First attempt at upwinding SBP operators. Don't use yet. They will change

soon to be more flexible.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@62 f69c4107-0314-4c4f-9ad4-17e986b73f4a

1 files changed, 292 insertions, 0 deletions

diff --git a/src/Derivatives_4_2.F90 b/src/Derivatives_4_2.F90
index 7fc40b1..85e7ab3 100644
--- a/src/Derivatives_4_2.F90
+++ b/src/Derivatives_4_2.F90
@@ -166,3 +166,295 @@ subroutine deriv_gf_4_2 ( var, ni, nj, nk, dir, bb, gsize, delta, dvar )
     end if
   end select direction
 end subroutine deriv_gf_4_2
+
+subroutine up_deriv_gf_4_2 ( var, ni, nj, nk, dir, bb, gsize, delta, up, dvar )
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_REAL, parameter :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  CCTK_INT, intent(IN) :: ni, nj, nk
+  CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: var
+  CCTK_INT, intent(IN) :: dir
+  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(OUT) :: dvar
+
+  CCTK_REAL, dimension(-2:2), save :: a1, a2
+  CCTK_REAL, dimension(-2:2) :: a
+  CCTK_REAL, dimension(6,4), save :: q1, q2
+  CCTK_REAL, dimension(6,4) :: q
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    a1(-2) = 0.1666666666666666666666666666666666666667_wp
+    a1(-1) = -1.000000000000000000000000000000000000000_wp
+    a1(0) = 0.5000000000000000000000000000000000000000_wp
+    a1(1) = 0.3333333333333333333333333333333333333333_wp
+    a1(2) = 0_wp
+
+    q1(1,1) = -1.176470588235294117647058823529411764706_wp
+    q1(2,1) = 1.264705882352941176470588235294117647059_wp
+    q1(3,1) = 0_wp
+    q1(4,1) = -0.08823529411764705882352941176470588235294_wp
+    q1(5,1) = 0_wp
+    q1(6,1) = 0_wp
+    q1(1,2) = -0.6355932203389830508474576271186440677966_wp
+    q1(2,2) = 0.3389830508474576271186440677966101694915_wp
+    q1(3,2) = 0.2288135593220338983050847457627118644068_wp
+    q1(4,2) = 0.06779661016949152542372881355932203389831_wp
+    q1(5,2) = 0_wp
+    q1(6,2) = 0_wp
+    q1(1,3) = 0.1860465116279069767441860465116279069767_wp
+    q1(2,3) = -1.058139534883720930232558139534883720930_wp
+    q1(3,3) = 0.5581395348837209302325581395348837209302_wp
+    q1(4,3) = 0.3139534883720930232558139534883720930233_wp
+    q1(5,3) = 0_wp
+    q1(6,3) = 0_wp
+    q1(1,4) = 0.03061224489795918367346938775510204081633_wp
+    q1(2,4) = 0.08163265306122448979591836734693877551020_wp
+    q1(3,4) = -0.9285714285714285714285714285714285714286_wp
+    q1(4,4) = 0.4897959183673469387755102040816326530612_wp
+    q1(5,4) = 0.3265306122448979591836734693877551020408_wp
+    q1(6,4) = 0_wp
+
+    a2(-2) = 0_wp
+    a2(-1) = -0.3333333333333333333333333333333333333333_wp
+    a2(0) = -0.5000000000000000000000000000000000000000_wp
+    a2(1) = 1.000000000000000000000000000000000000000_wp
+    a2(2) = -0.1666666666666666666666666666666666666667_wp
+
+    q2(1,1) = -1.647058823529411764705882352941176470588_wp
+    q2(2,1) = 2.205882352941176470588235294117647058824_wp
+    q2(3,1) = -0.4705882352941176470588235294117647058824_wp
+    q2(4,1) = -0.08823529411764705882352941176470588235294_wp
+    q2(5,1) = 0_wp
+    q2(6,1) = 0_wp
+    q2(1,2) = -0.3644067796610169491525423728813559322034_wp
+    q2(2,2) = -0.3389830508474576271186440677966101694915_wp
+    q2(3,2) = 0.7711864406779661016949152542372881355932_wp
+    q2(4,2) = -0.06779661016949152542372881355932203389831_wp
+    q2(5,2) = 0_wp
+    q2(6,2) = 0_wp
+    q2(1,3) = 0_wp
+    q2(2,3) = -0.3139534883720930232558139534883720930233_wp
+    q2(3,3) = -0.5581395348837209302325581395348837209302_wp
+    q2(4,3) = 1.058139534883720930232558139534883720930_wp
+    q2(5,3) = -0.1860465116279069767441860465116279069767_wp
+    q2(6,3) = 0_wp
+    q2(1,4) = 0.03061224489795918367346938775510204081633_wp
+    q2(2,4) = -0.08163265306122448979591836734693877551020_wp
+    q2(3,4) = -0.2755102040816326530612244897959183673469_wp
+    q2(4,4) = -0.4897959183673469387755102040816326530612_wp
+    q2(5,4) = 0.9795918367346938775510204081632653061224_wp
+    q2(6,4) = -0.1632653061224489795918367346938775510204_wp
+
+    first = .false.
+  end if
+
+  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,:,:) + &
+                      q(3,1) * var(3,:,:) + q(4,1) * var(4,:,:) ) * idel
+      dvar(2,:,:) = ( q(1,2) * var(1,:,:) + q(2,2) * var(2,:,:) + &
+                      q(3,2) * var(3,:,:) + q(4,2) * var(4,:,:) ) * idel
+      dvar(3,:,:) = ( q(1,3) * var(1,:,:) + q(2,3) * var(2,:,:) + &
+                      q(3,3) * var(3,:,:) + q(4,3) * var(4,:,:) + &
+                      q(5,3) * var(5,:,:) ) * idel
+      dvar(4,:,:) = ( q(1,4) * var(1,:,:) + q(2,4) * var(2,:,:) + &
+                      q(3,4) * var(3,:,:) + q(4,4) * var(4,:,:) + &
+                      q(5,4) * var(5,:,:) + q(6,4) * var(6,:,:) ) * idel
+      il = 5
+    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-3,:,:) = - ( q(1,4) * var(ni,:,:) + &
+                           q(2,4) * var(ni-1,:,:) + &
+                           q(3,4) * var(ni-2,:,:) + &
+                           q(4,4) * var(ni-3,:,:) + &
+                           q(5,4) * var(ni-4,:,:) + &
+                           q(6,4) * var(ni-5,:,:) ) * idel
+      dvar(ni-2,:,:) = - ( q(1,3) * var(ni,:,:) + &
+                           q(2,3) * var(ni-1,:,:) + &
+                           q(3,3) * var(ni-2,:,:) + &
+                           q(4,3) * var(ni-3,:,:) + &
+                           q(5,3) * var(ni-4,:,:) ) * idel
+      dvar(ni-1,:,:) = - ( q(1,2) * var(ni,:,:) + &
+                           q(2,2) * var(ni-1,:,:) + &
+                           q(3,2) * var(ni-2,:,:) + &
+                           q(4,2) * var(ni-3,:,:) ) * idel
+      dvar(ni,:,:) = - ( q(1,1) * var(ni,:,:) + &
+                         q(2,1) * var(ni-1,:,:) + &
+                         q(3,1) * var(ni-2,:,:) + &
+                         q(4,1) * var(ni-3,:,:) ) * idel
+      ir = ni - 4
+    end if
+    dvar(il:ir,:,:) = ( a(-2) * var(il-2:ir-2,:,:) + &
+                        a(-1) * var(il-1:ir-1,:,:) + &
+                        a(0)  * var(il:ir,:,:) + &
+                        a(1)  * var(il+1:ir+1,:,:) + &
+                        a(2)  * var(il+2:ir+2,:,:) ) * idel
+  case (1) direction
+    if ( zero_derivs_y /= 0 ) then
+      dvar = zero
+    else
+      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,:) + &
+                        q(3,1) * var(:,3,:) + q(4,1) * var(:,4,:) ) * idel
+        dvar(:,2,:) = ( q(1,2) * var(:,1,:) + q(2,2) * var(:,2,:) + &
+                        q(3,2) * var(:,3,:) + q(4,2) * var(:,4,:) ) * idel
+        dvar(:,3,:) = ( q(1,3) * var(:,1,:) + q(2,3) * var(:,2,:) + &
+                        q(3,3) * var(:,3,:) + q(4,3) * var(:,4,:) + &
+                        q(5,3) * var(:,5,:) ) * idel
+        dvar(:,4,:) = ( q(1,4) * var(:,1,:) + q(2,4) * var(:,2,:) + &
+                        q(3,4) * var(:,3,:) + q(4,4) * var(:,4,:) + &
+                        q(5,4) * var(:,5,:) + q(6,4) * var(:,6,:) ) * idel
+        jl = 5
+      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-3,:) = - ( q(1,4) * var(:,nj,:) + &
+                             q(2,4) * var(:,nj-1,:) + &
+                             q(3,4) * var(:,nj-2,:) + &
+                             q(4,4) * var(:,nj-3,:) + &
+                             q(5,4) * var(:,nj-4,:) + &
+                             q(6,4) * var(:,nj-5,:) ) * idel
+        dvar(:,nj-2,:) = - ( q(1,3) * var(:,nj,:) + &
+                             q(2,3) * var(:,nj-1,:) + &
+                             q(3,3) * var(:,nj-2,:) + &
+                             q(4,3) * var(:,nj-3,:) + &
+                             q(5,3) * var(:,nj-4,:) ) * idel
+        dvar(:,nj-1,:) = - ( q(1,2) * var(:,nj,:) + &
+                             q(2,2) * var(:,nj-1,:) + &
+                             q(3,2) * var(:,nj-2,:) + &
+                             q(4,2) * var(:,nj-3,:) ) * idel
+        dvar(:,nj,:) = - ( q(1,1) * var(:,nj,:) + &
+                           q(2,1) * var(:,nj-1,:) + &
+                           q(3,1) * var(:,nj-2,:) + &
+                           q(4,1) * var(:,nj-3,:) ) * idel
+        jr = nj - 4
+      end if
+      dvar(:,jl:jr,:) = ( a(-2) * var(:,jl-2:jr-2,:) + &
+                          a(-1) * var(:,jl-1:jr-1,:) + &
+                          a(0)  * var(:,jl:jr,:) + &
+                          a(1)  * var(:,jl+1:jr+1,:) + &
+                          a(2)  * var(:,jl+2:jr+2,:) ) * idel
+    end if
+  case (2) direction
+    if ( zero_derivs_z /= 0 ) then
+      dvar = zero
+    else
+      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) + &
+                        q(3,1) * var(:,:,3) + q(4,1) * var(:,:,4) ) * idel
+        dvar(:,:,2) = ( q(1,2) * var(:,:,1) + q(2,2) * var(:,:,2) + &
+                        q(3,2) * var(:,:,3) + q(4,2) * var(:,:,4) ) * idel
+        dvar(:,:,3) = ( q(1,3) * var(:,:,1) + q(2,3) * var(:,:,2) + &
+                        q(3,3) * var(:,:,3) + q(4,3) * var(:,:,4) + &
+                        q(5,3) * var(:,:,5) ) * idel
+        dvar(:,:,4) = ( q(1,4) * var(:,:,1) + q(2,4) * var(:,:,2) + &
+                        q(3,4) * var(:,:,3) + q(4,4) * var(:,:,4) + &
+                        q(5,4) * var(:,:,5) + q(6,4) * var(:,:,6) ) * idel
+        kl = 5
+      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-3) = - ( q(1,4) * var(:,:,nk) + &
+                             q(2,4) * var(:,:,nk-1) + &
+                             q(3,4) * var(:,:,nk-2) + &
+                             q(4,4) * var(:,:,nk-3) + &
+                             q(5,4) * var(:,:,nk-4) + &
+                             q(6,4) * var(:,:,nk-5) ) * idel
+        dvar(:,:,nk-2) = - ( q(1,3) * var(:,:,nk) + &
+                             q(2,3) * var(:,:,nk-1) + &
+                             q(3,3) * var(:,:,nk-2) + &
+                             q(4,3) * var(:,:,nk-3) + &
+                             q(5,3) * var(:,:,nk-4) ) * idel
+        dvar(:,:,nk-1) = - ( q(1,2) * var(:,:,nk) + &
+                             q(2,2) * var(:,:,nk-1) + &
+                             q(3,2) * var(:,:,nk-2) + &
+                             q(4,2) * var(:,:,nk-3) ) * idel
+        dvar(:,:,nk) = - ( q(1,1) * var(:,:,nk) + &
+                           q(2,1) * var(:,:,nk-1) + &
+                           q(3,1) * var(:,:,nk-2) + &
+                           q(4,1) * var(:,:,nk-3) ) * idel
+        kl = nk - 4
+      end if
+      dvar(:,:,kl:kr) = ( a(-2) * var(:,:,kl-2:kr-2) + &
+                          a(-1) * var(:,:,kl-1:kr-1) + &
+                          a(0)  * var(:,:,kl:kr) + &
+                          a(1)  * var(:,:,kl+1:kr+1) + &
+                          a(2)  * var(:,:,kl+2:kr+2) ) * idel
+    end if
+  end select direction
+end subroutine up_deriv_gf_4_2