On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time

A third-order time-accurate projection method for approximating the Navier-Stokes equations for incompressible flow is presented. In order to compute a pressure unpolluted by spurious modes, two Chebyshev collocation spatial discretizations, where the pressure is approximated by lower-order polynomials than for the velocity, are compared. Only one collocation grid is used, and no pressure boundary condition is needed. The Navier-Stokes problem is reduced to the successive solution of Helmholtz problems for the velocity and pseudo-Poisson problems for the pressure. These problems are solved by direct methods. Using an exact solution, spectral spatial accuracy, and third-order time accuracy, for both the velocity and the pressure, are checked. The stability properties are discussed by considering the regularized cavity flow at various Reynolds numbers. (C) 1997 Elsevier Science Ltd.