#include "misc.h"
module dynamics_vars 13,2
!BOP
!
! !MODULE: dynamics_vars --- Lin-Rood specific variables and methods
!
! !USES:
use shr_kind_mod, only: r8 => shr_kind_r8
!
! WS: ultimately we would like to uncouple fvcore from
! pmgrid since the latter has dependencies on params.h
! All of the follow variables could go in spmd_dyn
!
use pmgrid, only : twod_decomp, strip3dxyz, strip3dxzy, &
strip3dxzyp, strip3dxyzp, strip3kxyz, &
strip3kxyzp, strip3kxzy, strip3kxzyp
! !PUBLIC MEMBER FUNCTIONS:
public dynamics_init, dynamics_clean
! !PUBLIC DATA MEMBERS:
!--------------------------------------------------------
! Local variables specific to the Lin-Rood dynamical core
!--------------------------------------------------------
! Temporary variables to be removed at a later time
real(r8), allocatable, save :: yzt(:,:,:)
real(r8), allocatable, save :: yzt2(:,:,:)
real(r8), allocatable, save :: q3t(:,:,:,:)
! Variables set by dynamics_init
real(r8) dtime ! large time step
integer iord ! order of LR scheme in X
integer jord ! order of LR scheme in Y
integer im, jm, km ! global dimensions
integer nq ! number of tracers (adv. and non-adv)
integer ifirstxy, ilastxy !
integer jfirstxy, jlastxy !
integer jfirstyz, jlastyz !
integer kfirstyz, klastyz !
! General variables set by setrig
real (r8) pi
real(r8) dl ! Radians per (finite-volume) longitude
real(r8) dp ! Radians per (finite-volume) latitude
! Geometric arrays set by setrig
real(r8), allocatable, save :: cosp(:) ! Cos of latitude angle - volume mean
real(r8), allocatable, save :: sinp(:) ! Sin of latitude angle - volume mean
real(r8), allocatable, save :: cose(:) ! Cos of finite-volume edges
real(r8), allocatable, save :: sine(:) ! Sin of finite-volume edges
! Variables set by set_eta
real(r8) ptop ! pressure at top of atmosphere
real(r8) pint ! pressure at sig-p interface
real(r8), allocatable, save :: ak(:) ! A's of the ETA-coordinate
real(r8), allocatable, save :: bk(:) ! B's of the ETA-coordinate
integer ks ! Total number of pure-P layers
! Scalars set in dynpkg_init
integer icd, jcd
integer ng_c ! ghost zone needed by the c-gird dynamics
integer ng_d ! ghost zone needed by the d-gird dynamics
integer ng_s ! for certain arrays, max(ng_c+1,ng_d)
real (r8) acap ! scaled polar cap area
real (r8) rcap ! inverse of scaled polar cap area
! Arrays initialized by dynpkg_init
real(r8), allocatable, save :: coslon(:) ! Cos of longitudes - volume center
real(r8), allocatable, save :: sinlon(:) ! Sin of longitudes - volume center
real(r8), allocatable, save :: cosl5(:) ! Cos of longitudes - volume center
real(r8), allocatable, save :: sinl5(:) ! Sin of longitudes - volume center
real(r8), allocatable, save :: acosp(:)
! Scalars initialized by d_split
integer ns ! total number of splits for Lagrangian dynamics
!
! !DESCRIPTION:
!
! This module provides variables which are specific to the Lin-Rood
! dynamical core. Most of them were previously SAVE variables in
! different routines and were set with an "if (first)" statement.
!
! \begin{tabular}{|l|l|} \hline \hline
! lr\_init & Initialize the Lin-Rood variables \\ \hline
! lr\_clean & Deallocate all internal data structures \\ \hline
! \hline
! \end{tabular}
!
! !REVISION HISTORY:
! 01.06.06 Sawyer Consolidated from various code snippets
! 01.07.12 Sawyer Removed CCM common blocks comtim.h and commap.h
! 03.06.25 Sawyer Cleaned up, used ParPatternCopy (Create)
! 03.07.23 Sawyer Removed dependencies on params.h, constituents
! 03.08.05 Sawyer Removed rayf_init and hswf_init, related vars
! 03.08.13 Sawyer Removed xyt (no longer used)
! 03.10.31 Mirin Removed unneeded ghostings, comm. patterns
! 03.11.11 Mirin Added mod_method (opt. arg. parpatterncreate)
!
! !BUGS:
! o Where does the value of ns0 come from??
!
!EOP
!-----------------------------------------------------------------------
contains
!-----------------------------------------------------------------------
!BOP
! !IROUTINE: dynamics_init --- initialize the lin-rood dynamical core
!
! !INTERFACE:
subroutine dynamics_init( dtime_in, iord_in, jord_in, nsplit_in, & 2,5
im_in, jm_in, km_in, nq_in, &
ifirstxy_in, ilastxy_in, &
jfirstxy_in, jlastxy_in, &
jfirstyz_in, jlastyz_in, &
kfirstyz_in, klastyz_in )
! !USES:
implicit none
! !INPUT PARAMETERS:
real (r8), intent(in) :: dtime_in ! Large time step
integer, intent(in) :: iord_in ! Order of LR scheme in X
integer, intent(in) :: jord_in ! Order of LR scheme in Y
integer, intent(in) :: nsplit_in ! Order of LR scheme in Y
integer, intent(in) :: im_in, jm_in, km_in ! Global dims
integer, intent(in) :: nq_in ! No. tracers
integer, intent(in) :: ifirstxy_in, ilastxy_in ! Interval
integer, intent(in) :: jfirstxy_in, jlastxy_in ! Interval
integer, intent(in) :: jfirstyz_in, jlastyz_in ! Interval
integer, intent(in) :: kfirstyz_in, klastyz_in ! Interval
! !DESCRIPTION:
!
! Initialize Lin-Rood specific variables
!
! !REVISION HISTORY:
!
! 01.06.06 Sawyer Create
! 03.07.31 Sawyer Added the 'layout' arguments
! 03.08.05 Sawyer Removed hswf_init and rayf_init
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
dtime = dtime_in
iord = iord_in
jord = jord_in
im = im_in
jm = jm_in
km = km_in
nq = nq_in
ifirstxy = ifirstxy_in
ilastxy = ilastxy_in
jfirstxy = jfirstxy_in
jlastxy = jlastxy_in
jfirstyz = jfirstyz_in
jlastyz = jlastyz_in
kfirstyz = kfirstyz_in
klastyz = klastyz_in
call setrig
call set_eta
call dynpkg_init
call d_split(nsplit_in)
#if defined( SPMD )
call spmd_vars_init()
#endif
return
!EOC
end subroutine dynamics_init
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !IROUTINE: dynamics_clean -- clean up Lin-Rood-specific variables
!
! !INTERFACE:
subroutine dynamics_clean,1
implicit none
! !DESCRIPTION:
!
! Clean up (deallocate) Lin-Rood-specific variables
!
! !REVISION HISTORY:
!
! 01.06.06 Sawyer Creation
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! Temporary data structures
#if defined(SPMD)
call spmd_vars_clean()
#endif
return
!EOC
end subroutine dynamics_clean
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: setrig --- Specify the grid attributes
!
! !INTERFACE:
subroutine setrig 1
! !USES:
implicit none
!
! !DESCRIPTION:
!
! Specify the grid attributes, such as the spacing between
! grid points in latitude and longitude, the sines and cosines of
! latitude at cell midpoints and edges.
!
! !REVISION HISTORY:
! ??.??.?? Lin? Creation
! 01.03.26 Sawyer Added ProTeX documentation
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! !LOCAL VARIABLES:
integer j
real*8 pi, ph5 ! This is to ensure 64-bit for any choice of r8
pi = 4.0 * atan(1.)
dl = (pi+pi)/im
dp = pi/(jm-1)
allocate(cosp(jm))
allocate(sinp(jm))
allocate(cose(jm))
allocate(sine(jm))
do j=2,jm
ph5 = -0.5d0*pi + ((j-1)-0.5d0)*(pi/(jm-1))
sine(j) = sin(ph5)
enddo
cosp( 1) = 0.
cosp(jm) = 0.
do j=2,jm-1
cosp(j) = (sine(j+1)-sine(j)) / dp
enddo
! Define cosine at edges..
do j=2,jm
cose(j) = 0.5 * (cosp(j-1) + cosp(j))
enddo
cose(1) = cose(2)
sinp( 1) = -1.
sinp(jm) = 1.
do j=2,jm-1
sinp(j) = 0.5 * (sine(j) + sine(j+1))
enddo
return
!EOC
end subroutine setrig
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: set_eta --- Define vertical coordinate
!
! !INTERFACE:
subroutine set_eta 1
! !USES:
implicit none
!
! !DESCRIPTION:
!
! Specify the vertical coordinate system. Currently this is a
! dual pressure - sigma coordinate system (???), which transitions at
! level ks, but it could be just about anything reasonable.
!
! Choices for vertical resolutions are as follows:
! \begin{tabular}{l}
! NCAR: 18, 26, and 30 \\
! NASA DAO: smoothed version of CAM's 30-level, 32, 55, 64, and 96 \\
! New 32-layer setup with top at 0.4 mb for high horizontal
! resolution runs. pint = 176.93 mb \\
! Revised 55-level eta with pint at 176.93 mb SJL: 2000-03-20
! \end{tabular}
!
! !REVISION HISTORY:
! 98.01.15 Lin Creation
! ongoing Lin Fine tuning
! 01.03.26 Sawyer Added ProTeX documentation
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! !LOCAL VARIABLES:
! NCAR specific
real(r8) a18(19),b18(19) ! CCM3
real(r8) a26(27),b26(27) ! CAM
real(r8) a30(31),b30(31) ! CCM3
! NASA only
real(r8) a30m(31),b30m(31) ! smoothed CAM 30-L
real(r8) a32(33),b32(33)
real(r8) a32old(33),b32old(33)
real(r8) a55(56),b55(56)
real(r8) a55old(56),b55old(56)
real(r8) a64(65),b64(65)
real(r8) a96(97),b96(97)
integer k
! *** NCAR settings ***
data a18 /291.70, 792.92, 2155.39, 4918.34, 8314.25, &
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4879.13, 3998.95, 3096.31, 2219.02, 1420.39, &
754.13, 268.38, 0.0000, 0.0000 /
data b18 /0.0000, 0.0000, 0.0000, 0.0000, 0.0000, &
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0.9534761, 0.9851122, 1. /
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6332.34828710556, 8070.14182209969, 9494.10423636436, &
11169.321089983, 13140.1270627975, 15458.6806893349, &
18186.3352656364, 17459.799349308, 16605.0657629967, &
15599.5160341263, 14416.541159153, 13024.8308181763, &
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853.108894079924, 397.881818935275, 0., &
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data b30 /0., 0., &
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0., 0., 0.03935482725501,&
0.085653759539127, 0.140122056007385, 0.20420117676258,&
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0.576988518238068, 0.672786951065063, 0.75362843275070,&
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0.911346435546875, 0.938901245594025, 0.96355980634689,&
0.985112190246582, 1. /
! *** NASA DAO settings ***
! Smoothed CAM's 30-Level setup
data a30m / 300.00000, 725.00000, 1500.00000, &
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0.00000 /
data b30m / 0.00000, 0.00000, 0.00000, &
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0.94329, 0.98511, 1.00000 /
data a32old /300.0000, 454.1491, 652.5746, 891.9637, 1159.7102, &
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4541.1041, 5505.0739, 6607.2675, 7851.2298, 9236.5661, &
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10220.700, 8062.000, 5849.500, 3777.000, 2017.200, &
720.600, 0.000, 0.000 /
data b32old /0.00, 0.0000000, 0.0000000, 0.0000000, 0.0000000, &
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data a55old /1.0000, 2.0000, 3.2700, 4.7585, 6.6000, &
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20438.00586, 18288.83984, 15693.01172, &
12624.54199, 9584.35352, 6736.55713, &
4231.34326, 2199.57910, 747.11890, &
0.00000 /
data b96/0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00000, 0.00000, 0.00000, &
0.00315, 0.01263, 0.02853, &
0.05101, 0.08030, 0.11669, &
0.16055, 0.21231, 0.27249, &
0.34169, 0.42062, 0.51005, &
0.61088, 0.70748, 0.79593, &
0.87253, 0.93400, 0.97764, &
1.00000 /
allocate(ak(km+1))
allocate(bk(km+1))
select case (km)
! *** Original CCM3 18-Level setup ***
case (18)
ks = 4
do k=1,km+1
ak(k) = a18(k)
bk(k) = b18(k)
enddo
case (26)
! CAM 26-Level setup ***
ks = 7
do k=1,km+1
ak(k) = a26(k)
bk(k) = b26(k)
enddo
case (30)
! CAM 30-Level setup ***
ks = 12
do k=1,km+1
ak(k) = a30(k)
bk(k) = b30(k)
enddo
! *** Revised 32-L setup with ptop at 0.4 mb ***
case (32)
ks = 18
do k=1,km+1
ak(k) = a32(k)
bk(k) = b32(k)
enddo
! *** Revised 55-L setup with ptop at 0.01 mb ***
case (55)
ks = 41
do k=1,km+1
ak(k) = a55(k)
bk(k) = b55(k)
enddo
! *** Others ***
case (64)
ks = 51
do k=1,km+1
ak(k) = a64(k)
bk(k) = b64(k)
enddo
case (96)
ks = 77
do k=1,km+1
ak(k) = a96(k)
bk(k) = b96(k)
enddo
end select
ptop = ak(1)
pint = ak(ks+1)
return
!EOC
end subroutine set_eta
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: dynpkg_init --- Initialization for dynamics package
!
! !INTERFACE:
subroutine dynpkg_init 1
! !USES:
implicit none
! !DESCRIPTION:
!
! {\bf Purpose:} Initialization of the Rayleigh friction
!
! !REVISION HISTORY:
! 00.01.10 Grant Creation using code from SJ Lin
! 01.03.26 Sawyer Added ProTeX documentation
! 01.06.06 Sawyer Modified for dynamics_vars
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! !LOCAL VARIABLES:
integer i, j, imh
real (r8) zam5, zamda
allocate(coslon(im))
allocate(sinlon(im))
allocate(cosl5(im))
allocate(sinl5(im))
allocate(acosp(jm))
if( iord <= 2 ) then
icd = 1
else
icd = -2
endif
if( jord <= 2 ) then
jcd = 1
else
jcd = -2
endif
#if defined( SPMD )
!
! Calculate the ghost region sizes for the SPMD version (tricky stuff)
!
ng_c = min(abs(jcd ), 2)
ng_d = min(abs(jord), 3) ! SJL: number of max ghost latitudes
ng_d = max(ng_d, 2)
ng_s = max( ng_c+1, ng_d )
#else
ng_c = 0
ng_d = 0 ! No ghosting necessary for pure SMP runs
ng_s = 0
#endif
!
! Pole cap area and inverse
acap = im*(1.+sine(2)) / dp
rcap = 1.d0 / acap
imh = im/2
if(im .ne. 2*imh) then
write(6,*) 'im must be an even integer'
stop
endif
! Define logitude at the center of the volume
! i=1, Zamda = -pi
do i=1,imh
zam5 = ((i-1)-0.5d0) * dl
cosl5(i) = cos(zam5)
cosl5(i+imh) = -cosl5(i)
sinl5(i) = sin(zam5)
sinl5(i+imh) = -sinl5(i)
zamda = (i-1)*dl
coslon(i) = cos(zamda)
coslon(i+imh) = -coslon(i)
sinlon(i) = sin(zamda)
sinlon(i+imh) = -sinlon(i)
enddo
do j=2,jm-1
acosp(j) = 1.d0 / cosp(j)
enddo
acosp( 1) = rcap * im
acosp(jm) = rcap * im
return
!EOC
end subroutine dynpkg_init
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: d_split --- find proper value for nsplit if not specified
!
! !INTERFACE:
subroutine d_split(nsplit_in) 1
!
! !USES:
implicit none
! !INPUT PARAMETERS:
integer, intent(in) :: nsplit_in ! Small time steps in dtime
! !DESCRIPTION:
!
! If nsplit=0 (module variable) then determine a good value
! for ns (used in dynpkg) based on resolution and the large-time-step
! (pdt). The user may have to set this manually if instability occurs.
!
! !REVISION HISTORY:
! 00.10.19 Lin Creation
! 01.03.26 Sawyer ProTeX documentation
! 01.06.10 Sawyer Modified for dynamics_init framework
!
!EOP
!-----------------------------------------------------------------------
!BOC
! !LOCAL VARIABLES:
real (r8) pdt ! Time-step in seconds
! Negative dt (backward in time
! integration) is allowed
real (r8) dim
real (r8) dim0 ! base dimension
real (r8) dt0 ! base time step
real (r8) ns0 ! base nsplit for base dimension
parameter ( dim0 = 180. )
parameter ( dt0 = 1800. )
parameter ( ns0 = 4. )
if ( nsplit_in == 0 ) then
pdt = int(dtime) ! dtime is a variable internal to this module
dim = max ( im, 2*(jm-1) )
ns = int ( ns0*abs(pdt)*dim/(dt0*dim0) + 0.75 )
ns = max ( 1, ns ) ! for cases in which dt or dim is too small
else
ns = nsplit_in
endif
write(6,*) 'Lagrangian time splits (NSPLIT) =', ns
return
!EOC
end subroutine d_split
!---------------------------------------------------------------------
#if defined(SPMD)
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: spmd_vars_init --- Initialization of SPMD-related variables
!
! !INTERFACE:
subroutine spmd_vars_init 1,2
! !USES:
use pmgrid, only: mod_transpose
use spmd_dyn, only : ghostpe_yz, &
ghostpe1_yz, m_ttrans, q_ttrans, r_ttrans, &
ijk_yz_to_xy, ijk_xy_to_yz, &
ikj_xy_to_yz, q_to_qxy, qxy_to_q, &
pexy_to_pe, pkxy_to_pkc, r_to_rxy, rxy_to_r
use ghostmodule, only : ghostcreate
use parutilitiesmodule, only : gid, commglobal, parpatterncreate
implicit none
!------------------------------Commons----------------------------------
! !DESCRIPTION:
!
! {\bf Purpose:} Initialization of the SPMD related variables.
! This has to be done in this module since certain variables
! (in particular the ghost sizes {\tt ng\_d, ng\_s} are first
! defined here.
!
! !REVISION HISTORY:
! 02.11.08 Sawyer Creation
! 03.05.07 Sawyer Use ParPatternCopy for q_to_qxy, etc.
! 03.07.23 Sawyer Removed dependency on constituents module
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! !LOCAL VARIABLES:
! Temporary data structures
allocate( yzt(im,jfirstyz:jlastyz,kfirstyz:klastyz) )
allocate( yzt2(im,jfirstyz:jlastyz,kfirstyz:klastyz) )
allocate( q3t(im,jfirstyz:jlastyz,kfirstyz:klastyz,nq) )
if ( twod_decomp == 1 ) then
! Initialize ghost regions
!
call t_startf('ghost_creation')
call ghostcreate( strip3dxzyp, gid, im, 1, im, .true., &
km+1, kfirstyz, klastyz+1, .false., &
jm, jfirstyz, jlastyz, .false., ghostpe_yz)
call ghostcreate( strip3dxyzp, gid, im, 1, im, .true., &
jm, jfirstyz, jlastyz, .false., &
km+1, kfirstyz, klastyz+1, .false., ghostpe1_yz)
call t_stopf('ghost_creation')
! Initialize transposes
!
call t_startf('transpose_creation')
call parpatterncreate(commglobal, strip3dxyz, strip3kxyz, &
ijk_yz_to_xy, mod_method=mod_transpose)
call parpatterncreate(commglobal, strip3kxyz, strip3dxyz, &
ijk_xy_to_yz, mod_method=mod_transpose)
call parpatterncreate(commglobal, strip3kxzy, strip3dxzy, &
ikj_xy_to_yz, mod_method=mod_transpose)
call t_startf('q_to_qxy_creation')
if (q_ttrans .ne. 0) then
call parpatterncreate( ijk_yz_to_xy, q_to_qxy, m_ttrans )
call parpatterncreate( ijk_xy_to_yz, qxy_to_q, m_ttrans )
endif
if (r_ttrans .ne. 0) then
call parpatterncreate( ijk_yz_to_xy, r_to_rxy, r_ttrans )
call parpatterncreate( ijk_xy_to_yz, rxy_to_r, r_ttrans )
endif
call t_stopf('q_to_qxy_creation')
call parpatterncreate(commglobal, strip3kxzyp, ghostpe_yz, &
pexy_to_pe, mod_method=mod_transpose )
call parpatterncreate(commglobal, strip3kxyzp, ghostpe1_yz,&
pkxy_to_pkc, mod_method=mod_transpose )
call t_stopf('transpose_creation')
endif
return
!EOC
end subroutine spmd_vars_init
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
!BOP
! !ROUTINE: spmd_vars_clean --- Clean the SPMD-related variables
!
! !INTERFACE:
subroutine spmd_vars_clean 1,1
! !USES:
use spmd_dyn, only : ghostpe_yz, ghostpe1_yz, &
m_ttrans, q_ttrans, r_ttrans, &
ijk_yz_to_xy, ijk_xy_to_yz, &
ikj_xy_to_yz, q_to_qxy, qxy_to_q, &
pexy_to_pe, pkxy_to_pkc, r_to_rxy, rxy_to_r
use ghostmodule, only : ghostfree
use parutilitiesmodule, only : commglobal, parpatternfree
implicit none
!------------------------------Commons----------------------------------
! !DESCRIPTION:
!
! {\bf Purpose:} Clean the SPMD related variables.
!
! !REVISION HISTORY:
! 02.11.08 Sawyer Creation
!
!EOP
!-----------------------------------------------------------------------
!BOC
!
! !LOCAL VARIABLES:
! Temporary data structures
deallocate( yzt )
deallocate( yzt2 )
deallocate( q3t )
if ( twod_decomp == 1 ) then
! Clean the ghost regions
!
call ghostfree( ghostpe_yz )
call ghostfree( ghostpe1_yz )
! Clean transposes
!
call parpatternfree(commglobal,ijk_yz_to_xy)
call parpatternfree(commglobal,ijk_xy_to_yz)
call parpatternfree(commglobal,ikj_xy_to_yz)
if (q_ttrans .ne. 0) then
call parpatternfree(commglobal,q_to_qxy)
call parpatternfree(commglobal,qxy_to_q)
endif
if (r_ttrans .ne. 0) then
call parpatternfree(commglobal,r_to_rxy)
call parpatternfree(commglobal,rxy_to_r)
endif
call parpatternfree(commglobal,pexy_to_pe)
call parpatternfree(commglobal,pkxy_to_pkc)
endif
return
!EOC
end subroutine spmd_vars_clean
!-----------------------------------------------------------------------
#endif
end module dynamics_vars