[Nek5000-users] Clarification on Adjoint solver

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

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