Numerical Performance of Compact Fourth Order Formulation of the Navier-Stokes Equations
For researchers in computational fluid dynamics, this work provides a performance assessment of a higher-order compact scheme, but it is incremental as it applies existing methods to a standard benchmark.
This study evaluates the numerical performance of a compact fourth-order formulation for steady 2-D incompressible Navier-Stokes equations, solving the driven cavity flow problem. It quantifies the extra CPU work required to increase spatial accuracy from second-order to fourth-order.
In this study the numerical performance of the fourth order compact formulation of the steady 2-D incompressible Navier-Stokes equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436) will be presented. The benchmark driven cavity flow problem will be solved using the introduced compact fourth order formulation of the Navier-Stokes 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 (O(x2)) to fourth order (O(x4)) formulation will be presented.