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March 19, 2012, 12:09 
rhie chow interpolation

#1 
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G. S.
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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, 12:53 

#2  
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Filippo Maria Denaro
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Quote:


March 19, 2012, 20:52 

#3 
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Arjun
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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 22:48. 

March 20, 2012, 01:08 

#4 
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G. S.
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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, 03:25 

#5 
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zhiwei liu
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Hi, i also want to use Rhiechow 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, 16:42 
a question

#6 
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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 liddriven 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 xmomentum without pressure gradient term and obtain pseudo uvelocity (uhat). 3. Solve ymomentum without pressure gradient term and obtain pseudo vvelocity (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 = uhipdip*(dp/dx)ip vip = vhipdip*(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, 17:00 

#7  
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Filippo Maria Denaro
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Quote:
you are implementing an Approximate Projection Method, what differences do you see from the SIMPLEbased solution? what about the divergence of the velocity field at the end of each time step? 

March 12, 2014, 18:19 
rhie chow interpolation

#8 
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I solve governing equations for this problem in steadystate mode and I have no timestep in my algorithm because my problem is steadystate. 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 xmomentum with pressure gradient term and obtain a new ustar and then by subtracting the pressure gradient I obtain pseudo velocity (uhat) . 3 3. Solve ymomentum 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=uhatipdip*(dpstar/dx)ip vip=vhatipdip*(dpstar/dy)ip (In this step I use the latest value of pstar and obtain pressurecorrection instead of pressure.) 5 5. Modify velocities and pressures by pcorrection 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, 18:23 

#9  
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Filippo Maria Denaro
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Quote:
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, 18:35 
a question

#10  
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Quote:
MAXIMUM [umomentum error,vmomentum error and continuty error ]< 1E5 where: umomentum error = Summation of (un+1un)/Summation of (un+1) vmomentum error = Summation of (vn+1vn)/Summation of (vn+1) continuity error = Summation of (pn+1pn)/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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