Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

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On a Boundary Layer Problem

Studies in Applied Mathematics ◽

10.1111/1467-9590.01430 ◽

2002 ◽

Vol 108 (4) ◽

pp. 369-398 ◽

Cited By ~ 13

Author(s):

R. Wong ◽

Heping Yang

Keyword(s):

Boundary Layer ◽

Boundary Layer Problem ◽

Layer Problem

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Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2017108 ◽

2017 ◽

Vol 16 (6) ◽

pp. 2177-2199 ◽

Cited By ~ 1

Author(s):

Shu Wang ◽

◽

Chundi Liu

Keyword(s):

Boundary Layer ◽

Poisson System ◽

Boundary Layer Problem ◽

Compressible Euler ◽

Quasineutral Limit ◽

Layer Problem

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The boundary layer over an impulsively started flat plate

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1969.0083 ◽

1969 ◽

Vol 310 (1502) ◽

pp. 401-414 ◽

Cited By ~ 82

Keyword(s):

Boundary Layer ◽

Leading Edge ◽

Surface Shear Stress ◽

Unsteady State ◽

Similarity Condition ◽

Surface Shear ◽

Boundary Layer Problem ◽

Independent Variables ◽

Selection Of ◽

Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

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