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August 9, 2010, 12:48 
SIMPLE Algorithm  Questions from a Beginner

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Emre Turkoz
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I’m beginner in CFD and trying to implement SIMPLE algorithm using MATLAB. My guidebooks are “Numerical Heat Transfer and Fluid Flow” by Patankar and “An Introduction to Computational Fluid Dynamics” by Versteeg & Malalasekera. Using both books simultaneously really helped me a lot but still, I have a couple of questions. I have problems on the boundary conditions. I’m at the critical point where momentum and pressure correction equations are explained. As an explanation to the pressure correction equation, as far as I have understood, Patankar wrote that either the real values of normal velocity or the real values of pressure should be specified at boundaries. If we specify pressure values, then the correction pfield at boundaries should be zero. It’s clear so far. I wonder what happens in that case to the momentum equation’s boundary conditions. How do we specify them? Are they the ones from the previous iteration? And additionally: How do we set pressure difference values at these boundaries? Is it okey if I extend the pressure field from the previous iteration and extrapolate mirror nodes to get pressure difference and add it as a source term? Thank you all 

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August 9, 2010, 13:06 

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Akinola
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0= dp/dx+mhu*d2(vx)/dx2+rho*gx (ie vx=vy=vz=0 at the wall. also the shear velocity derivative will be zero cos they are still at the wall) From the equation above, you will be able to get the pressure outside of the domain. Hope this helps and I ve not confused you too much. Take care 

August 9, 2010, 13:45 

#3 
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Emre Turkoz
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falopsy, thank you very much for your answer. it really clarifies how i should deal with the pressure values at boundaries in umomentum equation.
i'm also confused at the uvalues part of that equation. are the boundary values of corrected velocity field from the previous iteration new boundary conditions for the next iteration? or should i deal with these nodes as i deal with the inner points, specifying no specific value for u? 

August 9, 2010, 15:13 

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Akinola
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August 9, 2010, 16:42 

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Emre Turkoz
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thank you, again. I'm reading further on the topic. I noticed, Ch.9 of the Versteeg book actually explains boundaries.
thanks! 

August 11, 2010, 11:58 
SIMPLE Algorithm  Questions from a Beginner

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V GURUPRASAD
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hi,
the initial pressure values in momentum equns shuid b assumed as zero oly..... 

August 11, 2010, 12:29 

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Akinola
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Yes, the initial condition doesnt really matter but what how will you treat it after the first iteration when the pressure will then be nonuniform? You still need a way to treat the boundary condition.


August 11, 2010, 14:01 

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Emre Turkoz
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I just solve pressure correction for the inner region, add it up to the pressure from the previous iteration and again impose boundary conditions to this corrected pressure. The results seem reasonable then.
I have another concern. I wrote the algorithm using finite differences with the help of the book "Computational Fluid Dynamics" by Hoffmann. I made no matrix calculations with conjugate gradient, gauss seidel or other iterative stuff. So why do we prefer other methods that includes them? Are they more accurate? Or faster? 

August 13, 2010, 00:21 
HI

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V GURUPRASAD
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hi, the guessed pr (i.e) ur initial pr. is assumed as zero.. then 4 d nxt iteration u will solve for pressure correction eqn to find new pr. correction value. Then with the pressure correction value v can find new pr value... Actually v r not finding the exact pr values.. V r jus finding the pr. gradient values in SIMPLEX method..... Then u ll compute new U & V values using corrected pr.... Then check for convergence criteria..... Incase of turbulence v shud multiply the under relaxation factor(usually 0.2 to 0.8) with the pr. correction term to reduce the pr. correction value, thus geting soln converged... 

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matlab, patankar, simple 
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