Merge branch 'compute-area-nek-expansion' into 'develop'

Compute area nek expansion

See merge request !18

examples/integration_example/integration_example.usr

@@ -20,11 +20,13 @@ c-----------------------------------------------------------------------
       return
       end
 c-----------------------------------------------------------------------
+! Sets the force term in the momentum equation. Use this to set body
+! forces such as gravity. Note that ffx, ffy, and ffz will later be
+! multiplied by the density.
       subroutine userf  (ix,iy,iz,eg)
       include 'SIZE'
       include 'TOTAL'
       include 'NEKUSE'
-      integer e,f,eg
       ffx=0.0
       ffy=0.0
       ffz=0.0
@@ -311,32 +313,35 @@ C=======================================================================
       integer e,f
 
       real*8 fmode(lx1,ly1,lz1,lelt), cache(lx1,ly1,lz1,lelt)
-      real*8 sint, sint1
+      real*8 sint, sint1, sarea, sarea1
+      real*8 pi
 
+      pi=4.0*atan(1.0)
       ntot=nx1*ny1*nz1*nelt
 
-      zmin=glmin(zm1,ntot)
-      zmax=glmax(zm1,ntot)
-
       call rzero(fmode,ntot)
       do i0=1,n_legendre
         do j0=1,m_fourier
           call nek_mode(fmode,i0,j0)
-             sint1=0.0 
+          sarea1=0.0
+          sint1= 0.0
           do e=1,nelt
             do f=1,6
               sint=0.0
+              sarea=0.0
               if (cbc(f,e,1).eq.'W  ') then
                 call col3(cache,fmode,t,ntot)
                 call surface_int(sint,sarea,cache,e,f)
                 sint1=sint1+sint
+                sarea1=sarea1+sarea
               endif
             enddo
           enddo
           call  gop(sint1,wtmp,'+  ',1)
+          call  gop(sarea1,wtmp,'+  ',1)
+!
+          coeff_tij(i0,j0)=sint1*4.0*pi/sarea1
 !
-          coeff_tij(i0,j0)=sint1*2.0/(0.5*(zmax-zmin))
-!         Note that R=0.5 here!!!!
         enddo
       enddo
 
@@ -535,40 +540,46 @@ c-----------------------
       return
       end
 c-----------------------------------------------------------------------
+! calculates Legendre polynomials using a recurrence relationship. If
+! n > the maximum Legendre order, the function returns 0.0.
       function pl_leg(x,n)
-!======================================
-!    calculates Legendre polynomials Pn(x)
-!    using the recurrence relation
-!    if n > 100 the function retuns 0.0
-!======================================
+      parameter (nl_max=100)
       real*8 pl,pl_leg
       real*8 x
       real*8 pln(0:n)
       integer n, k
+
       pln(0) = 1.0
       pln(1) = x
+
       if (n.le.1) then
         pl = pln(n)
-          else
+      else if (n.le.nl_max) then
         do k=1,n-1
-              pln(k+1)=
-     &  ((2.0*k+1.0)*x*pln(k)-dble(k)*pln(k-1))/(dble(k+1))
+          pln(k+1) = ((2.0*k+1.0)*x*pln(k)-dble(k)*pln(k-1))/(dble(k+1))
         end do
         pl = pln(n)
+      else
+        pl = 0.0
       end if
-      pl_leg=pl*sqrt(dble(2*n+1)/2.0)
+
+      pl_leg = pl*sqrt(dble(2*n+1)/2.0)
+
       return
       end
-!======================================
+c-----------------------------------------------------------------------
+! calculates Fourier polynomials Fn(x)
       function fl_four(x,n)
       real*8 fl_four,pi
       real*8 x, A
       integer n, k
+
       pi=4.0*atan(1.0)
-      A=1.0/sqrt(2*pi)
-      if (n.gt.0) A=1.0/sqrt(pi)  
+      A=1.0/sqrt(pi)
+
+      if (n.eq.0) A=1.0/sqrt(2*pi)
       fl_four=A*cos(n*x)
-c       fl_four=1.0/sqrt(pi)
+
       return
       end
 c-----------------------------------------------------------------------