[Nek5000-users] dealias; mass matrix; interp_rstd

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

Dear Sandeep,


Look for routines intp_rst, grad_rstd, etc., and calls to them

in convect.f and induct.f


There are several routines that map onto the finer GL mesh

from the base GLL mesh.


The metrics,   J*dr/dx,  J*dr/dy, etc., are already on the fine

mesh and collocated with the quadrature weight on that fine

mesh when they are constructed (in set_dealias_rx in induct.f).


The mathematics of these procedure is described in Sec. 3 of


Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry

  *   Johan Malm,
  *   Philipp Schlatter
  *   Paul F. Fischer
  *   Dan S. Henningson



NOTE:  After you create your nonlinear source term, you

should divide the value each point x_{ijke}  by bm1(i,j,k,e),

because Nek multiplies the entry in qvol by bm1(i,j,k,e).

In your case, however, you've already accounted for the mass

matrix by incorporated the mass matrix on the fine-GL points.


I would set up your u x nabla term via a call to userchk

and store the result (already divided by bm1), then just

dereference it inside qvol.  via:


      subroutine qvol(i,j,k,eg)

      ...

      ...

      common /mynonlin/ s(lx1,ly1,lz1,lelt,ldim)

      integer e,eg

      e=gllel(eg)

      qvol=s(i,j,k,e,ifield-2)

      return

      end


or something like that.


The time step will all be correct and you will get 2nd or

3rd-order accuracy in time via Nek's standard BDFk/EXTk


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: Wednesday, May 23, 2018 4:50:19 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: [Nek5000-users] dealias; mass matrix; interp_rstd

Dear Neks,
I solve
\partial A/\partial t = \nabla^2 A + u x Curl A,
where A = (s1,s2,s3)
I solve three scalar equations with respective components of u x Curl A as forcing terms in qvol.
I would like to compute the dealiased product of u x Curl A
I build my code based on kov_stokes_test.usr and  subroutines in induct.f
I compute local curl, project curl and U onto fine mesh, perform product and project the product back to coarse mesh using interp_rstd
However, I am not sure about the multiplication of mass matrices for the product in these subroutines.

I attach my usr, rea and SIZE files.
Your suggestions are welcome.
Thanks,
Sandeep
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