Hi,

I've a three-D compressible, finite volume, runge-kutta, edge-based solver, that uses Roe's FDS for the convective terms. Its turbulence model for RANS is k-e, high Reynolds number version, with wall functions, and the kato-Launder mod for the production term. I get unstable results for this, and I know it's to do with the needing to scale the time step by using a point implicit treatment of the k-e source terms. In fact there is already one in there but it doesn't work very well. The time marching as I've said is just plain old multi-stage RK, which I've no intention of changing, and the time-step computation is just based on the cfl and an additional viscous criteria.

Can anybody help with how to scale the time step based on the largest of the turbulence source terms?? Any papers that you could suggest??

I know its needs to be something like

new_time_step = old_time_step/( 1 + old_time_step*max(dS(rk)/dk, dS(re)/de) )

where rk is rho.tke and re is rho.tdr . S is the source terms for these, in fact usually it's only the negative component of the spectral radius that is used, so just the destruction term in the k-equation for example.

Anyway, anybody that's up on this and has some useful suggestion or papers....

Cheers

Andy

Dear Andy,

It is fine if you do not siwtch over from R/K, but source term treatment is very important. I do have a paper with me on the source term treatment by Prof. Dick and his group which I can sent to you. However, you would find more details in his AIAA Jl. paper whose soft copy I do not have, but I can provide you with the reference.

Regards,

Andy

Hi,

It would be great if you could send me the electronic copy, and the reference for the AIAA Journal. Any other material or support material would be great.

My email address is andy.john.parker@gmail.com

Many thanks again,

Andy

Hi,

I've manged to get the 2000 AIAA paper by Dick, I assume it was that year, vol 38, I'd still like the other one though. It's on the lines of what I want but a) it's for incompressible flow, and I'd like to see the equations cast for the compressible time-step reduction b) it's a nice paper, but not actually clear on how one implements it.

I'm really just after a formula that reduces the compressible normal CFL timestep, by using the jacobians of the k-e source terms, nothing more complicated, I know this will work for various reasons. And again, not interested in reformulating the time integration to be implicit. The code is fully parallel and I've just implemented reactive flow, so I'm not in a position at the moment to make large changes like that, all I really want is a fix!

Any thoughts would be more than welcome, given the above.

Cheers

Andy

something which you might be interested in

www-woolf.uta.edu/arc/dissertations/Thesis-Prashaanth.pdf

I am still puzzled about Dick's paper. on things like how dPk/dk terms are evaluated ... it is not mentioned in the paper.

B. Merci, J. Steelant , J. Vierendeels, K. Riemslagh and E. Dick, Computational Treatment of Source Terms in Two-Equation Turbulence Models, AIAA Journal, Vol. 38, No. 11, pp 2085-2093, November 2000.