!--------------------------------------------------------------------------
   !---------------------------- compute_vorticity ----------------------------------
   !$OMP DO SCHEDULE(STATIC)
   DO ij = 1, dual_num
      ! this VLOOP iterates over dual cell edges
      SELECT CASE(dual_deg(ij))
      CASE(3)
         edge1 = dual_edge(1,ij)
         edge2 = dual_edge(2,ij)
         edge3 = dual_edge(3,ij)
         de1 = de(edge1)
         de2 = de(edge2)
         de3 = de(edge3)
         sign1 = dual_ne(1,ij)
         sign2 = dual_ne(2,ij)
         sign3 = dual_ne(3,ij)
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            etav = etav + sign1*ue(l,edge1)*de1
            etav = etav + sign2*ue(l,edge2)*de2
            etav = etav + sign3*ue(l,edge3)*de3
            vort(l,ij) = etav / Av(ij)
         END DO
      CASE(4)
         edge1 = dual_edge(1,ij)
         edge2 = dual_edge(2,ij)
         edge3 = dual_edge(3,ij)
         edge4 = dual_edge(4,ij)
         de1 = de(edge1)
         de2 = de(edge2)
         de3 = de(edge3)
         de4 = de(edge4)
         sign1 = dual_ne(1,ij)
         sign2 = dual_ne(2,ij)
         sign3 = dual_ne(3,ij)
         sign4 = dual_ne(4,ij)
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            etav = etav + sign1*ue(l,edge1)*de1
            etav = etav + sign2*ue(l,edge2)*de2
            etav = etav + sign3*ue(l,edge3)*de3
            etav = etav + sign4*ue(l,edge4)*de4
            vort(l,ij) = etav / Av(ij)
         END DO
      CASE DEFAULT
         !DIR$ SIMD
         DO l = 1, llm
            etav = 0.d0
            DO iedge = 1, dual_deg(ij)
               edge = dual_edge(iedge,ij)
               etav = etav + dual_ne(iedge,ij)*ue(l,edge)*de(edge)
            END DO
            vort(l,ij) = etav / Av(ij)
         END DO
      END SELECT
   END DO
   !$OMP END DO
   !---------------------------- compute_vorticity ----------------------------------
   !--------------------------------------------------------------------------