[Nek5000-users] Further to ffx, ffy and ffz

[nek5000-users at lists.mcs.anl.gov]

Dear Zhai,


ffx will have no impact on the flow if you set p54=-1, p55=1.


The code fixes the flow rate by adding an auxiliary solution,

(U0,p0) such that <U+a*U0> = Ubar, where a is a constant

determined by the equation the requirement that <U+a*U0>=Ubar.


The velocity pressure pair (U0,p0) is the solution to the linear

unsteady Stokes problem:


      (1/dt) U0 - 1/Re \nabla^2 U0 = -grad p0  + F0

         div U0                                 = 0


where F0=[1 , 0 , 0 ] is a unit forcing in the x direction.


If you add your own ffx, then the net forcing will be:


     ffx + a*1


If you don't, it will be "a*1 = a".


Note that if you add your own forcing, then "a" will be smaller

because the preliminary solution, U, will be closer to the target

Ubar value, assuming your ffx value is reasonably close to the

actual mean pressure drop in your system.


Note that because these equations are _linear_ it really doesn't

matter how you satisfy the condition <U+a*U0> = Ubar.


Also, note that, in the above, I've been using "U" to represent the

solution computed by Nek5000  _prior_ to the addition of the auxiliary solution U0.


The real solution that is returned at the end of the tilmestep is:


    U := U + a*U0


    p :=  p + a*p0


(Of course, like U, p and p0 are periodic --- so, the "true" pressure is p + a linear term corresponding to the mean pressure drop...)


The reason I prefer p54/p55 to adjusting ffx via a feedback loop is that the feedback loop introduces its own timescale -- i.e., the response time that you find in any feedback system.   Since we already have multiple timescales in a turbulent flow, I prefer to not add an additional one that is not well characterized.


hth,


Paul


________________________________
From: Nek5000-users <nek5000-users-bounces at lists.mcs.anl.gov> on behalf of nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
Sent: Monday, March 26, 2018 10:39:52 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: [Nek5000-users] Further to ffx, ffy and ffz

Dear Paul and Phillip,

Thanks for your reply.

Paul, I am sorry say that I made an mistake for my question last time.

I intended to ask if I set
P54=-1
P55=1
ffx: non-zero (x is streamwise)

Will the fluid be changed by the effect of non-zero ffx which I am thinking can be considered as the effect of the particles acting on the fluid while I am doing the lagrangian paticle tracking.

By the way, can I fix the pressure gradient as (Re_t/Re_b)^2 for the pipe as well?

Kind regards,

Zhai
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