Solution to unsteady boundary-layer equations

In this article, we propose a high order method for solving steady and unsteady two-dimensional laminar boundary-layer equations. This method is convergent of sixth-order of accuracy. It is shown that this method is unconditionally stable. The unsteady separated stagnation point flow, the Falkner–Skan equation and Blasius equation are considered as special cases of these equations. Numerical experiments are given to illustrate our method and its convergence.

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Singularities in solutions of the three-dimensional laminar-boundary-layer equations

Journal of Fluid Mechanics ◽

10.1017/s0022112085003470 ◽

1985 ◽

Vol 160 ◽

pp. 257-279 ◽

Cited By ~ 6

Author(s):

James C. Williams

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Numerical Solutions ◽

Three Dimensional ◽

Two Dimensional ◽

Unsteady Boundary Layer ◽

Boundary Layer Flows ◽

Boundary Layer Equations ◽

New Type ◽

Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

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A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D ◽

10.1115/imece2012-85599 ◽

2012 ◽

Author(s):

Md. Abdus Sattar

Keyword(s):

Boundary Layer ◽

Numerical Solutions ◽

Similarity Solutions ◽

Length Scale ◽

Local Similarity ◽

Unsteady Boundary Layer ◽

Similarity Equation ◽

Boundary Layer Equations ◽

Dimensional Boundary ◽

The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

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