AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE-FLOW USING SPECTRAL ELEMENTS

An approximate projection scheme based on the pressure correction meth od is proposed to solve the Navier-Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm . The properties of the scheme are extensively tested by means of an a nalytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.