A High Order Numerical Scheme for Incompress ible Navier-Stokes Equations

To solve the incompressible navier-stokes equations in a generalized coordinate system, a high order solver is presented. an exact projection method/fractional-step scheme is used in this study. convective terms of the navier-stokes (n-s) equations are solved using fifth-order weno spatial operators, and for the diffusion terms, a sixth-order compact central difference scheme is employed. the third-order runge-kutta (r-k) explicit time-integrating scheme with total variation diminishing (tvd) is adopted for the unsteady flow computations. the advantage of using a weno scheme is that it can resolve applications using less number of grid points. benchmark cases such as, driven cavity flow, taylor-green (tg) vortex, double shear layer, backward-facing step, and skewed cavity are used to investigate the accuracy of the scheme for two dimensional flow.