Steady-state incompressible Navier-Stokes discretization

[Zoli]

Hi,
I would like to solve the steady-state incompressible Navier-Stokes equations by a spectral method. When I saw the classic primitive-variable finite element discretization of the time-dependent incompressible N-S, it turned out that the coefficient matrix of the derivatives of the unknowns makes the problem. However, if I solve the time-independent version of N-S, I do not have to bother with decoupling, etc, am I right?
My second question: do I have to use lower order approximation for the pressure than for the velocity if I regard the steady-state version?

Thank you!

 

[Valerie Park]

Yes, you are right. The time-independent version of the Navier-Stokes equations does not require decoupling or any other additional steps, as the coefficients of the derivatives of the unknowns are all known. In terms of the order of approximation for the pressure and velocity, it is generally recommended to use a lower order approximation for the pressure than for the velocity when solving the steady-state version of the Navier-Stokes equations. This is done in order to reduce numerical errors that can arise from the effects of convection and diffusion.