<p><b>ringler@lanl.gov</b> 2010-09-01 16:54:29 -0600 (Wed, 01 Sep 2010)</p><p><br>
adopted updated module_advection.F routine that is currently<br>
being tested in branches/atmos_nonhydrostatic.<br>
<br>
this routine deals with jumps in {X,Y,Z}Cell locations that <br>
occur across periodic boundaries.<br>
<br>
the adoption of this new routine requires the addition<br>
of a few variables in Registry that are not directly related<br>
to advection.<br>
</p><hr noshade><pre><font color="gray">Modified: branches/ocean_projects/advection/src/core_ocean/Registry
===================================================================
--- branches/ocean_projects/advection/src/core_ocean/Registry 2010-09-01 22:39:16 UTC (rev 490)
+++ branches/ocean_projects/advection/src/core_ocean/Registry 2010-09-01 22:54:29 UTC (rev 491)
@@ -106,6 +106,13 @@
var real deriv_two ( FIFTEEN TWO nEdges ) o deriv_two - -
var integer advCells ( TWENTYONE nCells ) - advCells - -
+# !! NOTE: the following arrays are needed to allow the use
+# !! of the module_advection.F w/o alteration
+# Space needed for deformation calculation weights
+var real defc_a ( maxEdges nCells ) - defc_a - -
+var real defc_b ( maxEdges nCells ) - defc_b - -
+var real kdiff ( nVertLevels nCells Time ) - kdiff - -
+
# Arrays required for reconstruction of velocity field
var real coeffs_reconstruct ( R3 maxEdges nCells ) - coeffs_reconstruct - -
Modified: branches/ocean_projects/advection/src/core_ocean/module_advection.F
===================================================================
--- branches/ocean_projects/advection/src/core_ocean/module_advection.F 2010-09-01 22:39:16 UTC (rev 490)
+++ branches/ocean_projects/advection/src/core_ocean/module_advection.F 2010-09-01 22:54:29 UTC (rev 491)
@@ -58,6 +58,7 @@
logical, parameter :: reset_poly = .true.
real (kind=RKIND) :: rcell, cos2t, costsint, sin2t
+ real (kind=RKIND), dimension(grid%maxEdges) :: angle_2d
!---
@@ -152,8 +153,18 @@
else ! On an x-y plane
do i=1,n-1
- xp(i) = grid % xCell % array(cell_list(i)) - grid % xCell % array(iCell)
- yp(i) = grid % yCell % array(cell_list(i)) - grid % yCell % array(iCell)
+
+ angle_2d(i) = grid%angleEdge%array(grid % EdgesOnCell % array(i,iCell))
+ iEdge = grid % EdgesOnCell % array(i,iCell)
+ if ( iCell .ne. grid % CellsOnEdge % array(1,iEdge)) &
+ angle_2d(i) = angle_2d(i) - pii
+
+! xp(i) = grid % xCell % array(cell_list(i)) - grid % xCell % array(iCell)
+! yp(i) = grid % yCell % array(cell_list(i)) - grid % yCell % array(iCell)
+
+ xp(i) = grid % dcEdge % array(grid % EdgesOnCell % array(i,iCell)) * cos(angle_2d(i))
+ yp(i) = grid % dcEdge % array(grid % EdgesOnCell % array(i,iCell)) * sin(angle_2d(i))
+
end do
end if
@@ -271,9 +282,11 @@
else
thetae(2,grid % EdgesOnCell % array (i,iCell)) = thetae_tmp
end if
- else
- xe(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (xv1 + xv2)
- ye(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (yv1 + yv2)
+! else
+!
+! xe(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (xv1 + xv2)
+! ye(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (yv1 + yv2)
+
end if
end do
@@ -312,13 +325,36 @@
+ 2.*sin2t*bmatrix(6,j)
end do
end if
+
else
- do j=1,n
- deriv_two(j,1,iEdge) = 2.*xe(iEdge)*xe(iEdge)*bmatrix(4,j) &
- + 2.*xe(iEdge)*ye(iEdge)*bmatrix(5,j) &
- + 2.*ye(iEdge)*ye(iEdge)*bmatrix(6,j)
- deriv_two(j,2,iEdge) = deriv_two(j,1,iEdge)
- end do
+
+ cos2t = cos(angle_2d(i))
+ sin2t = sin(angle_2d(i))
+ costsint = cos2t*sin2t
+ cos2t = cos2t**2
+ sin2t = sin2t**2
+
+! do j=1,n
+!
+! deriv_two(j,1,iEdge) = 2.*xe(iEdge)*xe(iEdge)*bmatrix(4,j) &
+! + 2.*xe(iEdge)*ye(iEdge)*bmatrix(5,j) &
+! + 2.*ye(iEdge)*ye(iEdge)*bmatrix(6,j)
+! end do
+
+ if (iCell == grid % cellsOnEdge % array(1,iEdge)) then
+ do j=1,n
+ deriv_two(j,1,iEdge) = 2.*cos2t*bmatrix(4,j) &
+ + 2.*costsint*bmatrix(5,j) &
+ + 2.*sin2t*bmatrix(6,j)
+ end do
+ else
+ do j=1,n
+ deriv_two(j,2,iEdge) = 2.*cos2t*bmatrix(4,j) &
+ + 2.*costsint*bmatrix(5,j) &
+ + 2.*sin2t*bmatrix(6,j)
+ end do
+ end if
+
end if
end do
@@ -326,6 +362,25 @@
if (debug) stop
+
+! write(0,*) ' check for deriv2 coefficients, iEdge 4 '
+!
+! iEdge = 4
+! j = 1
+! iCell = grid % cellsOnEdge % array(1,iEdge)
+! write(0,*) ' j, icell, coef ',j,iCell,deriv_two(j,1,iEdge)
+! do j=2,7
+! write(0,*) ' j, icell, coef ',j,grid % CellsOnCell % array(j-1,iCell),deriv_two(j,1,iEdge)
+! end do
+!
+! j = 1
+! iCell = grid % cellsOnEdge % array(2,iEdge)
+! write(0,*) ' j, icell, coef ',j,iCell,deriv_two(j,2,iEdge)
+! do j=2,7
+! write(0,*) ' j, icell, coef ',j,grid % CellsOnCell % array(j-1,iCell),deriv_two(j,2,iEdge)
+! end do
+! stop
+
end subroutine initialize_advection_rk
@@ -685,4 +740,194 @@
!
END SUBROUTINE ELGS
+!-------------------------------------------------------------
+
+ subroutine initialize_deformation_weights( grid )
+
+!
+! compute the cell coefficients for the deformation calculations
+! WCS, 13 July 2010
+!
+ implicit none
+
+ type (grid_meta), intent(in) :: grid
+
+ real (kind=RKIND), dimension(:,:), pointer :: defc_a, defc_b
+ integer, dimension(:,:), pointer :: cellsOnEdge, edgesOnCell
+
+! local variables
+
+ real (kind=RKIND), dimension(2, grid % nEdges) :: thetae
+ real (kind=RKIND), dimension(grid % nEdges) :: xe, ye
+ real (kind=RKIND), dimension(grid % nCells) :: theta_abs
+
+ real (kind=RKIND), dimension(25) :: xc, yc, zc ! cell center coordinates
+ real (kind=RKIND), dimension(25) :: thetav, thetat, dl_sphere
+ real (kind=RKIND) :: xm, ym, zm, dl, xec, yec, zec
+ real (kind=RKIND) :: thetae_tmp, xe_tmp, ye_tmp
+ real (kind=RKIND) :: xv1, xv2, yv1, yv2, zv1, zv2
+ integer :: i, j, k, ip1, ip2, m, n, ip1a, ii
+ integer :: iCell, iEdge
+ real (kind=RKIND) :: pii
+ real (kind=RKIND) :: x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, x5, y5
+ real (kind=RKIND) :: pdx1, pdx2, pdx3, pdy1, pdy2, pdy3, dx1, dx2, dy1, dy2
+ real (kind=RKIND) :: angv1, angv2, dl1, dl2
+ real (kind=RKIND), dimension(25) :: dxe, dye, x2v, y2v, xp, yp, xpt, ypt
+
+ real (kind=RKIND) :: length_scale
+ integer :: ma,na, cell_add, mw, nn
+ integer, dimension(25) :: cell_list
+
+ integer :: cell1, cell2, iv
+ logical :: do_the_cell
+ real (kind=RKIND) :: area_cell, sint2, cost2, sint_cost, sumw1, sumw2, xptt, area_cellt
+
+ logical, parameter :: debug = .false.
+
+ if (debug) write(0,*) ' in def weight calc '
+
+ defc_a => grid % defc_a % array
+ defc_b => grid % defc_b % array
+ cellsOnEdge => grid % cellsOnEdge % array
+ edgesOnCell => grid % edgesOnCell % array
+
+ defc_a(:,:) = 0.
+ defc_b(:,:) = 0.
+
+ pii = 2.*asin(1.0)
+
+ if (debug) write(0,*) ' beginning cell loop '
+
+ do iCell = 1, grid % nCells
+
+ if (debug) write(0,*) ' cell loop ', iCell
+
+ cell_list(1) = iCell
+ do i=2, grid % nEdgesOnCell % array(iCell)+1
+ cell_list(i) = grid % CellsOnCell % array(i-1,iCell)
+ end do
+ n = grid % nEdgesOnCell % array(iCell) + 1
+
+! check to see if we are reaching outside the halo
+
+ if (debug) write(0,*) ' points ', n
+
+ do_the_cell = .true.
+ do i=1,n
+ if (cell_list(i) > grid % nCells) do_the_cell = .false.
+ end do
+
+
+ if (.not. do_the_cell) cycle
+
+
+! compute poynomial fit for this cell if all needed neighbors exist
+ if (grid % on_a_sphere) then
+
+ xc(1) = grid % xCell % array(iCell)/a
+ yc(1) = grid % yCell % array(iCell)/a
+ zc(1) = grid % zCell % array(iCell)/a
+
+
+ do i=2,n
+ iv = grid % verticesOnCell % array(i-1,iCell)
+ xc(i) = grid % xVertex % array(iv)/a
+ yc(i) = grid % yVertex % array(iv)/a
+ zc(i) = grid % zVertex % array(iv)/a
+ end do
+
+ theta_abs(iCell) = pii/2. - sphere_angle( xc(1), yc(1), zc(1), &
+ xc(2), yc(2), zc(2), &
+ 0., 0., 1. )
+
+! angles from cell center to neighbor centers (thetav)
+
+ do i=1,n-1
+
+ ip2 = i+2
+ if (ip2 > n) ip2 = 2
+
+ thetav(i) = sphere_angle( xc(1), yc(1), zc(1), &
+ xc(i+1), yc(i+1), zc(i+1), &
+ xc(ip2), yc(ip2), zc(ip2) )
+
+ dl_sphere(i) = a*arc_length( xc(1), yc(1), zc(1), &
+ xc(i+1), yc(i+1), zc(i+1) )
+ end do
+
+ length_scale = 1.
+ do i=1,n-1
+ dl_sphere(i) = dl_sphere(i)/length_scale
+ end do
+
+ thetat(1) = 0. ! this defines the x direction, cell center 1 ->
+! thetat(1) = theta_abs(iCell) ! this defines the x direction, longitude line
+ do i=2,n-1
+ thetat(i) = thetat(i-1) + thetav(i-1)
+ end do
+
+ do i=1,n-1
+ xp(i) = cos(thetat(i)) * dl_sphere(i)
+ yp(i) = sin(thetat(i)) * dl_sphere(i)
+ end do
+
+ else ! On an x-y plane
+
+ xp(1) = grid % xCell % array(iCell)
+ yp(1) = grid % yCell % array(iCell)
+
+
+ do i=2,n
+ iv = grid % verticesOnCell % array(i-1,iCell)
+ xp(i) = grid % xVertex % array(iv)
+ yp(i) = grid % yVertex % array(iv)
+ end do
+
+ end if
+
+! thetat(1) = 0.
+ thetat(1) = theta_abs(iCell)
+ do i=2,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ thetat(i) = plane_angle( 0.,0.,0., &
+ xp(i)-xp(i-1), yp(i)-yp(i-1), 0., &
+ xp(ip1)-xp(i), yp(ip1)-yp(i), 0., &
+ 0., 0., 1.)
+ thetat(i) = thetat(i) + thetat(i-1)
+ end do
+
+ area_cell = 0.
+ area_cellt = 0.
+ do i=1,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ dl = sqrt((xp(ip1)-xp(i))**2 + (yp(ip1)-yp(i))**2)
+ area_cell = area_cell + 0.25*(xp(i)+xp(ip1))*(yp(ip1)-yp(i)) - 0.25*(yp(i)+yp(ip1))*(xp(ip1)-xp(i))
+ area_cellt = area_cellt + (0.25*(xp(i)+xp(ip1))*cos(thetat(i)) + 0.25*(yp(i)+yp(ip1))*sin(thetat(i)))*dl
+ end do
+ if (debug) write(0,*) ' area_cell, area_cellt ',area_cell, area_cellt,area_cell-area_cellt
+
+ do i=1,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ dl = sqrt((xp(ip1)-xp(i))**2 + (yp(ip1)-yp(i))**2)
+ sint2 = (sin(thetat(i)))**2
+ cost2 = (cos(thetat(i)))**2
+ sint_cost = sin(thetat(i))*cos(thetat(i))
+ defc_a(i,iCell) = dl*(cost2 - sint2)/area_cell
+ defc_b(i,iCell) = dl*2.*sint_cost/area_cell
+ if (cellsOnEdge(1,EdgesOnCell(i,iCell)) /= iCell) then
+ defc_a(i,iCell) = - defc_a(i,iCell)
+ defc_b(i,iCell) = - defc_b(i,iCell)
+ end if
+
+ end do
+
+ end do
+
+ if (debug) write(0,*) ' exiting def weight calc '
+
+ end subroutine initialize_deformation_weights
+
end module advection
Modified: branches/ocean_projects/advection/src/core_sw/Registry
===================================================================
--- branches/ocean_projects/advection/src/core_sw/Registry 2010-09-01 22:39:16 UTC (rev 490)
+++ branches/ocean_projects/advection/src/core_sw/Registry 2010-09-01 22:54:29 UTC (rev 491)
@@ -93,6 +93,13 @@
var real deriv_two ( FIFTEEN TWO nEdges ) o deriv_two - -
var integer advCells ( TWENTYONE nCells ) - advCells - -
+# !! NOTE: the following arrays are needed to allow the use
+# !! of the module_advection.F w/o alteration
+# Space needed for deformation calculation weights
+var real defc_a ( maxEdges nCells ) - defc_a - -
+var real defc_b ( maxEdges nCells ) - defc_b - -
+var real kdiff ( nVertLevels nCells Time ) - kdiff - -
+
# Arrays required for reconstruction of velocity field
var real coeffs_reconstruct ( R3 maxEdges nCells ) - coeffs_reconstruct - -
Modified: branches/ocean_projects/advection/src/core_sw/module_advection.F
===================================================================
--- branches/ocean_projects/advection/src/core_sw/module_advection.F 2010-09-01 22:39:16 UTC (rev 490)
+++ branches/ocean_projects/advection/src/core_sw/module_advection.F 2010-09-01 22:54:29 UTC (rev 491)
@@ -58,6 +58,7 @@
logical, parameter :: reset_poly = .true.
real (kind=RKIND) :: rcell, cos2t, costsint, sin2t
+ real (kind=RKIND), dimension(grid%maxEdges) :: angle_2d
!---
@@ -152,8 +153,18 @@
else ! On an x-y plane
do i=1,n-1
- xp(i) = grid % xCell % array(cell_list(i)) - grid % xCell % array(iCell)
- yp(i) = grid % yCell % array(cell_list(i)) - grid % yCell % array(iCell)
+
+ angle_2d(i) = grid%angleEdge%array(grid % EdgesOnCell % array(i,iCell))
+ iEdge = grid % EdgesOnCell % array(i,iCell)
+ if ( iCell .ne. grid % CellsOnEdge % array(1,iEdge)) &
+ angle_2d(i) = angle_2d(i) - pii
+
+! xp(i) = grid % xCell % array(cell_list(i)) - grid % xCell % array(iCell)
+! yp(i) = grid % yCell % array(cell_list(i)) - grid % yCell % array(iCell)
+
+ xp(i) = grid % dcEdge % array(grid % EdgesOnCell % array(i,iCell)) * cos(angle_2d(i))
+ yp(i) = grid % dcEdge % array(grid % EdgesOnCell % array(i,iCell)) * sin(angle_2d(i))
+
end do
end if
@@ -271,9 +282,11 @@
else
thetae(2,grid % EdgesOnCell % array (i,iCell)) = thetae_tmp
end if
- else
- xe(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (xv1 + xv2)
- ye(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (yv1 + yv2)
+! else
+!
+! xe(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (xv1 + xv2)
+! ye(grid % EdgesOnCell % array (i,iCell)) = 0.5 * (yv1 + yv2)
+
end if
end do
@@ -312,13 +325,36 @@
+ 2.*sin2t*bmatrix(6,j)
end do
end if
+
else
- do j=1,n
- deriv_two(j,1,iEdge) = 2.*xe(iEdge)*xe(iEdge)*bmatrix(4,j) &
- + 2.*xe(iEdge)*ye(iEdge)*bmatrix(5,j) &
- + 2.*ye(iEdge)*ye(iEdge)*bmatrix(6,j)
- deriv_two(j,2,iEdge) = deriv_two(j,1,iEdge)
- end do
+
+ cos2t = cos(angle_2d(i))
+ sin2t = sin(angle_2d(i))
+ costsint = cos2t*sin2t
+ cos2t = cos2t**2
+ sin2t = sin2t**2
+
+! do j=1,n
+!
+! deriv_two(j,1,iEdge) = 2.*xe(iEdge)*xe(iEdge)*bmatrix(4,j) &
+! + 2.*xe(iEdge)*ye(iEdge)*bmatrix(5,j) &
+! + 2.*ye(iEdge)*ye(iEdge)*bmatrix(6,j)
+! end do
+
+ if (iCell == grid % cellsOnEdge % array(1,iEdge)) then
+ do j=1,n
+ deriv_two(j,1,iEdge) = 2.*cos2t*bmatrix(4,j) &
+ + 2.*costsint*bmatrix(5,j) &
+ + 2.*sin2t*bmatrix(6,j)
+ end do
+ else
+ do j=1,n
+ deriv_two(j,2,iEdge) = 2.*cos2t*bmatrix(4,j) &
+ + 2.*costsint*bmatrix(5,j) &
+ + 2.*sin2t*bmatrix(6,j)
+ end do
+ end if
+
end if
end do
@@ -326,6 +362,25 @@
if (debug) stop
+
+! write(0,*) ' check for deriv2 coefficients, iEdge 4 '
+!
+! iEdge = 4
+! j = 1
+! iCell = grid % cellsOnEdge % array(1,iEdge)
+! write(0,*) ' j, icell, coef ',j,iCell,deriv_two(j,1,iEdge)
+! do j=2,7
+! write(0,*) ' j, icell, coef ',j,grid % CellsOnCell % array(j-1,iCell),deriv_two(j,1,iEdge)
+! end do
+!
+! j = 1
+! iCell = grid % cellsOnEdge % array(2,iEdge)
+! write(0,*) ' j, icell, coef ',j,iCell,deriv_two(j,2,iEdge)
+! do j=2,7
+! write(0,*) ' j, icell, coef ',j,grid % CellsOnCell % array(j-1,iCell),deriv_two(j,2,iEdge)
+! end do
+! stop
+
end subroutine initialize_advection_rk
@@ -685,4 +740,194 @@
!
END SUBROUTINE ELGS
+!-------------------------------------------------------------
+
+ subroutine initialize_deformation_weights( grid )
+
+!
+! compute the cell coefficients for the deformation calculations
+! WCS, 13 July 2010
+!
+ implicit none
+
+ type (grid_meta), intent(in) :: grid
+
+ real (kind=RKIND), dimension(:,:), pointer :: defc_a, defc_b
+ integer, dimension(:,:), pointer :: cellsOnEdge, edgesOnCell
+
+! local variables
+
+ real (kind=RKIND), dimension(2, grid % nEdges) :: thetae
+ real (kind=RKIND), dimension(grid % nEdges) :: xe, ye
+ real (kind=RKIND), dimension(grid % nCells) :: theta_abs
+
+ real (kind=RKIND), dimension(25) :: xc, yc, zc ! cell center coordinates
+ real (kind=RKIND), dimension(25) :: thetav, thetat, dl_sphere
+ real (kind=RKIND) :: xm, ym, zm, dl, xec, yec, zec
+ real (kind=RKIND) :: thetae_tmp, xe_tmp, ye_tmp
+ real (kind=RKIND) :: xv1, xv2, yv1, yv2, zv1, zv2
+ integer :: i, j, k, ip1, ip2, m, n, ip1a, ii
+ integer :: iCell, iEdge
+ real (kind=RKIND) :: pii
+ real (kind=RKIND) :: x0, y0, x1, y1, x2, y2, x3, y3, x4, y4, x5, y5
+ real (kind=RKIND) :: pdx1, pdx2, pdx3, pdy1, pdy2, pdy3, dx1, dx2, dy1, dy2
+ real (kind=RKIND) :: angv1, angv2, dl1, dl2
+ real (kind=RKIND), dimension(25) :: dxe, dye, x2v, y2v, xp, yp, xpt, ypt
+
+ real (kind=RKIND) :: length_scale
+ integer :: ma,na, cell_add, mw, nn
+ integer, dimension(25) :: cell_list
+
+ integer :: cell1, cell2, iv
+ logical :: do_the_cell
+ real (kind=RKIND) :: area_cell, sint2, cost2, sint_cost, sumw1, sumw2, xptt, area_cellt
+
+ logical, parameter :: debug = .false.
+
+ if (debug) write(0,*) ' in def weight calc '
+
+ defc_a => grid % defc_a % array
+ defc_b => grid % defc_b % array
+ cellsOnEdge => grid % cellsOnEdge % array
+ edgesOnCell => grid % edgesOnCell % array
+
+ defc_a(:,:) = 0.
+ defc_b(:,:) = 0.
+
+ pii = 2.*asin(1.0)
+
+ if (debug) write(0,*) ' beginning cell loop '
+
+ do iCell = 1, grid % nCells
+
+ if (debug) write(0,*) ' cell loop ', iCell
+
+ cell_list(1) = iCell
+ do i=2, grid % nEdgesOnCell % array(iCell)+1
+ cell_list(i) = grid % CellsOnCell % array(i-1,iCell)
+ end do
+ n = grid % nEdgesOnCell % array(iCell) + 1
+
+! check to see if we are reaching outside the halo
+
+ if (debug) write(0,*) ' points ', n
+
+ do_the_cell = .true.
+ do i=1,n
+ if (cell_list(i) > grid % nCells) do_the_cell = .false.
+ end do
+
+
+ if (.not. do_the_cell) cycle
+
+
+! compute poynomial fit for this cell if all needed neighbors exist
+ if (grid % on_a_sphere) then
+
+ xc(1) = grid % xCell % array(iCell)/a
+ yc(1) = grid % yCell % array(iCell)/a
+ zc(1) = grid % zCell % array(iCell)/a
+
+
+ do i=2,n
+ iv = grid % verticesOnCell % array(i-1,iCell)
+ xc(i) = grid % xVertex % array(iv)/a
+ yc(i) = grid % yVertex % array(iv)/a
+ zc(i) = grid % zVertex % array(iv)/a
+ end do
+
+ theta_abs(iCell) = pii/2. - sphere_angle( xc(1), yc(1), zc(1), &
+ xc(2), yc(2), zc(2), &
+ 0., 0., 1. )
+
+! angles from cell center to neighbor centers (thetav)
+
+ do i=1,n-1
+
+ ip2 = i+2
+ if (ip2 > n) ip2 = 2
+
+ thetav(i) = sphere_angle( xc(1), yc(1), zc(1), &
+ xc(i+1), yc(i+1), zc(i+1), &
+ xc(ip2), yc(ip2), zc(ip2) )
+
+ dl_sphere(i) = a*arc_length( xc(1), yc(1), zc(1), &
+ xc(i+1), yc(i+1), zc(i+1) )
+ end do
+
+ length_scale = 1.
+ do i=1,n-1
+ dl_sphere(i) = dl_sphere(i)/length_scale
+ end do
+
+ thetat(1) = 0. ! this defines the x direction, cell center 1 ->
+! thetat(1) = theta_abs(iCell) ! this defines the x direction, longitude line
+ do i=2,n-1
+ thetat(i) = thetat(i-1) + thetav(i-1)
+ end do
+
+ do i=1,n-1
+ xp(i) = cos(thetat(i)) * dl_sphere(i)
+ yp(i) = sin(thetat(i)) * dl_sphere(i)
+ end do
+
+ else ! On an x-y plane
+
+ xp(1) = grid % xCell % array(iCell)
+ yp(1) = grid % yCell % array(iCell)
+
+
+ do i=2,n
+ iv = grid % verticesOnCell % array(i-1,iCell)
+ xp(i) = grid % xVertex % array(iv)
+ yp(i) = grid % yVertex % array(iv)
+ end do
+
+ end if
+
+! thetat(1) = 0.
+ thetat(1) = theta_abs(iCell)
+ do i=2,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ thetat(i) = plane_angle( 0.,0.,0., &
+ xp(i)-xp(i-1), yp(i)-yp(i-1), 0., &
+ xp(ip1)-xp(i), yp(ip1)-yp(i), 0., &
+ 0., 0., 1.)
+ thetat(i) = thetat(i) + thetat(i-1)
+ end do
+
+ area_cell = 0.
+ area_cellt = 0.
+ do i=1,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ dl = sqrt((xp(ip1)-xp(i))**2 + (yp(ip1)-yp(i))**2)
+ area_cell = area_cell + 0.25*(xp(i)+xp(ip1))*(yp(ip1)-yp(i)) - 0.25*(yp(i)+yp(ip1))*(xp(ip1)-xp(i))
+ area_cellt = area_cellt + (0.25*(xp(i)+xp(ip1))*cos(thetat(i)) + 0.25*(yp(i)+yp(ip1))*sin(thetat(i)))*dl
+ end do
+ if (debug) write(0,*) ' area_cell, area_cellt ',area_cell, area_cellt,area_cell-area_cellt
+
+ do i=1,n-1
+ ip1 = i+1
+ if (ip1 == n) ip1 = 1
+ dl = sqrt((xp(ip1)-xp(i))**2 + (yp(ip1)-yp(i))**2)
+ sint2 = (sin(thetat(i)))**2
+ cost2 = (cos(thetat(i)))**2
+ sint_cost = sin(thetat(i))*cos(thetat(i))
+ defc_a(i,iCell) = dl*(cost2 - sint2)/area_cell
+ defc_b(i,iCell) = dl*2.*sint_cost/area_cell
+ if (cellsOnEdge(1,EdgesOnCell(i,iCell)) /= iCell) then
+ defc_a(i,iCell) = - defc_a(i,iCell)
+ defc_b(i,iCell) = - defc_b(i,iCell)
+ end if
+
+ end do
+
+ end do
+
+ if (debug) write(0,*) ' exiting def weight calc '
+
+ end subroutine initialize_deformation_weights
+
end module advection
</font>
</pre>