Hello everyone

I implemented the SIMPLE algorithm for incompressible fluid flow in a 2D channel using finite volumes with central differences. The code seems to work fine for coarse meshes and the pressure correction goes to zero to the third decimal. However, when I make the grid finer, the pressure correction does not exactly become zero, I guess there is mass accumulation. Any thoughts on how to possibly overcome this problem would be very helpful.

Hi:

The use of coarse meshes may sometimes gives a converged solution, perhaps due to the diffusion level associated with the coarse grid system, which is relatively large as compared to fine grid.. I think the reason why you fail to achieve convergence at fine grid level is due to the fact that its dammping effect (fine grid) is not strong enough to dampen the unphysical oscillations associated with the unbounded Central Differencing (CD).

I suggest to use bounded schemes like the first-order Upwind scheme or High-Resolution schemes..

TQ

-khai ching-

Hi khai ching: Thanks for your response. It was useful. However, even when i change the code with upwin or power law scheme, i still see spurious oscillations in pressure correction. Also, i use very low underrelaxation factor. The whole formulation of SIMPLE seems to exteremely sensitive to te value of under-relaxation parameter used and the convergence criterion for pressure correction.

Any thoughts on this!!!!!

Hi Bharat:

May I know what is the grid arrangement are u using? Is it staggered / non-staggered? In the case of using non-staggered grid, u need to have some special interpolation technique for the pressure field..

-khai ching-

I'm using staggered grid. I dont use collocated grid for the moment.

The simulatneous approach seems to be more reliable and fater than fixed point iteration techniques like SIMPLE. My experience is that the convergence and the rate of convergence in SIMPLE is very sensitive to 1. tolerance the user specifies for pressure correction 2. the discretization scheme used 3. the under-relaxation factors that becomes a function of grid size. If one uses simultaneous soluion approach, we dont have to use these tricks and the solution methodology is straightforward. And, that too with today's computing power, i still wonder in what way given the above mentioned short cuts for SIMPLE, people still prefer SIMPLE over simulataneous solution approach. Any thoughts on this would be very helpful!!

Hi Bharat:

I come across the coupled solution approach like Artificial Compressibility Technique dedicated for incompressible flow.. From my experience, although this technique leaves the compressible flow solver largely unmodified, its convergence is very dependent on the artificial sound speed imposed on the continuity equation. (it sounds like the relaxation factor for SIMPLE algorithm).

-khai ching-

in which zone from channel this mass accumulation take place?

The problem has to do with the relative weighting of the numeric terms in your numeric equation. Mesh size will affect this weighting. As you reduce element dimension you can sometimes move towards an unstable solution-form.

I did not see that you are using a transient solver. If not, you may very well be moving towards an unstable solution which you may not be able to accomodate in your solution scheme. This is inherent in the mathematics of the N-S equations, where certain combinations of terms are inherently unstable.

Move towards a transient solver & you may be able to contain your solution a little better. Upwind & its friends are often like applying a band-aid to the problem. In some cases the oscillations have a right to be there - they are telling you something.

Under-relaxation basically reduces the 'numeric shock' you introduce during the solution convergence around your instantaneous velocity operating point/s - but, is not allowed to defeat the inherent physics - that would be cheating.

As a point-of-reference, I *never* use direct convection stabilisation techniques (upwind etc), but, instead, concentrate on the underlying mathematics & numerics themselves.

diaw... (Des Aubery)