Application of FCT to Incompressible Flows

Flux-corrected transport, FCT, has been applied to incompressible flows on a collocated grid. LCPFCT, a standard version of FCT, has been used to calculate the advection term in the momentum equation. The flux limiter embedded in the FCT algorithm helps to stabilize oscillations introduced by the discretization of the advection term. It is found that if the pressure-gradient term is included in the computation of intermediate velocities, the discretization of the pressure gradient term introduces odd-even decoupling to the discretization of the Poisson equation, and results in pressure oscillations. Therefore, to avoid this odd-even decoupling problem, the pressure gradient term is either not included in the calculation of the intermediate velocities, or is removed from the intermediate velocities after the integration of the momentum equations. This extension of the FCT algorithm to incompressible flow provides us with a time accurate and robust approach. It gives satisfactory results to a variety of problems over a wide range of velocity and Reynolds number.