[Nek5000-users] 2D simulation for 3D perturbation mode with a 2D baseflow

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

Hi Neks,

I have a 2D baseflow and I am doing 3D perturbation mode calculation at 
a prescribed spatial wavelength lambda=2pi/k (k the wavenumber) in the 
third direction. The baseflow is assumed to be invariant in this third 
direction therefore the perturbation can be chosen in the form 
u=uhat(x,y,t) e(ikz) where z is the third direction and u=(u,v,w) and 
the baseflow is in the form (U,V)(x,y) (in particular W=0).

In this case the 3D linearized equations simplify to the following form
duhat/dx+dvhat/dy+kwhat=0
duhat/dt + U duhat/dx + V duhat/dy = -uhat dU/dx - vhat dU/dy + nu ( 
d^2uhat/dxx+d^2uhat/dyy-k^2uhat )
dvhat/dt + U dvhat/dx + V dvhat/dy = -uhat dV/dx - vhat dV/dy + nu ( 
d^2vhat/dxx+d^2vhat/dyy-k^2vhat )
dwhat/dt + U dwhat/dx + V dwhat/dy =  nu ( d^2what/dxx+d^2what/dyy-k^2what )

I am currently doing 3D perturbation simulations with the box dimension 
in the third dimension set to lambda but I was wondering if Nek offers 
the possibility to run 2D simulations instead to solve for uhat(x,y,t).

Indeed in the above equations, one does not need any mesh in the z 
direction. A 2D mesh is enough but this means modifying slightly the 
linearized equations to insert the k terms.

I have been looking in the source files and I have found nothing like 
that so I guess this is not currently in Nek.
Any idea if that would be possible/easy to implement?

Thanks a lot,

Vincent.