Investigation of some finitedifference techniques for solving the boundary layer equations
Abstract
The LevyLees form of the laminar boundary layer equations is solved with several secondorder accurate finitedifference schemes. For incompressible flow the methods investigated include three forms of the CrankNicolson scheme, four variations of the Keller box scheme and a modified box scheme. The number of iterations required at each step along the surface to obtain a secondorder accurate scheme is studied. The accuracy of the schemes with various stepsizes is determined for the boundary layer flow with a linearly retarded edge velocity. In addition, one form of the CrankNicolson scheme is extended to compressible flows and its accuracy and behavior are also examined for the linearly retarded flow case. The results of this investigation show that the coupled continuitymomentum form of the CrankNicolson scheme is secondorder with one iteration at each step and requires less time than the Keller box scheme.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 July 1975
 DOI:
 10.1016/00457825(75)900122
 Bibcode:
 1975CMAME...6....1B
 Keywords:

 Boundary Layer Equations;
 Boundary Layer Flow;
 Finite Difference Theory;
 Incompressible Boundary Layer;
 Partial Differential Equations;
 Compressible Flow;
 Computer Techniques;
 Continuity Equation;
 Convergence;
 Error Analysis;
 Iterative Solution;
 Linearization;
 Fluid Mechanics and Heat Transfer