# Pressure equation in presence of obstacles with a Co-located grid

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 February 18, 2013, 00:35 Pressure equation in presence of obstacles with a Co-located grid #1 New Member   Aryan Join Date: Jan 2013 Posts: 8 Rep Power: 6 Hi I have written a 2D code for the SIMPLE method on the co-located grid. I want to study the fluid flow around an obstacle. For this purpose, I alter the source terms appeared in the momentum equation such that the velocity in the obstacle region is zero. But I have problem with the pressure equation. Since the velocities in the solid zone are zero, all of the coefficient s of aW, aE, aS, aN, Su, Sp and aP are zero for the pressure equation (actually very small values because of the numerical and round off errors). This causes a wrong solution for the pressure and consequently the momentum equations. I was wondering if someone could help me to solve this problem. Regards

 February 18, 2013, 00:51 #2 New Member   Lipo Wang Join Date: Dec 2012 Posts: 14 Rep Power: 7 Hi, You need to deal with the boundary cells specially to ensure the correct boundary conditions of pressure (to solve the Poission eq.). It may not be feasible to treat all of the cells in a general way.

 February 18, 2013, 01:01 #3 New Member   Aryan Join Date: Jan 2013 Posts: 8 Rep Power: 6 Hi nickna But I think this is practical: "Computational Flow Modeling for Chemical Reactor Engineering" By Vivek V. Ranade, Page 172.

February 18, 2013, 07:43
#4
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andy
Join Date: May 2009
Posts: 129
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Quote:
 Originally Posted by aryan Hi I have written a 2D code for the SIMPLE method on the co-located grid. I want to study the fluid flow around an obstacle. For this purpose, I alter the source terms appeared in the momentum equation such that the velocity in the obstacle region is zero. But I have problem with the pressure equation. Since the velocities in the solid zone are zero, all of the coefficient s of aW, aE, aS, aN, Su, Sp and aP are zero for the pressure equation (actually very small values because of the numerical and round off errors). This causes a wrong solution for the pressure and consequently the momentum equations. I was wondering if someone could help me to solve this problem. Regards
The SIMPLE method staggers the velocity components and so this problem does not arise.

A co-located arrangement requires the introduction of "pressure smoothing" in order to prevent pressure-velocity decoupling. It looks as if you are doing this in an implicit manner by fiddling/averaging coefficients rather than with explicit pressure gradient terms. A first step could be to work out what your smoothing fluxes actually are and whether you want to apply them at the boundaries. For example, swirling flow in collocated schemes tends to jump badly at boundaries when the large pressure smoothing term at the boundary is not included.

For incompressible flows a pressure equation can be derived from the momentum equations and then constrained to be divergence free. This can be used to determine good treatments for pressure on the boundary given your particular numerical scheme. There is plenty in the literature on this topic.

 February 19, 2013, 00:23 #5 New Member   Aryan Join Date: Jan 2013 Posts: 8 Rep Power: 6 Hi andy Thanks for your guidance but I still think that the problem remains, as it occures in my code apparently. When the velocity in the block zone is zero the fluxes are zero and consequently the pressure equation coefficients are also zero. Correct?

February 19, 2013, 00:25
#6
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Aryan
Join Date: Jan 2013
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Quote:
 Originally Posted by andy_ The SIMPLE method staggers the velocity components and so this problem does not arise.
Hi andy

Thanks for your guidance but I still think that the problem remains, as it occures in my code apparently. When the velocity in the block zone is zero the fluxes are zero and consequently the pressure equation coefficients are also zero. Correct?

February 19, 2013, 02:26
#7
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Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
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Quote:
 Originally Posted by aryan Hi andy Thanks for your guidance but I still think that the problem remains, as it occures in my code apparently. When the velocity in the block zone is zero the fluxes are zero and consequently the pressure equation coefficients are also zero. Correct?
Depends.

If you decided to treat the solid part as fluid then it has viscosity and thus coefficients are not 0.

If you decided to treat solid part as solid then you do not need to solve pressure correction equation in this part and thus this does not go into matrix so coefficients have no meaning.

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