Fourth order compact formulation of steady Navier-Stokes equations on non-uniform grids

Abstract

In the present work, the fourth order compact formulation introduced by Erturk and Gokcol (Int. J. Numer. Methods Fluids, 50, 421-436) will be extended to non-uniform grids. The advantage of this formulation is that the final form of the compact formulation is in the same form with the non-uniform grid formulation of the Navier-Stokes equations such that any existing second order ∆ code for Navier-Stokes equations on non-uniform grids can be easily altered to provide fourth order ∆ solutions by just adding some coefficients into the existing code. The efficiency of the formulation is demonstrated on the lid driven cavity flow benchmark problem. © 2018 Elsevier B.V., All rights reserved.