# rhie chow interpolation

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 March 19, 2012, 11:09 rhie chow interpolation #1 Member   G. S. Join Date: Nov 2010 Posts: 53 Rep Power: 8 Sponsored Links Hi cfd users... according to the rhie chow interpolation several quantities must be interpolated to the cell face. My concern is whats the right way to interpolate the volume to the cell face if i´m working with control volume finite element method on triangular grids (dual control volume). Thanks in advance...

March 19, 2012, 11:53
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Filippo Maria Denaro
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Quote:
 Originally Posted by gerardosrez Hi cfd users... according to the rhie chow interpolation several quantities must be interpolated to the cell face. My concern is whats the right way to interpolate the volume to the cell face if i´m working with control volume finite element method on triangular grids (dual control volume). Thanks in advance...
Try starting from linear interpolation on Lagrangian simplex, then you can also improve accuracy with second degree polynomials

 March 19, 2012, 19:52 #3 Senior Member   Arjun Join Date: Mar 2009 Location: Nurenberg, Germany Posts: 702 Rep Power: 19 There are many ways to interpolate volume and AP to face center. Starccm+ probably uses harmonic mean(for vol and AP) and some places (other variables) volume weighted interpolation. Fluent does not say what they do. Some people use linear interpolation and some people (most common though) use simple averaging (phi1 + phi2) / 2 I, after some testing (very subjective) have come to conclude that inverse distance based weighting works best so I now am trying to use everywhere in my code. Last edited by arjun; March 19, 2012 at 21:48.

 March 20, 2012, 00:08 #4 Member   G. S. Join Date: Nov 2010 Posts: 53 Rep Power: 8 thanks guys, I appreciate your comments. I'll try some method for the interpolations, then I'll tell you about my results. if you want to we can share information for this subject Best regards...

 May 2, 2012, 02:25 #5 New Member   zhiwei liu Join Date: Mar 2009 Posts: 22 Rep Power: 10 Hi, i also want to use Rhie-chow interpolation in CVFEM. I read theory of CFX( based on CVFEM). it use finite elem shape function to perform the face interpolation.

 March 12, 2014, 15:42 a question #6 New Member   Join Date: Mar 2014 Posts: 9 Rep Power: 5 I have written a computer code to solving incompressible viscous governing equations using CVFEM and collocated grid (based on Rhie and Chow's interpolation). At first I wrote this code in context of SIMPLE algorithm and run it to analysis the fluid in a square lid-driven cavity. I could simulate this problem even for high Reynolds number and my code worked properly to solve this problem. Then I prepared a code with the following algorithm: 1. Guess an initial velocity pressure field. 2. Solve x-momentum without pressure gradient term and obtain pseudo u-velocity (uhat). 3. Solve y-momentum without pressure gradient term and obtain pseudo v-velocity (vhat). 4. Solve continuity equation in which velocities at integration points are replaced by following formula (based on Rhie and Chow's interpolation) and obtain pressure in all nodal points uip = uhip-dip*(dp/dx)ip vip = vhip-dip*(dp/dy)ip 5. Correction of uhat and vhat by obtained pressure from previous step . 6. Checking convergence criterion. If this criterion is satisfied the algorithm will be stopped otherwise go to step 2 and the process will continue until this criterion is satisfied. But the above algorithm is not working properly and my obtained results are false and different from those obtained by SIMPLE algorithm. Do you know What is wrong with my algorithm? Thanks for your help

March 12, 2014, 16:00
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Filippo Maria Denaro
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Quote:
 Originally Posted by phdcandidate I have written a computer code to solving incompressible viscous governing equations using CVFEM and collocated grid (based on Rhie and Chow's interpolation). At first I wrote this code in context of SIMPLE algorithm and run it to analysis the fluid in a square lid-driven cavity. I could simulate this problem even for high Reynolds number and my code worked properly to solve this problem. Then I prepared a code with the following algorithm: 1. Guess an initial velocity pressure field. 2. Solve x-momentum without pressure gradient term and obtain pseudo u-velocity (uhat). 3. Solve y-momentum without pressure gradient term and obtain pseudo v-velocity (vhat). 4. Solve continuity equation in which velocities at integration points are replaced by following formula (based on Rhie and Chow's interpolation) and obtain pressure in all nodal points uip = uhip-dip*(dp/dx)ip vip = vhip-dip*(dp/dy)ip 5. Correction of uhat and vhat by obtained pressure from previous step . 6. Checking convergence criterion. If this criterion is satisfied the algorithm will be stopped otherwise go to step 2 and the process will continue until this criterion is satisfied. But the above algorithm is not working properly and my obtained results are false and different from those obtained by SIMPLE algorithm. Do you know What is wrong with my algorithm? Thanks for your help

you are implementing an Approximate Projection Method, what differences do you see from the SIMPLE-based solution?

what about the divergence of the velocity field at the end of each time step?

 March 12, 2014, 17:19 rhie chow interpolation #8 New Member   Join Date: Mar 2014 Posts: 9 Rep Power: 5 I solve governing equations for this problem in steady-state mode and I have no time-step in my algorithm because my problem is steady-state. In proposed algorithm my code is converged but my solution is not right. In SIMPLE algorithm I do the following steps. 1- 1. Set an initial guess for velocity and pressure fields (ustar = vstar = pstar = 0). 2- 2. Solve x-momentum with pressure gradient term and obtain a new ustar and then by subtracting the pressure gradient I obtain pseudo velocity (uhat) . 3- 3. Solve y-momentum with pressure gradient term and obtain a new ustar and then by subtracting the pressure gradient I obtain pseudo velocity (vhat ). 4- 4. I solve continuity equation by approximating velocities at integration points in this way uip=uhatip-dip*(dpstar/dx)ip vip=vhatip-dip*(dpstar/dy)ip (In this step I use the latest value of pstar and obtain pressure-correction instead of pressure.) 5- 5. Modify velocities and pressures by p-correction obtained in step 4. 6- 6. checking convergence if it is satisfied the process will be stopped otherwise go to step 2 with new pressure and velocity and the algorithm continue until convergence is achieved. The results of this algorithm is right but the previous algorithm I mentioned before not. What is wrong?

March 12, 2014, 17:23
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Filippo Maria Denaro
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Quote:
 Originally Posted by phdcandidate I solve governing equations for this problem in steady-state mode and I have no time-step in my algorithm because my problem is steady-state. In proposed algorithm my code is converged but my solution is not right. In SIMPLE algorithm I do the following steps. 1- 1. Set an initial guess for velocity and pressure fields (ustar = vstar = pstar = 0). 2- 2. Solve x-momentum with pressure gradient term and obtain a new ustar and then by subtracting the pressure gradient I obtain pseudo velocity (uhat) . 3- 3. Solve y-momentum with pressure gradient term and obtain a new ustar and then by subtracting the pressure gradient I obtain pseudo velocity (vhat ). 4- 4. I solve continuity equation by approximating velocities at integration points in this way uip=uhatip-dip*(dpstar/dx)ip vip=vhatip-dip*(dpstar/dy)ip (In this step I use the latest value of pstar and obtain pressure-correction instead of pressure.) 5- 5. Modify velocities and pressures by p-correction obtained in step 4. 6- 6. checking convergence if it is satisfied the process will be stopped otherwise go to step 2 with new pressure and velocity and the algorithm continue until convergence is achieved. The results of this algorithm is right but the previous algorithm I mentioned before not. What is wrong?

but you did not aswer to my question..what about the divergence of the velocity (at converged solution)? what differences you see?

March 12, 2014, 17:35
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Quote:
 Originally Posted by FMDenaro but you did not aswer to my question..what about the divergence of the velocity (at converged solution)? what differences you see?
I do not any thing about projection method but I have heared about it. My convergence criterion is defined as follows:

MAXIMUM [u-momentum error,v-momentum error and continuty error ]< 1E-5

where:

u-momentum error = Summation of (un+1-un)/Summation of (un+1)
v-momentum error = Summation of (vn+1-vn)/Summation of (vn+1)
continuity error = Summation of (pn+1-pn)/Summation of (pn+1)

which n denotes for the number of iteration. DO you understand my meaning? Could I answer your question? My solution converged to a false answer.

 Tags collocated grid, cvfem, interpolation, rhie chow

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