Splitting methods for high order solution of the incompressible Navier–Stokes equations in 3D

Abstract

AbstractThe incompressible Navier–Stokes equations are discretized in space by a hybrid method and integrated in time by the method of lines. The solution is determined on a staggered curvilinear grid in two space dimensions and by a Fourier expansion in the third dimension. The space derivatives are approximated by a compact finite difference scheme of fourth‐order on the grid. The solution is advanced in time by a semi‐implicit method. In each time step, systems of linear equations have to be solved for the velocity and the pressure. The iterations are split into one outer iteration and three inner iterations. The accuracy and efficiency of the method are demonstrated in a numerical experiment with rotated Poiseuille flow perturbed by Orr–Sommerfeld modes in a channel. Copyright © 2005 John Wiley & Sons, Ltd.