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How to implement equation of mixture fraction and variance of mixture fraction? 

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April 23, 2012, 04:13 
How to implement equation of mixture fraction and variance of mixture fraction?

#1 
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Tobias Holzmann
Join Date: Oct 2010
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Hi all,
I am using OF for two years now and wanna get deeper into the code and wanna make a new solver using an old one and transform the steady equations into the time dependent equations. Okay my problem for now is, that I am not sure if I interpret the *Eqn.H files correct. I read a few threats here in the forum which helped me a lot but now I need your help. I added an attachment with my problem. There you can see my solving equations. I just wanna have a look at the differential equations but I think that I transformed them not right, or? Further more I do not know what "Sp" means. Thx in advance. Regards Tobi 

April 23, 2012, 08:17 

#2 
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Anton Kidess
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fvm::Sp denotes an implicit source term. You can ignore it when translating code into equations, it's purely related to numerics.
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April 23, 2012, 09:32 

#3 
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Niklas Nordin
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suppose you want to solve this equation
dU/dt = A + BU implemented like fvm:ddt(U) == A + B*U using euler scheme, this results in U^n  U^{n1} = dt*A + dt*B*U^{n1} => U^n = dt*A + (dt*B + 1)*U_{n1} implemented like this fvm::ddt(U) == A + fvm::Sp(B, U) this results in U^n  U^{n1} = dt*A + dt*B*U^n => (1  dt*B)*U^n = dt*A + U^{n1} so the first implementation is explicit treatment of the B*U term, while the other is implicit treatment. Hope this makes it clearer This also makes it possible to do some 'cheating' of large explicit sourceterms by linearizing them again... dU/dt = A + B*U = A*1 + B*U + A*(U/U) + B*U which can be implemented like fvm::ddt(U) = fvm:Sp(A/U, U) + B*U which in turn is treated numerically like U^{n}  U ^{n1} = dt*(A*U^n / U^{n1} + B*U^{n1}) so you see now that A is no longer multiplied by 1, but by something else, which for the converged solution hopefully is 1 and have a stabilizing effect on the solver. 

April 24, 2012, 04:24 

#4 
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Tobias Holzmann
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Hi nicklas,
thanks for your good explanation! I used your statement and generated a file (attachment). can you have a look at the file? I am interessted in the last line I added. Thats my understanding of your post. The second file is a transformation from openfoam equation code into scalar equation. Is that correct? Its a while ago that I used grad, div and laplacian. thx in advance tobi 

December 1, 2015, 14:23 

#5 
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Tobias Holzmann
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Location: Leoben (Austria)
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Hi all,
I just want to comment, that the "Schemes.pdf" file is incorrect.
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