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October 28, 2013, 05:17 
How can I solve nondimensional equations in FOAM

#1 
New Member
Sean McGinty
Join Date: Sep 2013
Posts: 4
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I'm interested in solving (as a starting point) a nondimensionalised version of laplacianFoam.
After I have chosen my nondimensionalisation, how can I implement this in Foam? I'm worried that foam checks dimensions! For example: How do I change the timestep and spatial coordinates (in blockMeshDict) to be nondimensional, and how do I deal with diffusion coefficients (which will become ratios of diffusion coefficients after the nondimensionalisation) Is it possible to do this. Does anyone know how? Any help would be much appreciated. 

October 28, 2013, 16:02 

#2  
Member
Ping
Join Date: Dec 2011
Posts: 63
Rep Power: 6 
Quote:
Do not change the unit of variables! Regards, 

October 28, 2013, 17:08 

#3  
Senior Member
Lieven
Join Date: Dec 2011
Location: Mol, Belgium
Posts: 295
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Quote:
Second, you could change all the equations you want to solve ... but alternatively you could also simply solve the existing equations and rescale your solution when writing the solution. That works best for me (for one reason, you'll always be stuck with the time derivative and nabla operator which keep their dimensions). Cheers, Lieven 

March 20, 2014, 07:29 

#4 
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Tony
Join Date: Nov 2013
Posts: 35
Rep Power: 4 
Hi Lieven,
I just wonder how did you rescale your solution? Can you give me a hint please? Thank you very much. Kind regards, Tony 

March 22, 2014, 08:23 

#5 
Senior Member
Lieven
Join Date: Dec 2011
Location: Mol, Belgium
Posts: 295
Rep Power: 14 
Hi Tony,
Have a look at http://en.wikipedia.org/wiki/Dimensional_analysis Basically, you rescale your solution by multiplying it with reference quantities. For example, a concentration in [kg/m³] can be rescaled as: Code:
c+ [] = c [kg/m³]* L² [m²]*V[m/s] / R [kg/s] This is merely an example but I hope you got the picture. Cheers, L 

March 22, 2014, 08:35 

#6 
Member
Tony
Join Date: Nov 2013
Posts: 35
Rep Power: 4 
Hi Lieven,
It is really nice of you to give me the explanation. My case is I want to rescale my result to nondimensional value and continue the simulation, I wonder how you achieve it in OpenFOAM? I have done nondimensionalisation for U, p fields and geometry size, however, the simulation didn't run continuously. The simulation should continue without gap, right? Kind regards, Tony 

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