A High Order Numerical Scheme for Incompressible Navier-Stokes Equations

Abstract

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 in detail for two dimensional flow. The code is further extended to three dimensions thus increasing the utility of the developed code for more complex problems. A simple example of flow thorough infinite long pipe has been solved in order to validate the 3D code.