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October 29, 2015, 04:35 
ddt schemes in openFoam

#1 
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M. Salman Siddiqui
Join Date: Mar 2015
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Hi guys!
I am new to openFoam, my first task is to check the difference in results for different ddt schemes available in openFoam (Euler, backward, crankNicholson) using pimpleFoam algorithm on a NACA foil. But developed the case files and ran it as well. But can someone please explain me what is the difference between these temporal schemes? And once, we switch from one scheme to another what changes are been made in the background solution of Navier Stokes Equations? Your quick help is highly appreciated! 

October 30, 2015, 10:17 

#2 
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Eric Robertson
Join Date: Jul 2012
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The Euler scheme is firstorder accurate. CrankNicholson is secondorder, but in my personal research can be unstable for a range of problems. It can actually be blended with Euler for boundedness. The backward scheme uses a threepoint difference (uses n1 and n2) and is also secondorder, but is not bounded.
Euler will generally give you fastest convergence. A lot of the tutorial cases use the Euler scheme. However, you should not expect it to give you the best accuracy in transient space. I suggest you choose a variable X(t), record it over a time range for each temporal scheme, and record the results. One example where having a 2ndorder temporal scheme may be important is when predicting the Strouhal number (St) of oscillation in the flow past a sphere using DES or LES. St is simply a measure of wake shedding frequencies. If you choose Euler, you might expect a lag with respect to higher order though it is something I have not studied. 

October 30, 2015, 10:25 

#3 
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M. Salman Siddiqui
Join Date: Mar 2015
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The Euler scheme is firstorder accurate. (Do you mean the leading term in the truncation error is of the order of 1st order?). And is it forward Euler or backward Euler? We need to take the value of Crank Nicholson to be 0.5 in order to solve a point midway between n and n+1, right? If we take the value of 1 it will be implicit and if 0 it will be explicit, right?
What do you really mean by boundedness, i didn’t get it? And one thing, does open form solves the time term using finite difference? if it does that how come it is a finite volume code. I am actually confused about it. 

October 30, 2015, 10:40 

#4  
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Eric Robertson
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Quote:
For the remainder of your questions, the best resource is Hrv Jasak's thesis: http://powerlab.fsb.hr/ped/kturbo/Op...jeJasakPhD.pdf Particularly, section 3.6.2 gives a good explanation. 

November 19, 2015, 02:58 
Euler & men values

#5  
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Amir
Join Date: Jul 2011
Location: Shiraz
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Quote:
I'm running a LES case and I have to report the mean value of the results so is Euler scheme a good choice to increase the courant number to 1 or 0.7? 

November 19, 2015, 12:01 

#6  
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Eric Robertson
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Quote:


April 30, 2016, 09:48 

#7 
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SM
Join Date: Dec 2010
Posts: 90
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I get decent results for RANS of 2D channel flow (channel 395) using simpleFoam on same mesh with y+ < 1 with SSTkomega.
On Same mesh when using pimpleFoam and fvOptions to check the ddtSchemes  backward scheme simulation runs but gives kind of laminar velocity profile Euler gives again decent results with everything remaining same CrankNicolson 1 explodes! The Courant number ~ 0.3 for Euler and Backward cases that run. Starting with Euler and then moving to second order later on works fine too.


July 4, 2016, 08:17 

#8  
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Timofey Mukha
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Location: Uppsala, Sweden
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Quote:
So you are doing unsteady rans then, right? With LES I get good results using both backward and CN. Best, Timofey 

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