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

[+] Author and Article Information
J. A. Schetz

Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

E. Hytopoulos

Aerospace and Ocean Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

M. Gunzburger

Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Fluids Eng 114(4), 504-511 (Dec 01, 1992) (8 pages) doi:10.1115/1.2910061 History: Received February 20, 1992; Online May 23, 2008


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.

Copyright © 1992 by The American Society of Mechanical Engineers
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