Modify the interface to allow for spatial dependence on the upwinding

direction for the upwinding derivatives. The directions are specified in a
real 3d array with the sign choosing the upwinding direction.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@64 f69c4107-0314-4c4f-9ad4-17e986b73f4a

1 files changed, 112 insertions, 85 deletions

diff --git a/src/Derivatives_2_1.F90 b/src/Derivatives_2_1.F90
index ed97d9b..4a0adc1 100644
--- a/src/Derivatives_2_1.F90
+++ b/src/Derivatives_2_1.F90
@@ -120,13 +120,11 @@ subroutine up_deriv_gf_2_1 ( var, ni, nj, nk, dir, bb, gsize, delta, up, dvar )
   CCTK_INT, intent(IN) :: bb(2)
   CCTK_INT, intent(IN) :: gsize
   CCTK_REAL, intent(IN) :: delta
-  CCTK_INT, intent(IN) :: up
+  CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: up
   CCTK_REAL, dimension(ni,nj,nk), intent(OUT) :: dvar
 
   CCTK_REAL, dimension(-1:1), save :: a1, a2
-  CCTK_REAL, dimension(-1:1) :: a
   CCTK_REAL, dimension(3,2), save :: q1, q2 
-  CCTK_REAL, dimension(3,2) :: q
   CCTK_REAL :: idel
 
   CCTK_INT :: il, ir, jl, jr, kl, kr
@@ -161,50 +159,55 @@ subroutine up_deriv_gf_2_1 ( var, ni, nj, nk, dir, bb, gsize, delta, up, dvar )
 
   idel = 1.0_wp / delta
 
-  upwinding: select case (up)
-  case (-1) upwinding
-    a = a1
-  case (1) upwinding
-    a = a2
-  end select upwinding
-
   direction: select case (dir)
   case (0) direction
     if ( bb(1) == 0 ) then
       il = 1 + gsize
     else
-      upwinding_xl: select case (up)
-      case (-1) upwinding_xl
-        q = q1
-      case (1) upwinding_xl
-        q = q2
-      end select upwinding_xl
- 
-      dvar(1,:,:) = ( q(1,1) * var(1,:,:) + q(2,1) * var(2,:,:) ) * idel
-      dvar(2,:,:) = ( q(1,2) * var(1,:,:) + q(2,2) * var(2,:,:) + &
-                      q(3,2) * var(3,:,:) ) * idel
+      where ( up(1,:,:) < zero )
+        dvar(1,:,:) = ( q1(1,1) * var(1,:,:) + q1(2,1) * var(2,:,:) ) * idel
+      elsewhere
+        dvar(1,:,:) = ( q2(1,1) * var(1,:,:) + q2(2,1) * var(2,:,:) ) * idel
+      end where
+      where ( up(2,:,:) < zero ) 
+        dvar(2,:,:) = ( q1(1,2) * var(1,:,:) + q1(2,2) * var(2,:,:) + &
+                        q1(3,2) * var(3,:,:) ) * idel
+      elsewhere
+        dvar(2,:,:) = ( q2(1,2) * var(1,:,:) + q2(2,2) * var(2,:,:) + &
+                        q2(3,2) * var(3,:,:) ) * idel
+      end where
       il = 3
     end if
     if ( bb(2) == 0 ) then
       ir = ni - gsize
     else
-      upwinding_xr: select case (up)
-      case (-1) upwinding_xr
-        q = q2
-      case (1) upwinding_xr
-        q = q1
-      end select upwinding_xr
- 
-      dvar(ni-1,:,:) = - ( q(1,2) * var(ni,:,:) + &
-                           q(2,2) * var(ni-1,:,:) + &
-                           q(3,2) * var(ni-2,:,:) ) * idel
-      dvar(ni,:,:) = - ( q(1,1) * var(ni,:,:) + &
-                         q(2,1) * var(ni-1,:,:) ) * idel
+      where ( up(ni-1,:,:) < zero )
+        dvar(ni-1,:,:) = - ( q2(1,2) * var(ni,:,:) + &
+                             q2(2,2) * var(ni-1,:,:) + &
+                             q2(3,2) * var(ni-2,:,:) ) * idel
+      elsewhere
+        dvar(ni-1,:,:) = - ( q1(1,2) * var(ni,:,:) + &
+                             q1(2,2) * var(ni-1,:,:) + &
+                             q1(3,2) * var(ni-2,:,:) ) * idel
+      end where
+      where ( up(ni,:,:) < zero )
+        dvar(ni,:,:) = - ( q2(1,1) * var(ni,:,:) + &
+                           q2(2,1) * var(ni-1,:,:) ) * idel
+      elsewhere
+        dvar(ni,:,:) = - ( q1(1,1) * var(ni,:,:) + &
+                           q1(2,1) * var(ni-1,:,:) ) * idel
+      end where
       ir = ni - 2
     end if
-    dvar(il:ir,:,:) = ( a(-1) * var(il-1:ir-1,:,:) + &
-                        a(0)  * var(il:ir,:,:) + &
-                        a(1)  * var(il+1:ir+1,:,:) ) * idel
+    where ( up(il:ir,:,:) < zero ) 
+      dvar(il:ir,:,:) = ( a1(-1) * var(il-1:ir-1,:,:) + &
+                          a1(0)  * var(il:ir,:,:) + &
+                          a1(1)  * var(il+1:ir+1,:,:) ) * idel
+    elsewhere
+      dvar(il:ir,:,:) = ( a2(-1) * var(il-1:ir-1,:,:) + &
+                          a2(0)  * var(il:ir,:,:) + &
+                          a2(1)  * var(il+1:ir+1,:,:) ) * idel
+    end where
   case (1) direction
     if ( zero_derivs_y /= 0 ) then
       dvar = zero
@@ -212,38 +215,50 @@ subroutine up_deriv_gf_2_1 ( var, ni, nj, nk, dir, bb, gsize, delta, up, dvar )
       if ( bb(1) == 0 ) then
         jl = 1 + gsize
       else
-        upwinding_yl: select case (up)
-        case (-1) upwinding_yl
-          q = q1
-        case (1) upwinding_yl
-          q = q2
-        end select upwinding_yl
- 
-        dvar(:,1,:) = ( q(1,1) * var(:,1,:) + q(2,1) * var(:,2,:) ) * idel
-        dvar(:,2,:) = ( q(1,2) * var(:,1,:) + q(2,2) * var(:,2,:) + &
-                        q(3,2) * var(:,3,:) ) * idel
+        where ( up(:,1,:) < zero )
+          dvar(:,1,:) = ( q1(1,1) * var(:,1,:) + q1(2,1) * var(:,2,:) ) * idel
+        elsewhere
+          dvar(:,1,:) = ( q2(1,1) * var(:,1,:) + q2(2,1) * var(:,2,:) ) * idel
+        end where
+        where ( up(:,2,:) < zero )
+          dvar(:,2,:) = ( q1(1,2) * var(:,1,:) + q1(2,2) * var(:,2,:) + &
+                          q1(3,2) * var(:,3,:) ) * idel
+        elsewhere
+          dvar(:,2,:) = ( q2(1,2) * var(:,1,:) + q2(2,2) * var(:,2,:) + &
+                          q2(3,2) * var(:,3,:) ) * idel
+        end where
         jl = 3
       end if
       if ( bb(2) == 0 ) then
         jr = nj - gsize
       else
-        upwinding_yr: select case (up)
-        case (-1) upwinding_yr
-          q = q2
-        case (1) upwinding_yr
-          q = q1
-        end select upwinding_yr
- 
-        dvar(:,nj-1,:) = - ( q(1,2) * var(:,nj,:) + &
-                             q(2,2) * var(:,nj-1,:) + &
-                             q(3,2) * var(:,nj-2,:) ) * idel
-        dvar(:,nj,:) = - ( q(1,1) * var(:,nj,:) + &
-                           q(2,1) * var(:,nj-1,:) ) * idel
+        where ( up(:,nj-1,:) < zero )
+          dvar(:,nj-1,:) = - ( q2(1,2) * var(:,nj,:) + &
+                               q2(2,2) * var(:,nj-1,:) + &
+                               q2(3,2) * var(:,nj-2,:) ) * idel
+        elsewhere
+          dvar(:,nj-1,:) = - ( q1(1,2) * var(:,nj,:) + &
+                               q1(2,2) * var(:,nj-1,:) + &
+                               q1(3,2) * var(:,nj-2,:) ) * idel
+        end where
+        where ( up(:,nj,:) < zero )
+          dvar(:,nj,:) = - ( q2(1,1) * var(:,nj,:) + &
+                             q2(2,1) * var(:,nj-1,:) ) * idel
+        elsewhere
+          dvar(:,nj,:) = - ( q1(1,1) * var(:,nj,:) + &
+                             q1(2,1) * var(:,nj-1,:) ) * idel
+        end where
         jr = nj - 2
       end if
-      dvar(:,jl:jr,:) = ( a(-1) * var(:,jl-1:jr-1,:) + &
-                          a(0)  * var(:,jl:jr,:) + &
-                          a(1)  * var(:,jl+1:jr+1,:) ) * idel
+      where ( up(:,jl:jr,:) < zero ) 
+        dvar(:,jl:jr,:) = ( a1(-1) * var(:,jl-1:jr-1,:) + &
+                            a1(0)  * var(:,jl:jr,:) + &
+                            a1(1)  * var(:,jl+1:jr+1,:) ) * idel
+      elsewhere
+        dvar(:,jl:jr,:) = ( a2(-1) * var(:,jl-1:jr-1,:) + &
+                            a2(0)  * var(:,jl:jr,:) + &
+                            a2(1)  * var(:,jl+1:jr+1,:) ) * idel
+      end where
     end if
   case (2) direction
     if ( zero_derivs_z /= 0 ) then
@@ -252,38 +267,50 @@ subroutine up_deriv_gf_2_1 ( var, ni, nj, nk, dir, bb, gsize, delta, up, dvar )
       if ( bb(1) == 0 ) then
         kl = 1 + gsize
       else
-        upwinding_zl: select case (up)
-        case (-1) upwinding_zl
-          q = q1
-        case (1) upwinding_zl
-          q = q2
-        end select upwinding_zl
- 
-        dvar(:,:,1) = ( q(1,1) * var(:,:,1) + q(2,1) * var(:,:,2) ) * idel
-        dvar(:,:,2) = ( q(1,2) * var(:,:,1) + q(2,2) * var(:,:,2) + &
-                        q(3,2) * var(:,:,3) ) * idel
+        where ( up(:,:,1) < zero )
+          dvar(:,:,1) = ( q1(1,1) * var(:,:,1) + q1(2,1) * var(:,:,2) ) * idel
+        elsewhere
+          dvar(:,:,1) = ( q2(1,1) * var(:,:,1) + q2(2,1) * var(:,:,2) ) * idel
+        end where
+        where ( up(:,:,2) < zero )  
+          dvar(:,:,2) = ( q1(1,2) * var(:,:,1) + q1(2,2) * var(:,:,2) + &
+                          q1(3,2) * var(:,:,3) ) * idel
+        elsewhere
+          dvar(:,:,2) = ( q2(1,2) * var(:,:,1) + q2(2,2) * var(:,:,2) + &
+                          q2(3,2) * var(:,:,3) ) * idel
+        end where
         kl = 3
       end if
       if ( bb(2) == 0 ) then
         kr = nk - gsize
       else 
-        upwinding_zr: select case (up)
-        case (-1) upwinding_zr
-          q = q2
-        case (1) upwinding_zr
-          q = q1
-        end select upwinding_zr
- 
-        dvar(:,:,nk-1) = - ( q(1,2) * var(:,:,nk) + &
-                             q(2,2) * var(:,:,nk-1) + &
-                             q(3,2) * var(:,:,nk-2) ) * idel
-        dvar(:,:,nk) = - ( q(1,1) * var(:,:,nk) + &
-                           q(2,1) * var(:,:,nk-1) ) * idel
+        where ( up(:,:,nk-1) < zero )
+          dvar(:,:,nk-1) = - ( q2(1,2) * var(:,:,nk) + &
+                               q2(2,2) * var(:,:,nk-1) + &
+                               q2(3,2) * var(:,:,nk-2) ) * idel
+        elsewhere
+          dvar(:,:,nk-1) = - ( q1(1,2) * var(:,:,nk) + &
+                               q1(2,2) * var(:,:,nk-1) + &
+                               q1(3,2) * var(:,:,nk-2) ) * idel
+        end where
+        where ( up(:,:,nk) < zero )
+          dvar(:,:,nk) = - ( q2(1,1) * var(:,:,nk) + &
+                             q2(2,1) * var(:,:,nk-1) ) * idel
+        elsewhere
+          dvar(:,:,nk) = - ( q1(1,1) * var(:,:,nk) + &
+                             q1(2,1) * var(:,:,nk-1) ) * idel
+        end where
         kr = nk - 2
       end if
-      dvar(:,:,kl:kr) = ( a(-1) * var(:,:,kl-1:kr-1) + &
-                          a(0)  * var(:,:,kl:kr) + &
-                          a(1)  * var(:,:,kl+1:kr+1) ) * idel
+      where ( up(:,:,kl:kr) < zero )
+        dvar(:,:,kl:kr) = ( a1(-1) * var(:,:,kl-1:kr-1) + &
+                            a1(0)  * var(:,:,kl:kr) + &
+                            a1(1)  * var(:,:,kl+1:kr+1) ) * idel
+      elsewhere
+        dvar(:,:,kl:kr) = ( a2(-1) * var(:,:,kl-1:kr-1) + &
+                            a2(0)  * var(:,:,kl:kr) + &
+                            a2(1)  * var(:,:,kl+1:kr+1) ) * idel
+      end where
     end if
   end select direction
 end subroutine up_deriv_gf_2_1