Wall unit normal

[Filipe Brandao]

Hi,

I am trying to implement a BC in userbc that I may need to use the variables unx, uny and unz which are the x, y, and z components of face unit normal, repectively.

I thought that by accessing them inside the userbc subroutine, we only would have access to the values of the boundary face, but we actually have access to the all the 6 faces of the element adjacent to the wall. How can we know which face exactly is the one at the boundary?

Thanks,
Filipe

[YuHsiang Lan]

Hi Filipe,

I assume you want to add surface integral term via userbc like this

  flux = Fx * unx + Fy * uny + Fz * unz

This can be tricky because we pass the volumetric index (ix,iy,iz,iel) to userbc.

And, what you really want is the face index (ia,iface,iel)

Nek5000 typically maps from face index to the volume one 

like this:

         DO 2000 IE=1,NEL
         DO 2000 IFACE=1,NFACES
            IA=0
            CALL FACIND (KX1,KX2,KY1,KY2,KZ1,KZ2,lx1,ly1,lz1,IFACE)
            DO 200 IZ=KZ1,KZ2
            DO 200 IY=KY1,KY2
            DO 200 IX=KX1,KX2
               IA = IA + 1
               S(IX,IY,IZ,IE) = S(IX,IY,IZ,IE) +
     $            HC*AREA(IA,1,IFACE,IE)/BM1(IX,IY,IZ,IE)

but the reverse mapping is rarely used (it's also not unique on edges and corners)

Two approaches to consider:

a). You could define dummy arrays for each face and assign values in userchk:

    real my_flux(lx1,ly1,lz1,6,lelt)

    common /my_fld/ my_flux

    ! set up my_flux

    and then reference them in userbc

    iel = gllel(ieg)

    flux = my_flux(ix,iy,iz,iface,iel)

    However, this requires 6 volume arrays, which is quite a waste as we only care of some surface point.

    Face based array is required. Otherwise, edges will be double counted.

    The is an exception: if the desired face doesn't intersect with other faces with Neumann BC.

b). Add surface integral to right hand side like userq

    (Also see BCNEUSC in bdry.f in terms of how to select the faces)

    What you eventually need is 

         q(ix,iy,iz,ie) = q(ix,iy,iz,ie) 

     $                  + flux(ia,1,iface,ie) * conductivity * area(ia,1,iface,ie) / bm1(ix,iy,iz,ie)

    You can then save 1 volume array, pre-compute it in userchk, and reference it in userq via a common block.

Note that, a) and b) are not identical:

a) computes the flux based on current solution and use it as Neumann BC for the next.

b) directly computes the needed surface integral at right hand side. Then, Nek will do extrapolation on the top of it.

I'd assume b) is more accurate but can sometimes be unstable depending on how dynamic the BC changes.

Hope this helps,

Yu-Hsiang

--

[Fischer, Paul]

Hi Yu-Hsiang,

I see I did not reply all...  pasting here.

Paul

The "f" variable indicates the face, "eg" indicates the global element number --- local to the processor is given by:

      Integer e,eg,f

      e = gllel(eg)

f is in the range [1:6] for 3D, [1:ndim] for ndim = 2 or 3

The following should provide your desired unit normals for any face data that is passed to userbc(),

 which is called point-by-point but only for faces that have BCs which are user functions.

        subroutine userbc(i,j,k,f,eg)

      

        include 'SIZE'

        include 'TOTAL'

      

        integer e,eg,f

      

        e = gllel(eg)  ! Local element number

      

        if (f.eq.1.or.f.eq.3) then

           ip=i

           jp=k

        elseif (f.eq.2.or.f.eq.4) then   

           ip=j  

           jp=k  

        else     

           ip=i

           jp=j

        endif

         

        unl = unx(ip,jp,f,e)

        vnl = uny(ip,jp,f,e)

        wnl = unz(ip,jp,f,e)

            

            

You should test this to make sure it conforms with your intuition.

Look at subroutine setedge in connect1.f for the preprocessor face

notation, which governs the assignment of "f" to faces.

---

From: nek...@googlegroups.com <nek...@googlegroups.com> on behalf of YuHsiang Lan <seanl...@gmail.com>
Sent: Saturday, June 20, 2026 9:41 PM
To: Nek5000 <nek...@googlegroups.com>
Subject: [nek5000] Re: Wall unit normal

 

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