Ljp. Timmermans et al., AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE-FLOW USING SPECTRAL ELEMENTS, International journal for numerical methods in fluids, 22(7), 1996, pp. 673-688
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.