Hi all.
Lately I am performing an URANS simulation with a 2-phase fluid. The domain is devided into 2 parts: a steady region and a rotating region. The interface model is the sliding mesh approach. The turbulence closure is obtained by the SST-komega model.
I selected a variable time step to achive for each step a suitable Courant number. Observing the convergence history and the time step values, automatically selected during the simulation, I figured out that up to now (in my case study) the best stability is reached when the Courant number is lower than 1/2. Maybe the problem is a bit diffusive. In few words this means I am working with an average time step of about 10^-8 sec ...
A week ago I fall into a first order discretization scheme that automatically adjust the time step locally so that the Courant Number is locally limited by an user specified value.Well, once I used this scheme the average time step skipped to about 5*10^-7 sec. In OpenFOAM this scheme is called CoEuler (in OF2.3, localEuler in OF30x). Up to know I do not find how does the scheme work.
Could you please tell me where I can find a description of this scheme? papers or books where I can read about this?
Thank you in advance.
Cheers, Vincenzo
Try to seach on the CFD-online forum. There are a lot of material and a lot of discussions: maybe you will find something. Otherwise search the function in the OF code and try to understand how it works from there.
Franco
Tnx Franco, I just do this, but did not find anything. Cheers, Vincenzo
Dear Malik, I just read the source code....to me it is not really clear. It seems like the scheme estimates a local time step according to the higher value between 1 and the MaxCo you settled in the fvscheme file at the temporal discretization section. Thank you
I think that the Courant number is simply computed at each time-step based on the computed velocity field and the time-step is accordingly updated for computing the next time step. For the first order Euler equation this is quite simple.
Dear Filippo, here I am talking about the "local time adaptation" scheme adopted in the CoEuler method based on the simple Euler first-order numerical procedure. You are right, but in this case the scheme is a bit different.
Finally I have found the answer I was looking for. The "random" reading of "The OpenFOAM Technogy Primer" book let me to figure out that the CoEuler scheme adjusts the time step locally so that the LOCAL Courant number is limited by a specified value (say maxCo). The scheme computes a local time step field using the current time step value and a scaling coefficient field computed from the local courant number field (Cof). The reciprocal of the Courant number limited local time step (1/dt_fCo) is calculated:
(dt_fco)^-1 = max [(Cof/maxCo), 1]*(dt^-1)
The Cof is the local face centered Courant number.
This way the temporal derivate is evaluated locally. So a local estimation of the temporal derivate based on the Local Courant Number allows for larger time steps to be applied in those parts of the flow where Courant Number are lower. Thus the simulation speed is increased: numerical time is artificially going faster in those part of the domain, since the flow there is expected to experiece a smaller amount of change (OpenFOAM Technology Primer pp.108-109). Thank you for the suggestions. Regards
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