A Numerical Solution to the Incompressible Navier-Stokes Equations

Abstract: A finite difference based solution method is derived for the velocity-pressure formulation of the two-dimensional incompressible Navier-Stokes equations. The method is proven stable using the energy method, facilitated by SBP operators, for characteristic and Dirichlet boundary condition implemented using the SAT technique. The numerical experiments show the utility of high-order finite difference methods as well as emphasize the problem of pressure boundary conditions. Furthermore, we demonstrate that a discretely divergence free solution can be obtained by use of the projection method.