the i/^ term.

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“…Furthermore, the present method is tht inly one which effectively employs second-order-accurate central differences for the first derivativ . the streamwise direction and therefore is anticipated to be more accurate (for an equivalent mesh) to methods resorting to first-order-accurate upwind differences [8] or to the FLARE approximation in the separated region [7]. Finally, the convergence of the proposed approach can be improved by using backward sweeping (at least in the separated region) at successive iterations, horizontal line relaxations every once in a while, or a multigrid approach [19].…”

Section: Resultsmentioning

confidence: 99%

“…The PNS equations can then be considered from an asymptotic point of view as a composite set of equations uniformly valid in both the inner (viscous) and the outer (inviscid) regions and therefore 'equivalent" to the complete NS equations. The IBL equations are valid instead only in the viscous region, whereas the inviscidilow is computed by means of another set, of equations; and the viscous-inviscid interaction phenomenon is accounted for iteratively, e. g., by solving the inviscid and viscous flow equations using the same displacement thickness To date, a large number of numerical studies have shown that for many flow fields of' ractical interest, namely for all of the high Re weakly separated flows, the PNS or even the IBL equations provide a satisfactory answer, so that it would appear as an unnecessary waste of computational effort to resort to the complete NS equations, see, e. g., [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

High Re separated flow solutions using the Navier-Stokes and approximate equations

Napolitano

1985

18th Fluid Dynamics and Plasmadynamics and Lasers Conference

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Calculation of separation bubbles using boundary-layer-type equations

Cited by 10 publications

References 11 publications

Time‐dependent flow across a step: the slip with friction boundary condition

Time‐dependent flow across a step: the slip with friction boundary condition

Comparison of iterative and direct solution methods for viscous flowproblems

High Re separated flow solutions using the Navier-Stokes and approximate equations

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