Development of a Dispersion Relation-Preserving Upwinding Scheme for Incompressible Navier–Stokes Equations on NonStaggered Grids

Abstract

ABSTRACT In this article a scheme which preserves the dispersion relation for convective terms is proposed for solving the two-dimensional incompressible Navier–Stokes equations on nonstaggered grids. For the sake of computational efficiency, the splitting methods of Adams-Bashforth and Adams-Moulton are employed in the predictor and corrector steps, respectively, to render second-order temporal accuracy. For the sake of convective stability and dispersive accuracy, the linearized convective terms present in the predictor and corrector steps at different time steps are approximated by a dispersion relation-preserving (DRP) scheme. The DRP upwinding scheme developed within the 13-point stencil framework is rigorously studied by virtue of dispersion and Fourier stability analyses. To validate the proposed method, we investigate several problems that are amenable to exact solutions. Results with good rates of convergence are obtained for both scalar and Navier–Stokes problems.