Development of an Upwinding Scheme through the Minimization of Modified Wavenumber Error for the Incompressible Navier-Stokes Equations

Abstract

In this article we develop a computationally stable and dispersively accurate convective scheme for the incompressible Navier-Stokes equations predicted in non-staggered grids. To enhance the convective stability and improve the dispersion accuracy, the convective terms are approximated by conducting the dispersion analysis to minimize dispersion relation error and Fourier stability analysis. To validate the proposed third-order-accurate two-dimensional numerical scheme, we solve four problems that are all amenable to exact solutions and the lid-driven cavity problem investigated at high Reynolds numbers. Results with good rates of convergence are obtained for the scalar and Navier-Stokes problems.