Comparison of some upwind-biased high-order formulations with a second-order central-difference scheme for time integration of the incompressible Navier-Stokes equations

The paper compares high-order finite-difference discretizations with a second-order central-difference scheme for the time integration of the incompressible Navier-Stokes equations. Conservative and non-conservative forms of the convection terms are discretized using fifth-order accurate upwind-biased based approximations. The high-order non-conservative treatment of the convection terms exhibits the best accuracy at high resolutions bur deteriorates rapidly as the resolution decreases. The high-order conservative treatment of the convection terms, despite the second-order finite-volume operator, exhibits high-order accuracy but does not show any advantage over the non-conservative formulation. Combinations of the divergence and gradient operators based on second and fourth-order accurate central-difference approximations are used to construct high-order Laplacians in the pressure equation. There is little evidence that the high-order treatment of the pressure equation adds sufficiently to the overall accuracy of the scheme to justify the extra computational effort associated with it. Simulations of turbulent channel flow indicate that the second-order central-difference scheme resolves the turbulent spectrum better than the high-order upwind schemes. Copyright (C) 1996 Elsevier Science Ltd.