Transformation Between Compressible and Incompressible Boundary-Layer Equations

1953 ◽  
Vol 20 (8) ◽  
pp. 583-584 ◽  
Author(s):  
Nguyen Van Le
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Equations ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary

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.

Self-similar solutions to the second-order incompressible boundary-layer equations

1970 ◽  
Vol 40 (2) ◽  
pp. 343-360 ◽  
Author(s):  
M. J. Werle ◽  
R. T. Davis
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Second Order ◽  
Closed Form Solutions ◽  
Boundary Layer Equations ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary ◽  
Self Similar ◽  
Displacement Speed ◽  
Similar Solutions

Solutions are obtained for the self-similar form of the incompressible boundary-layer equations for all four second-order contributors, i.e. vorticity interaction, displacement speed, longitudinal and transverse curvature. These results are found to contain all previous self-similar solutions as members of the much larger family of solutions presented here. Numerical solutions are presented for a large number of cases, and several closed form solutions, which may have special significance for the separation problem, are also discussed.

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