scholarly journals Generalization of a Class of Solutions of the Laminar, Incompressible Boundary-Layer Equations

1961 ◽  
Vol 83 (3) ◽  
pp. 328-332 ◽  
Author(s):  
Ward O. Winer ◽  
Arthur G. Hansen
Keyword(s):  
Boundary Layer ◽  
Similarity Solutions ◽  
Boundary Layer Equations ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary ◽  
Energy Equations ◽  
Special Case

The momentum, continuity, and energy equations of the laminar incompressible boundary layer in a skew-linear co-ordinate system are similar in form to those in a rectangular co-ordinate system. This fact is used to generalize the requirements for similarity solutions in rectangular co-ordinates. The requirements for all possible similarity solutions of the boundary-layer and energy equations in skew-linear co-ordinates are presented. The usual Cartesian co-ordinate system is a special case of co-ordinate systems considered.

Numerical Solution of the Incompressible Boundary-Layer Equations Using the Finite Element Method

1992 ◽  
Vol 114 (4) ◽  
pp. 504-511 ◽  
Author(s):  
J. A. Schetz ◽  
E. Hytopoulos ◽  
M. Gunzburger
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Memory Storage ◽  
The Finite Element Method ◽  
Boundary Layer Equations ◽  
Numerical Predictions ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary ◽  
Element Method

A new approach to the solution of the two-dimensional, incompressible, boundary-layer equations based on the Finite Element Method in both directions is investigated. Earlier Finite Element Method treatments of parabolic boundary-layer problems used finite differences in the streamwise direction, thus sacrificing some of the possible advantages of the Finite Element Method. The accuracy and computational efficiency of different interpolation functions for the velocity field are evaluated. A new element especially designed for boundary layer flows is introduced. The effect that the treatment of the continuity equation has on the stability and accuracy of the numerical results is also discussed. The parabolic nature of the equations is exploited in order to reduce the memory requirements. The solution is obtained for one line at a time, thus only two levels are required to be stored at any time. Efficient solvers for tridiagonal and pentadiagonal forms are used for solving the resulting matrix problem. Numerical predictions are compared to analytical and experimental results for laminar and turbulent flows, with and without pressure gradients. The comparisons show very good agreement. Although most of the cases were tested on a mainframe, the low requirements in CPU time and memory storage allows the implementation of the method on a conventional PC.

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