What does bm1 represent in glsc3?

[Chinthaka Jacob]

Dear Nek Community,

  I am after a quick verification of an implementation. I am computing the volume-integrated squared velocity gradient (see attached equation), and the snippet below is from userchk.

  My understanding is that bm1 stores the lumped nodal volume weight so that summing bm1 over all nodes recovers the domain volume. Is this assumption correct? If not, what is the recommended/most accurate way to evaluate this integral?

Thanks,
Chinthaka.

c-----------------------------------------------------------------------

      subroutine userchk

      include 'SIZE'

      include 'TOTAL'

      real viscous_diss

      parameter(lt=lx1*ly1*lz1*lelv)

      common /myjunk/ dxux(lx1,ly1,lz1,lelv),

     $     dxuz(lx1,ly1,lz1,lelv),dyux(lx1,ly1,lz1,lelv),

     $     dyuz(lx1,ly1,lz1,lelv),dzux(lx1,ly1,lz1,lelv),

     $     dzuz(lx1,ly1,lz1,lelv),dxuy(lx1,ly1,lz1,lelv),

     $     dyuy(lx1,ly1,lz1,lelv),dzuy(lx1,ly1,lz1,lelv)

       call gradm1(dxux,dyux,dzux,vx) ! 1st derivative

       call gradm1(dxuy,dyuy,dzuy,vy)

       call gradm1(dxuz,dyuz,dzuz,vz)

       viscous_diss = (glsc3(dxux,bm1,dxux,lt)

     $   +glsc3(dyux,bm1,dyux,lt)+glsc3(dzuz,bm1,dzuz,lt)

     $   +glsc3(dzux,bm1,dzux,lt)+glsc3(dxuy,bm1,dxuy,lt)

     $   +glsc3(dyuy,bm1,dyuy,lt)+glsc3(dzuy,bm1,dzuy,lt)

     $   +glsc3(dxuz,bm1,dxuz,lt)+glsc3(dyuz,bm1,dyuz,lt))

      return

      end

c-----------------------------------------------------------------------

[Philipp Schlatter]

yes, that seems correct to me. bm1 is the (lumped) mass matrix.

Philipp

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[Fischer, Paul]

Correct.

 bm1 is the diagonal mass matrix on "mesh 1"  (the velocity mesh on the GLL points)

 bm2 is the diagonal mass matrix on "mesh 2"  (the pressure mesh)

For PN-PN (equal order pressure and velocity approximations), bm1 == bm2.

For PN-PN-2, bm2 is the diagonal mass matrix on the Gauss-Legendre (GL) points

---

From: nek...@googlegroups.com <nek...@googlegroups.com> on behalf of Philipp Schlatter <psch...@gmail.com>
Sent: Monday, September 8, 2025 3:54 AM
To: nek...@googlegroups.com <nek...@googlegroups.com>
Subject: Re: [nek5000] What does bm1 represent in glsc3?

 

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