SIMPLE on collocated grid

dshawul · August 17, 2010, 17:15

Hello,
I am a newbie so please bare with me. I am trying to write a SIMPLE steady state solver on unstructured grid using collocated storage. So far it can solve convection-diffusion transport equations for a given correct velocity-pressure field. But I am now stuck on the pressure-correction for collocated storage of variables. It seems that from the momentum equation I can get velocity correction (at center) in terms of face pressure corrections by dropping the neighboring cells contribution (according to SIMPLE) :

Code:

up' =  Sum(N dot pf') / ap

From continuity :

Code:

Sum(N dot (rho * uf)) = 0

The velocity correction obtained from continuity is at the faces but the one I have from the momentum eqn is at the cell centers. How do I go on from this ? Do I just interpolate the corrections too and form a discretized equation ?

I was under the impression that the collocated scheme will be easier to implement atleast until I try to solve the "checker board" problem with rhie-chow or other methods. I have books but none of them give numerical example of SIMPLE on collocated grid, and I am content with having the checkerboard problem and other problems due to non-orthogonality of mesh at least for the time being.
Thanks in advance.

dshawul · August 17, 2010, 21:31

Ok I got it now. The velocity correction is actually not done at the centre but the faces. After an odd way of interpolating the coefficents (1/ap) , it will be similar to the procedure given in Patankar's book.

August 17, 2010, 17:15	SIMPLE on collocated grid	#1
dshawul New Member Join Date: Jun 2009 Posts: 27 Rep Power: 16	Hello, I am a newbie so please bare with me. I am trying to write a SIMPLE steady state solver on unstructured grid using collocated storage. So far it can solve convection-diffusion transport equations for a given correct velocity-pressure field. But I am now stuck on the pressure-correction for collocated storage of variables. It seems that from the momentum equation I can get velocity correction (at center) in terms of face pressure corrections by dropping the neighboring cells contribution (according to SIMPLE) : Code: up' = Sum(N dot pf') / ap From continuity : Code: Sum(N dot (rho * uf)) = 0 The velocity correction obtained from continuity is at the faces but the one I have from the momentum eqn is at the cell centers. How do I go on from this ? Do I just interpolate the corrections too and form a discretized equation ? I was under the impression that the collocated scheme will be easier to implement atleast until I try to solve the "checker board" problem with rhie-chow or other methods. I have books but none of them give numerical example of SIMPLE on collocated grid, and I am content with having the checkerboard problem and other problems due to non-orthogonality of mesh at least for the time being. Thanks in advance.

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August 17, 2010, 21:31		#2
dshawul New Member Join Date: Jun 2009 Posts: 27 Rep Power: 16	Ok I got it now. The velocity correction is actually not done at the centre but the faces. After an odd way of interpolating the coefficents (1/ap) , it will be similar to the procedure given in Patankar's book.