Numerical Performance of Compact Fourth Order Formulation of the Navier-Stokes Equations

TL;DR

This paper evaluates the numerical performance of a fourth order compact formulation of the 2-D steady incompressible Navier-Stokes equations, focusing on accuracy, computational cost, and effectiveness in benchmark cavity flow simulations.

Contribution

It presents a detailed assessment of the fourth order compact formulation's performance and compares it with second order methods using iterative semi-implicit schemes.

Findings

Fourth order formulation improves spatial accuracy.

Increased CPU work for higher order accuracy.

Effective in benchmark cavity flow simulations.

Abstract

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.