The component-consistent pressure correction projection method for the incompressible Navier-Stokes equations

In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the component-consistent condition between components of the solution at every time step. We also propose, in particular, the CNMT2 + CCPC method and the RKMT + CCPC method, both involving one pressure Poisson solution per time step. We show that they are both of O(Δt2) for the velocity and O(Δt) for the pressure on fixed meshes and finite time intervals. Numerical tests on flow simulation support our claim that the component-consistent pressure correction projection method solves the deviation problem encountered sometimes by the original pressure correction projection method.