Dear all, I wish to enquire something about FD schemes.

I am solving an incompressible viscous steady state flow using a finite difference, fractional step method on the Navier Stokes equations on a non-staggered grid. I use the SOR method to solve for the Pressure Poisson equation.

I realise that my momentum residues and mass residue (using the momentum and continuity equations) do not fall to machine zero. Instead, most often the residues will only drop to magnitudes of around order 10^-3 to 10^-5. Is this because that finite difference schemes are essentially non-conservative in nature?

Thank you!

A common cause for failure of convergence is the use of non-differentiable limiters like min-max. Are you using some sort of limiter ? Also look at the L_∞ residue and find where the maximum change is taking place. That might shed some light on your problem.

Hi,

I don't believe I'm using any limiters, and the residues don't really show anything significant. So it is possible for residues to fall to machine zero using finite difference? Or does the use of a non-staggered, collocated grid cause the "non-conservativeness"?

Non-conservativity need not be the cause of failure to converge (in terms of residue fall). There are huge number of finite difference schemes that do give good residue convergence.