SIMPLER PRESSURE CORRECTION
IS IT POSSIBLE TO USE UNDERRELAXATION FOR PRESSURE CORRECTION EQUATION WITH SIMPLER ? DO WE GET THE CORRECT SOLUTION ? NOTE : I AM NOT ASKING WHETHER SIMPLER REQUIRES OR NOT UNDERRELAXATION OF PRESSURE CORRECTION ( I ALREADY KNOW THAT THE ANSWER IS NO). BUT I WANT TO USE UNDERRELAXATION, SO IS IT POSSIBLE OR NOT ?
THANKS PATRICK 
Re: SIMPLER PRESSURE CORRECTION
Relaxation just changes the convergence (& rate) of your solution (If at all it will converge). So yes I believe you can use relaxation if you desire. It may help or it may not. There is no simple (ha ha I made a joke) answer to your question. Convergence rates are problem dependent so it is best to do a parametric study yourself to see whether or not it is worth using for your specific problem.

Re: SIMPLER PRESSURE CORRECTION
Be careful with the underrelaxation of the pressure correction equation. Underrelaxation causes that the corrected velocity field (or mass flow rates at the surfaces) does not conserve mass. So whether you can use underrelaxation or not depends on the fact if your algorithm requires mass conservation at each outer iteration. Some terms cancel out from the equations if the mass conservation is always satisfied.
N.B., when properly formulated, the pressure correction equation does not need underrelaxation, or very little (0.99) if because of the boundary conditions the coefficient matrix is singular. regards DML 
Re: SIMPLER PRESSURE CORRECTION
Thanks for the answer. Do you mean that underrelaxation is actually "REQUIRED" when Neumann boundary conditions for pressure are used on the entire boundary making the matrix singular. Patrick

Re: SIMPLER PRESSURE CORRECTION
Yes, I think that if you define allNeumann boundary conditions, relaxation (but very little of it) is required. You can check that even setting the relaxation factor to 0.995 helps to get faster convergence (inner iteration!). Moving to 0.99, the impact is even more clear. This is true for both, standard conjugate gradienttype solvers (CG, ICCG) and the GMRES (Krylov) or SIP (Strongly Implicit) solves.
The risk of adding relaxation is that it destroys the mass conservation. Most of the algorithms do not conserve momentum when the mass is not conserved. The result is oscillatory solution or divergence. The other thing you could try, would be to change the boundary conditions for the pressure. If possible, assume Dirichlet conditions for the pressure at the outlet (if you have one). Then the pressure correction will be zero at these locations. The matrix will no longer be singular and your algorithm may like it. Please note that setting Dirichlet conditions on the pressure at the outlet may unintentionally set the pressure difference within the domain. This, of course, must be avoided. Regards DML 
Re: SIMPLER PRESSURE CORRECTION
I did notice that underrelaxation of pressure improved convergence that's why I wanted to use it for pressure correction. But then there is the problem of mass conservation. Outer iter will have to converge more. No I cannot change boundary conditions. Thanks again. Patrick.

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