JOURNAL OF COMPUTATIONAL PHYSICS 52, 524-544 (1983) A Spectral Numerical Method for the Navier-Stokes Equations with Applications to Taylor-Couette Flow R. D. MOSER Department of Mechanical Engineering, Stanford University, Stanford, California 94305 P. MOIN AND A. LEONARD Ames Research Center, NASA, Moffelt Field, California 94035 Received November 23. 1982 A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good. 1. INTRODUCTION The purpose of this paper is to present a new spectral numerical method for simulating wall-bounded shear flows in Cartesian and cylindrical geometries. These flows have been under extensive theoretical and experimental investigation aimed at understanding the mechanics of transition and turbulence. Numerical simulations of these basic flows have become an important supplement to laboratory measurements. Among the problems that have been simulated are transition to turbulence in a channel [ 1, 21 and in pipes [3], the evolution of Taylor vortices in Taylor-Couette flow 141,and turbulent flow in a channel [5]. In these similations, spectral methods are often used to solve the incompressible Navier-Stokes equations all -=-VP--&vXvX”+uX”, at v.u=o, (lb) 0021-9991/83 $3.00 Copyright 0 1983 by Academic Press, Inc. All rights of reproduction in any form reserved. 524