A Second-Order Accurate Procedure for Solving the Boundary Layer Equations Based on the Predictor-Corrector Form of the Crank-Nicolson Scheme

摘要

The numerical accuracy of a predictor-corrector form of the Crank-Nicolson scheme for solving boundary layer equations is examined. The Crank-Nicolson Scheme, with a predictor-corrector step to deal with nonlinearity, exhibits only first-order accuracy unless the boundary layer continuity and momentum equations are solved in a coupled manner. A predictor-corrector form of the Crank-Nicolson scheme, based on a coupled solution for the continuity and momentum equations, is presented for both the incompressible and compressible flows. The present scheme was subjected to a computer experiment using the problem of the laminar boundary layer development in a linearly retarded edge velocity field. The results are compared with the Davis coupled scheme. It is shown that the present scheme posesses second-order accuracy and is more efficient than the Davis coupled scheme.