Numerical methods of higher order of accuracy for incompressible flows Original Research Article

The work deals with numerical solution of the Navier–Stokes equations for incompressible fluid using finite volume and finite difference methods. The first method is based on artificial compressibility where continuity equation is changed by adding pressure time derivative. The second method is based on solving momentum equations and the Poisson equation for pressure instead of continuity equation. The numerical solution using both methods is compared for backward facing step flows. The equations are discretized on orthogonal grids with second, fourth and sixth orders of accuracy as well as third order accurate upwind approximation for convective terms. Not only laminar but also turbulent regimes using two-equation turbulence models are presented.