[hnemati]

Dear all
I am working on Hybrid RANS/LES code for flat plate boundary layer simulation. From RANS area to LES zone I am introducing some random fluctuations to develop turbulence. The problem is that those fluctuations are not div-free and cause my pressure solver become expensive. Does anybody here know how I can add div-free fluctuations (somewhere inside the flow domain, not inlet or outlet)?
Any help is highly appreciated especially to a very stressed person...

[FMDenaro]

Originally Posted by hnemati

Dear all
I am working on Hybrid RANS/LES code for flat plate boundary layer simulation. From RANS area to LES zone I am introducing some random fluctuations to develop turbulence. The problem is that those fluctuations are not div-free and cause my pressure solver become expensive. Does anybody here know how I can add div-free fluctuations (somewhere inside the flow domain, not inlet or outlet)?
Any help is highly appreciated especially to a very stressed person...

Actually, if the fluctuation field added to the initial condition has small magnitude, the non divergence-free field will be corrected immediately at the first time step.
You can find in literature some strategies (that is relevant in the inlet plane), however just try to compute the third component of the velocity field from the relation dw/dz= -(du/dx+dv/dy). That has still some issues but will smooth enough the field.

[hnemati]

Originally Posted by FMDenaro

Actually, if the fluctuation field added to the initial condition has small magnitude, the non-divergence-free field will be corrected immediately at the first time step.
You can find in literature some strategies (that is relevant in the inlet plane), however just try to compute the third component of the velocity field from the relation dw/dz= -(du/dx+dv/dy). That has still some issues but will smooth enough the field.

Dear FMDenaro
Thank you very much for your reply.
I am applying this field every time step in a very small region (see the attached figure) and every time this field is different (this random number is generated based on the turbulent kinetic energy). I already tried what you suggested, but the problem is that the third component (w) will be extended to the areas that I am not interested. I also tried to decompose the fluctuations field to solenoidal and dilatational part and solve the Poisson equation for the solenoidal part and subtract to compute it div-free part. The problem here is that it needs an iterative solver for Poisson equation.

[FMDenaro]

Originally Posted by hnemati

Dear FMDenaro
Thank you very much for your reply.
I am applying this field every time step in a very small region (see the attached figure) and every time this field is different (this random number is generated based on the turbulent kinetic energy). I already tried what you suggested, but the problem is that the third component (w) will be extended to the areas that I am not interested. I also tried to decompose the fluctuations field to solenoidal and dilatational part and solve the Poisson equation for the solenoidal part and subtract to compute it div-free part. The problem here is that it needs an iterative solver for Poisson equation.

That makes no sense to me...why you force it to each time step? Only at the interface between RANS and LES? if you see the literature for the Embedded LES you will find several suggestions?
However, the Poisson problem is still a part of the method you cannot avoid.

[Jonas Holdeman]

Without more deep thought, I would try adding a localized perturbation in the form of a vector potential. Taking the curl of this perturbation should give a localized divergence-free perturbation to the velocity field.

[hnemati]

Originally Posted by FMDenaro

That makes no sense to me...why you force it to each time step? Only at the interface between RANS and LES? if you see the literature for the Embedded LES you will find several suggestions?
However, the Poisson problem is still a part of the method you cannot avoid.

Can you give me some references? Because I could not anything...

[hnemati]

Originally Posted by Jonas Holdeman

Without more deep thought, I would try adding a localized perturbation in the form of a vector potential. Taking the curl of this perturbation should give a localized divergence-free perturbation to the velocity field.

I have tried it, but in discretized form, it is not working. u = grad(phi)+ curl(psi) is the way that you mean. u is know and by taking the div of both sides we have laplacian (phi) = div(u). by solving laplacian we have phi and sumbracting u-grad(phi) should give me the filed that I want. but since I am solving it numaricallly, it has some error.

[FMDenaro]

Originally Posted by hnemati

I have tried it, but in discretized form, it is not working. u = grad(phi)+ curl(psi) is the way that you mean. u is know and by taking the div of both sides we have laplacian (phi) = div(u). by solving laplacian we have phi and sumbracting u-grad(phi) should give me the filed that I want. but since I am solving it numaricallly, it has some error.

The Hodge decomposition works both in the continuous and discrete formulation. Be careful to the type of collocation (staggered or non-staggered colocation) and boundary conditions you are using, I suspect you did some errors. Without errors, it gives a divergence-free up to numerical precision.
Have a look here
https://www.researchgate.net/publica...ary_conditions