A Defect Correction Method for the Time-Dependent Navier-Stokes Equations

A method for solving the time dependent Navier-Stokes equations, aiming at higher Reynolds' number, is presented. The direct numerical simulation of flows with high Reynolds' number is computationally expensive. The method presented is unconditionally stable, computationally cheap, and gives an accurate approximation to the quantities sought. In the defect step, the artificial viscosity parameter is added to the inverse Reynolds number as a stability factor, and the system is antidiffused in the correction step. Stability of the method is proven, and the error estimations for velocity and pressure are derived for the one- and two-step defect-correction methods. The spacial error is O(h) for the one-step defect-correction method, and O(h(2)) for the two-step method, where It is the diameter of the mesh. The method is compared to an alternative approach, and both methods are applied to a singularly perturbed convection-diffusion problem. The numerical results are given, which demonstrate the advantage (stability, no oscillations) of the method presented. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 1-25, 2009