[Nek5000-users] Clarification on Adjoint solver

Mon Feb 8 03:26:35 CST 2016

Hi Saleh

If I understand you correctly, you ask about a base flow, i.e. the 
velocity field you do your linearisation about (the one you use to 
advect prturbation). If this is the case, than it is possible to do with 
nek. Otherwise you have to wait for the code Oana mentioned. What we do 
in our stability calculations, we take the solution of non-linear NS 
(steady state reached with e.g. SFD) and next we load it into nek as 
non-linear filed. One can do it by setting restart options in ###.rea 
file. It should look like:
    3.33333       3.33333     -0.833333      -1.16667 XFAC,YFAC,XZERO,YZERO
  **MESH DATA** 1st line is X of corner 1,2,3,4. 2nd line is Y.
        -1472  2          1472     NELT,NDIM,NELV
            1  PRESOLVE/RESTART OPTIONS  *****
bfext_cyl?.f00000
            7          INITIAL CONDITIONS *****
C Default
C Default

Where bfext_cyl0.f00000 is our restart file (we usually save this 
velocity field in double precision). Next you have to set linear solver 
with non-evolving base flow (nek is able to evolve both so be careful). 
You freeze baseflow by setting negative value of parameter 31 in ###.rea:
    0.00000     p030 > 0 ==> properties set in uservp()
   -1.00000     p031 NPERT: #perturbation modes
    0.00000     p032 #BCs in re2 file, if > 0

Nek is able of evolving number of perturbation fields set by 
abs(param(31)) (in ###.rea) and lpert in SIZE. I have to mention that 
nek by itself outputs the non-linear fields only, so to see perturbation 
you should add to your userchk something like this

       subroutine userchk

       include 'SIZE'            ! NX1, NY1, NZ1, NELV, NIO
       include 'TSTEP'           ! ISTEP, IOSTEP
       include 'SOLN'            ! V[XYZ]P, TP
       include 'INPUT'           ! IF3D, PARAM
       include 'ADJOINT'         ! IFADJ

!     direct or adjoint run
       IFADJ = .FALSE.

!     write perturbation field
       if (mod(ISTEP,int(PARAM(15))).eq.0) then
          call outpost2(VXP,VYP,VZP,PRP,TP,0,'prt')
       endif

I hope it is an answer to your question.
regards
adam

On 2016-02-06 19:15, nek5000-users at lists.mcs.anl.gov wrote:
> Hi Saleh,
>
> There is no easily accessible implementation for this, one has to do the change of the velocities himself. In fact we have ongoing work on this and once we are done I guess we can share it.
> What kind of case are you looking at, long time horizons are quite tricky to handle. We can take this conversation off the mailing list if needed.
>
> Oana
>
>
>
> ________________________________________
> From: nek5000-users-bounces at lists.mcs.anl.gov [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: Friday, February 05, 2016 2:15 PM
> To: nek5000-users at lists.mcs.anl.gov
> Subject: Re: [Nek5000-users] Clarification on Adjoint solver
>
> Adams,
>
> I really appreciate your detailed answer. I definitely clarified the Nek
> functionality for adjoint solvers. One question remains is how to
> include the velocity of the forward solver into adjoint equations. I
> assume this is also the case when you do linear stability analysis with
> Nek, since the velocity in convective terms is not completely part of
> the solution. Mathematically, my question is:
>
> in $V. \nabla u_a$ term, as the advection, how can we substitute $V$ (as
> the forward velocity which is already solved for in a regular NS
> solution) in adjoint equations. suppose that the velocity, along with
> other quantities are saved in afield out put such as fld.f0000X for X
> time-step. So we have access to that velocity but how can we include it
> in adjoint equations?
>
> Many thanks again,
> Saleh
>
> On 2/2/2016 3:09 AM, nek5000-users at lists.mcs.anl.gov wrote:
>> Hi
>>
>> The adjoint implementation in nek assumes change of the direction of
>> time evolution. The goal is to use the standard nek solver with
>> minimal modifications (only advection terms have to be changed). You
>> get these equations from you standard one by changing the time and
>> pressure sign (t -> -t; p-> -p). This of course changes your time
>> integration limits, but it shouldn't be a problem. So when you  have
>> your linear direct simulation, to turn it into dual one it is enough
>> to include  in your userchk include files ADJOINT and TSTEP, and for
>> ISTEP.eq.0 set IFADJOINT to true. Something like:
>>        subroutine userchk
>>
>>        include 'SIZE'
>>        include 'TSTEP'           ! ISTEP
>>        include 'ADJOINT'            ! IFADJ
>>
>>        if(ISTEP.eq.0) ADJOINT=.TRUE.
>>
>> There is no need to modify ###.rea or ###.map files. The only problem
>> are boundary conditions for open flows, as they would require
>> non-homogeneous bc. In this case to avoid problems we usually use
>> sufficiently large domain together with zero Dirichlet bc. The last
>> issue is sufficient resolution for both direct and adjoin runs. I hope
>> this gives you some idea about nek implementation.
>> Regards
>> Adam
>>
>> On 2016-02-01 22:17, nek5000-users at lists.mcs.anl.gov wrote:
>>> Hi Neks,
>>>
>>> To my knowledge, Nek5000 is able to solve adjoint equations of the form:
>>> $\partial u_a/\partial t + V.\nabla u_a - u_a.(\nabla V)^T + \nabla
>>> \p_a + 1/Re \nabla^2 u_a=0$ and $\nabla.u_a=0$
>>> where u_a and p_a are adjoint velocity and pressure. (Slightly
>>> different formulation may be seen in literature).
>>>
>>> Let's assume the forward problem is already solved so that $V$, i.e.
>>> velocity, (and possibly $p$ as the pressure) is (are) already know.
>>> Thus, the initial and boundary conditions for adjoint NS are also
>>> known. How can we now solve the dual/adjoint NS problem with Nek5000?
>>> Is there any example on how to modify .rea files? Specailly, the
>>> "convection term of $V.\nabla u_a - u_a.(\nabla V)^T$ needs to be
>>> modified compared to forward NS but am not sure how.
>>> My search of mailing list entails some modifications in "perturb.f"
>>> subroutine, but a little bit more clarification on that would be
>>> really appreciated.
>>>
>>> Yours,
>>> Saleh
>>> _______________________________________________
>>> Nek5000-users mailing list
>>> Nek5000-users at lists.mcs.anl.gov
>>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
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