Confined wakes: A numerical solution of the Navier‐Stokes equations

Abstract

AbstractA numerical solution of the two‐dimensional Navier‐Stokes equations is presented for the confined wake formed by the merging of two‐plane Poiseuille flow streams. The system of finite‐difference equations for the stream function and vorticity is solved by the Peaceman‐Rachford elimination method for Reynolds numbers of 1, 50, 387, and 647. While the stability of the numerical method is not a problem for this range of Reynolds numbers, the number of points in the finite‐difference network (and hence the computation time) does become burdensome.At high Reynolds numbers, the primary boundary‐layer simplification is imposed to yield a set of parabolic equations for the vorticity and stream function. These equations are solved by a straightforward “marching” technique, thus providing a solution with a minimum of computational effort. The “boundary‐layer equations” presented in this paper are not subject to the order to obtain the Prandtl boundary‐layer equations. The method outlined here represents an approximate solution for high Reynolds numbers, which gives surprisingly good agreement with the complete solution.