I am a novice. I try to solve primitive variable Navier-Stokes Equation using projection method in combination with multigrid. Without introducing turbulence model. I don¡¯t know how to deal with the nonlinear convective term of the momentum equation before iteration. Who can help me? Thanks. David Yang

Usually people use it as a source term, so by using Taylor expansion and high order Godnov upwind method, you can get, convection term at time n+1/2.

on introductory level of CFD, nonlinearity is nothing.

in FDM, one simple idea to deal with nonlinear terms in time dependent problem: for example, f(u) du/dx, treat f(u) as something known at time n+1, which can be calculated from data at time n; du/dx is discretized at time n+1.

but, later on, you'll find out it's nonlinearity that causes CFD much harder than computational solid mechanics.