A high order numerical scheme for incompressible 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