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Steve Moore September 5, 2005 22:23

secondary diffusion term

I've been trying to figure out how fluent discretizes the generalized transport equation and have gotten stuck on the discretization of the diffusive term. Basically the diffusive term is split up into a 'primary diffusion' and a 'secondary diffusion' term (sect 5.2.3 of the udf manual about 'cell definitions') but I have no idea as to how, why or what they mean?


zxaar September 6, 2005 02:17

Re: secondary diffusion term
for the diffusive term what you need is gradient in normal direction to face. Now a simple gradient between two space points c0 and c1 would be :

grad_c0_c1 = (phi_1 - phi_0) / (r_1 - r_0) ,where r is postion. this gradient (the primary gradient), is in direction c_0 and c_1, but we need in direction to face normal.

That means when the face normal and line joining cell to cell center are not parallel, this gradient is not accurate. So what we do is we add another terms to account for the error we introduced in primary gradient. The second terms is secondary gradient, so as the cell non orthogoniality increases the secondary gradient term becomes important.

Steve Moore September 6, 2005 21:31

Re: secondary diffusion term
Thanks for that... How do you derive the expression for the secondary gradient term though?

zxaar September 6, 2005 21:40

Re: secondary diffusion term
This part i am also searching a proper answer, this (as i understand) comes from vector sum or law of trianlge. That is if we draw a triangle between three points as mentioned the figure of udf manual (same page as u suggested). But i am not sure of its derivation.

Its that i know of four distinct ways of doing it. The method fluent uses is sometimes called over-relaxed method.

Steve Moore September 7, 2005 19:26

Re: secondary diffusion term

I was wondering what it means when it is said that the primary diffusion term is treated implicitly and the secondary diffusion term explicitly?

Also I've found a fluent paper where the evaluation of the cell gradient in the secondary diffusive term is given as:

grad(phi)_c0 = 1/V*sum( ( (phi_f)_c0+(phi_f)_c1 )/2 . A_f )


(phi_f)_c0 = phi_c0 + ( dr . grad(phi)_r )_c0


(phi_f)_c1 = phi_c1 + ( dr . grad(phi)_r )_c1

which is a second order evaluation of the face values of phi. In the paper though a second order upwind scheme was used and I was wondering if the face values of phi are still evaluated in this way if you select a first order upwind scheme? Or does the upwind scheme play no part in the evaluation of the diffusive term?


zxaar September 7, 2005 21:44

Re: secondary diffusion term
the primary diffusion term go into matrix and serve as a coefficient,

D_diff (phi_0 - phi_1) + Sec_diff_terms (by last iteration)

so now for eql Ap * phi_p + sum(A_l * phi_l) = Su

Ap = Ap + D_diff Al = Al(convection) - D_diff

and Su = Su - Sec_diff_terms (by last iteration)

this is what they mean.

Now about the face values for first order schemes, as far as i rem fluent does not clearly mention how they calculate gradients. Can not comment much.

I will be out of station, so may not reply ur message.

zxaar September 7, 2005 21:45

Re: secondary diffusion term
this line goofed up

Ap = Ap + D_diff

Al = Al(convection) - D_diff

zxaar September 7, 2005 22:49

Re: secondary diffusion term
can you send me the paper to have a look,

Steve Moore September 7, 2005 22:56

Re: secondary diffusion term
sure... what's your email address? Or can I attach files through this site?


zxaar September 7, 2005 23:14

Re: secondary diffusion term u can mail me on this.

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