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

 Register Blogs Members List Search Today's Posts Mark Forums Read

April 23, 2012, 04:13
How to implement equation of mixture fraction and variance of mixture fraction?
#1
Senior Member

Tobias Holzmann
Join Date: Oct 2010
Location: Leoben (Austria)
Posts: 1,506
Blog Entries: 6
Rep Power: 26
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, 42 views)

 April 23, 2012, 08:17 #2 Senior Member     Anton Kidess Join Date: May 2009 Location: Delft, Netherlands Posts: 1,141 Rep Power: 20 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. *Join the OpenFOAM stackexchange Q&A site: http://area51.stackexchange.com/prop...oHPxcPqde7HtA2

 April 23, 2012, 09:32 #3 Super Moderator     Niklas Nordin Join Date: Mar 2009 Location: Stockholm, Sweden Posts: 693 Rep Power: 21 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
Senior Member

Tobias Holzmann
Join Date: Oct 2010
Location: Leoben (Austria)
Posts: 1,506
Blog Entries: 6
Rep Power: 26
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, 42 views) Niklas2.pdf (79.4 KB, 28 views) Niklas1.pdf (96.1 KB, 29 views)

 December 1, 2015, 14:23 #5 Senior Member     Tobias Holzmann Join Date: Oct 2010 Location: Leoben (Austria) Posts: 1,506 Blog Entries: 6 Rep Power: 26 Hi all, I just want to comment, that the "Schemes.pdf" file is incorrect. __________________ Best regards, Tobias Holzmann Some interesting OpenFOAM tutorials and videos on www.Holzmann-cfd.de

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Tobi OpenFOAM Programming & Development 507 March 4, 2016 05:30 Hugo FLUENT 3 April 20, 2015 21:24 AdidaKK CFX 0 October 17, 2009 05:33

All times are GMT -4. The time now is 07:52.