Numerical performance of compact fourth‐order formulation of the Navier–Stokes equations

In this study, the numerical performance of the fourth-order compact formulation of the steady 2-D incompressible Navier–Stokes (NS) equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids 2006; 50:421–436) will be presented. The benchmark-driven cavity flow problem will be solved using the introduced compact fourth-order formulation of the NS equations with two different line iterative semi-implicit methods for both second- and fourth-order spatial accuracy. The extra CPU work needed for increasing the spatial accuracy from second-order ((Δx2)) formulation to fourth-order ((Δx4)) formulation will be presented. Copyright © 2008 John Wiley & Sons, Ltd.