[Nek5000-users] Projection of linearized equations onto reduced basis

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

Hey Juan!

It turns out I had been working on a similar problem for the past few days
and came up with a small subroutine. It probably is not the most efficient
way to do it, but it at least work when I use global direct and adjoint
modes . I'll send it to you tomorrow, and if you wanna discuss, I can drop
by ONERA next week.

Cheers.
JC


2014/1/21 <nek5000-users at lists.mcs.anl.gov>

> Hi Neks,
>
> I would like to project the linearized NS equations onto a reduced basis
> formed by some POD modes (velocity vectors).
> We know that the perturbation equations can be read as du(t)/dx = A u(t),
> where
>
> // A = ( -U.grad(u) - u.grad(U) - grad(p) + 1/Re Lap(u)//
>
> To obtain the projected system, I need to compute the matrix Ar_i,j =
>  <U_i, AU_j> where U_j is the j mode (a vector containing the velocity
>  field).
> The step that  I  can't clearly see is the matrix-vector product A U_j.
>  Do  I  have to explicitily compute the matrix A  and then obtain the
> product? or is there a direct  way to  do  it  without this matrix (using
> the time-stepper)?
>
> Thanks in advance!
> Sincerely,
> Juan--
>
>
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-- 
Jean-Christophe Loiseau
Homepage <https://sites.google.com/site/loiseaujc/>
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