[Nek5000-users] Spectral interpolation of velocity gradients

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

Hi Neks,

I study particles in a turbulent flow and need to know velocity gradients dvi_dxj at particle positions x_p.

In order to do this, I modified the subroutine interp_v(uvw,xyz,n) from the particle tracking example ''hemi''. First, I calculate the velocity gradients with the subroutine gradm1():

                 call gradm1(vxx,vxy,vxz,vx)
                 call gradm1(vyx,vzy,vzz,vy)
                 call gradm1(vzx,vzy,vzz,vz)

Second, I interpolate the velocity gradients to the particle positions with the subroutine intpts():

                 call opcopy(wrk(1,1),wrk(1,2),wrk(1,3),vxx,vyx,vzx)
                 call intpts(wrk,ndm,pts,npart,outint,ifjac,ifpts,ihandle)

I have a few questions regarding this approach:
1. Is intpts() capable of interpolating derived fields like the velocity gradient field?
2. Do you have a good explanatory reference where the mathematical principles behind intpts() are explained?
3. As far as I understand, the fields vx, vy, vz and consequently the derived fields vxx, vxy, vxz, ... are local and defined on the local coordinate fields xm1, ym1, zm1. What is happens if an interpolation point is on a different processor and outside the coordinates stored in xm1, ym1, zm1?

Best regards, Philipp Weiss
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