# Equation question

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April 23, 2012, 04:13
Equation question
#1
Senior Member

Tobias Holzmann
Join Date: Oct 2010
Location: Leoben (Austria)
Posts: 1,087
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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.

Regards Tobi
Attached Files
 mixtureFraction.pdf (90.9 KB, 30 views)

 April 23, 2012, 08:17 #2 Senior Member     Anton Kidess Join Date: May 2009 Location: Delft, Netherlands Posts: 919 Rep Power: 17 fvm::Sp denotes an implicit source term. You can ignore it when translating code into equations, it's purely related to numerics. __________________ *On twitter @akidTwit *Spend as much time formulating your questions as you expect people to spend on their answer. *Help define the OpenFOAM stackexchange Q&A site: http://area51.stackexchange.com/prop...oam-technology

 April 23, 2012, 09:32 #3 Super Moderator     Niklas Nordin Join Date: Mar 2009 Location: Stockholm, Sweden Posts: 693 Rep Power: 19 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^{n-1} = dt*A + dt*B*U^{n-1} => U^n = dt*A + (dt*B + 1)*U_{n-1} implemented like this fvm::ddt(U) == A + fvm::Sp(B, U) this results in U^n - U^{n-1} = dt*A + dt*B*U^n => (1 - dt*B)*U^n = dt*A + U^{n-1} 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 source-terms 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 ^{n-1} = dt*(A*U^n / U^{n-1} + B*U^{n-1}) 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. sylvester and Tobi like this.

April 24, 2012, 04:24
#4
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Tobias Holzmann
Join Date: Oct 2010
Location: Leoben (Austria)
Posts: 1,087
Blog Entries: 6
Rep Power: 19
Hi nicklas,

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.

tobi
Attached Files
 schemes.pdf (85.5 KB, 27 views) Niklas2.pdf (79.4 KB, 17 views) Niklas1.pdf (96.1 KB, 18 views)

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