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scaledep_dynamic.f90
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scaledep_dynamic.f90
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!!
!! Copyright (C) 2009-2017 Johns Hopkins University
!!
!! This file is part of lesgo.
!!
!! lesgo is free software: you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation, either version 3 of the License, or
!! (at your option) any later version.
!!
!! lesgo is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with lesgo. If not, see <http://www.gnu.org/licenses/>.
!!
!*******************************************************************************
subroutine scaledep_dynamic(Cs_1D)
!*******************************************************************************
!
! Subroutine uses the scale dependent dynamic model to calculate the Smagorinsky
! coefficient Cs_1D and |S|. This is done layer-by-layer to save memory.
!
use types, only : rprec
use param, only : ld, nx, ny, nz, coord
use sim_param, only : u, v, w
use test_filtermodule
use sgs_stag_util, only : rtnewt
use sgs_param, only : S11, S12, S13, S22, S23, S33, delta, S, ee_now, &
u_bar, v_bar, w_bar, L11, L12, L13, L22, L23, L33, S_bar, &
S11_bar, S12_bar, S13_bar, S22_bar, S23_bar, S33_bar, &
S_S11_bar, S_S12_bar, S_S13_bar, S_S22_bar, S_S23_bar, S_S33_bar, &
u_hat, v_hat, w_hat, &
S_hat, S11_hat, S12_hat, S13_hat, S22_hat, S23_hat, S33_hat, &
S_S11_hat, S_S12_hat, S_S13_hat, S_S22_hat, S_S23_hat, S_S33_hat
implicit none
integer :: jz
real(rprec), dimension(nz), intent (inout) :: Cs_1D
real(rprec), save, allocatable, target, dimension(:,:) :: Q11, Q12, Q13, Q22, &
Q23, Q33
real(rprec), pointer, dimension(:,:) :: M11, M12, M13, M22, M23, M33
real(rprec), save, dimension(:), allocatable :: beta
logical, save :: arrays_allocated = .false.
real(rprec) :: const
real(rprec), dimension(0:5) :: A
real(rprec) :: a1, b1, c1, d1, e1, a2, b2, c2, d2, e2
real(rprec), dimension(ld,ny) :: LM,MM
! Allocate arrays
if( .not. arrays_allocated ) then
allocate ( Q11(ld,ny), Q12(ld,ny), Q13(ld,ny), &
Q22(ld,ny), Q23(ld,ny), Q33(ld,ny) )
allocate ( beta(nz) )
arrays_allocated = .true.
endif
! Associate pointers
M11 => Q11
M12 => Q12
M13 => Q13
M22 => Q22
M23 => Q23
M33 => Q33
do jz = 1, nz
! using L_ij as temp storage here
if ( (coord == 0) .and. (jz == 1) ) then
!!! watch the 0.25's: w = c*z**z near wall, so get 0.25
! put on uvp-nodes
L11(:,:) = u(:,:,1)*u(:,:,1) ! uv-node
L12(:,:) = u(:,:,1)*v(:,:,1) ! uv-node
L13(:,:) = u(:,:,1)*0.25_rprec*w(:,:,2) ! assume parabolic near wall
L22(:,:) = v(:,:,1)*v(:,:,1) ! uv-node
L23(:,:) = v(:,:,jz)*0.25_rprec*w(:,:,2) ! uv-node
L33(:,:) = (0.25_rprec*w(:,:,2))**2 ! uv-node
u_bar(:,:) = u(:,:,1)
v_bar(:,:) = v(:,:,1)
w_bar(:,:) = 0.25_rprec*w(:,:,2)
else ! w-nodes
L11(:,:) = 0.5_rprec*(u(:,:,jz) + u(:,:,jz-1))* &
0.5_rprec*(u(:,:,jz) + u(:,:,jz-1))
L12(:,:) = 0.5_rprec*(u(:,:,jz) + u(:,:,jz-1))* &
0.5_rprec*(v(:,:,jz) + v(:,:,jz-1))
L13(:,:) = 0.5_rprec*(u(:,:,jz) + u(:,:,jz-1))*w(:,:,jz)
L22(:,:) = 0.5_rprec*(v(:,:,jz) + v(:,:,jz-1))* &
0.5_rprec*(v(:,:,jz) + v(:,:,jz-1))
L23(:,:) = 0.5_rprec*(v(:,:,jz) + v(:,:,jz-1))*w(:,:,jz)
L33(:,:) = w(:,:,jz)*w(:,:,jz)
u_bar(:,:) = 0.5_rprec*(u(:,:,jz) + u(:,:,jz-1))
v_bar(:,:) = 0.5_rprec*(v(:,:,jz) + v(:,:,jz-1))
w_bar(:,:) = w(:,:,jz)
end if
u_hat = u_bar
v_hat = v_bar
w_hat = w_bar
! Filter first term and add the second term to get the final value
! in-place filtering
call test_filter ( u_bar )
call test_filter ( v_bar )
call test_filter ( w_bar )
call test_filter ( L11 )
L11 = L11 - u_bar*u_bar
call test_filter ( L12 )
L12 = L12 - u_bar*v_bar
call test_filter ( L13 )
L13 = L13 - u_bar*w_bar
call test_filter ( L22 )
L22 = L22 - v_bar*v_bar
call test_filter ( L23 )
L23 = L23 - v_bar*w_bar
call test_filter ( L33 )
L33 = L33 - w_bar*w_bar
Q11 = u_bar*u_bar
Q12 = u_bar*v_bar
Q13 = u_bar*w_bar
Q22 = v_bar*v_bar
Q23 = v_bar*w_bar
Q33 = w_bar*w_bar
call test_test_filter ( u_hat )
call test_test_filter ( v_hat )
call test_test_filter ( w_hat )
call test_test_filter ( Q11 )
Q11 = Q11 - u_hat*u_hat
call test_test_filter ( Q12 )
Q12 = Q12 - u_hat*v_hat
call test_test_filter ( Q13 )
Q13 = Q13 - u_hat*w_hat
call test_test_filter ( Q22 )
Q22 = Q22 - v_hat*v_hat
call test_test_filter ( Q23 )
Q23 = Q23 - v_hat*w_hat
call test_test_filter ( Q33 )
Q33 = Q33 - w_hat*w_hat
! calculate |S|
S(:,:) = sqrt(2._rprec*(S11(:,:,jz)**2 + S22(:,:,jz)**2 +&
S33(:,:,jz)**2 + 2._rprec*(S12(:,:,jz)**2 + &
S13(:,:,jz)**2 + S23(:,:,jz)**2)))
! already on w-nodes
S11_bar(:,:) = S11(:,:,jz)
S12_bar(:,:) = S12(:,:,jz)
S13_bar(:,:) = S13(:,:,jz)
S22_bar(:,:) = S22(:,:,jz)
S23_bar(:,:) = S23(:,:,jz)
S33_bar(:,:) = S33(:,:,jz)
S11_hat = S11_bar
S12_hat = S12_bar
S13_hat = S13_bar
S22_hat = S22_bar
S23_hat = S23_bar
S33_hat = S33_bar
call test_filter ( S11_bar )
call test_filter ( S12_bar )
call test_filter ( S13_bar )
call test_filter ( S22_bar )
call test_filter ( S23_bar )
call test_filter ( S33_bar )
call test_test_filter ( S11_hat )
call test_test_filter ( S12_hat )
call test_test_filter ( S13_hat )
call test_test_filter ( S22_hat )
call test_test_filter ( S23_hat )
call test_test_filter ( S33_hat )
S_bar = sqrt(2._rprec*(S11_bar**2 + S22_bar**2 + S33_bar**2 + &
2._rprec*(S12_bar**2 + S13_bar**2 + S23_bar**2)))
S_hat = sqrt(2._rprec*(S11_hat**2 + S22_hat**2 + S33_hat**2 + &
2._rprec*(S12_hat**2 + S13_hat**2 + S23_hat**2)))
S_S11_bar = S*S11(:,:,jz)
S_S12_bar = S*S12(:,:,jz)
S_S13_bar = S*S13(:,:,jz)
S_S22_bar = S*S22(:,:,jz)
S_S23_bar = S*S23(:,:,jz)
S_S33_bar = S*S33(:,:,jz)
S_S11_hat = S_S11_bar
S_S12_hat = S_S12_bar
S_S13_hat = S_S13_bar
S_S22_hat = S_S22_bar
S_S23_hat = S_S23_bar
S_S33_hat = S_S33_bar
call test_filter ( S_S11_bar )
call test_filter ( S_S12_bar )
call test_filter ( S_S13_bar )
call test_filter ( S_S22_bar )
call test_filter ( S_S23_bar )
call test_filter ( S_S33_bar )
call test_test_filter ( S_S11_hat )
call test_test_filter ( S_S12_hat )
call test_test_filter ( S_S13_hat )
call test_test_filter ( S_S22_hat )
call test_test_filter ( S_S23_hat )
call test_test_filter ( S_S33_hat )
! note: check that the Nyquist guys are zero!
! the 1./(nx*ny) is not really neccessary, but in practice it does
! affect the results.
a1 = -2._rprec*(delta**2)*4._rprec*sum( S_bar*(S11_bar*L11 + S22_bar*L22 + &
S33_bar*L33 + 2._rprec*( S12_bar*L12 + S13_bar*L13 + S23_bar*L23)))/ &
(nx*ny)
b1 = -2._rprec*(delta**2)*sum( S_S11_bar*L11 + S_S22_bar*L22 + &
S_S33_bar*L33 + 2._rprec*( S_S12_bar*L12 + S_S13_bar*L13 + &
S_S23_bar*L23))/(nx*ny)
c1 = (2._rprec*delta**2)**2 * sum( S_S11_bar**2 + S_S22_bar**2 + &
S_S33_bar**2 + &
2._rprec*( S_S12_bar**2 + S_S13_bar**2 + S_S23_bar**2))/(nx*ny)
d1 = (2._rprec*delta**2)**2 * 16._rprec*sum( 0.5_rprec*S_bar**4 )/(nx*ny)
e1 = 2._rprec*(2._rprec*delta**2)**2*4._rprec*sum( S_bar*( S11_bar* &
S_S11_bar +S22_bar*S_S22_bar + S33_bar*S_S33_bar + 2._rprec*( &
S12_bar*S_S12_bar + S13_bar*S_S13_bar + S23_bar*S_S23_bar)))/ &
(nx*ny)
a2 = -2._rprec*(delta**2)*16._rprec*sum( S_hat*(S11_hat*Q11 + S22_hat*Q22 +&
S33_hat*Q33 + 2._rprec*( S12_hat*Q12 + S13_hat*Q13 + S23_hat*Q23)))/&
(nx*ny)
b2 = -2._rprec*(delta**2)*sum( S_S11_hat*Q11 + S_S22_hat*Q22 +&
S_S33_hat*Q33 + 2._rprec*( S_S12_hat*Q12 + S_S13_hat*Q13 + &
S_S23_hat*Q23))/(nx*ny)
c2 = (2._rprec*delta**2)**2 * sum( S_S11_hat**2 + S_S22_hat**2 +&
S_S33_hat**2 + &
2._rprec*( S_S12_hat**2 + S_S13_hat**2 + S_S23_hat**2))/(nx*ny)
d2 = (2._rprec*delta**2)**2 *256._rprec*sum( 0.5_rprec*S_hat**4 )/(nx*ny)
e2 = 2._rprec*(2._rprec*delta**2)**2*16._rprec*sum( S_hat*( S11_hat* &
S_S11_hat + S22_hat*S_S22_hat + S33_hat*S_S33_hat + 2.*( &
S12_hat*S_S12_hat + S13_hat*S_S13_hat + S23_hat*S_S23_hat)))/ &
(nx*ny)
A(0) = b2*c1 - b1*c2
A(1) = a1*c2 - b2*e1
A(2) = b2*d1 + b1*e2 - a2*c1
A(3) = a2*e1 - a1*e2
A(4) = -a2*d1 - b1*d2
A(5) = a1*d2
beta(jz) = rtnewt(A,jz)
! now put beta back into M_ij: using Q_ij as storage
const = 2._rprec*delta**2
M11 = const*(S_S11_bar - 4._rprec*beta(jz)*S_bar*S11_bar)
M12 = const*(S_S12_bar - 4._rprec*beta(jz)*S_bar*S12_bar)
M13 = const*(S_S13_bar - 4._rprec*beta(jz)*S_bar*S13_bar)
M22 = const*(S_S22_bar - 4._rprec*beta(jz)*S_bar*S22_bar)
M23 = const*(S_S23_bar - 4._rprec*beta(jz)*S_bar*S23_bar)
M33 = const*(S_S33_bar - 4._rprec*beta(jz)*S_bar*S33_bar)
Cs_1D(jz) = sum(L11*M11 + L22*M22 + L33*M33 + 2._rprec*(L12*M12 + &
L13*M13 + L23*M23)) / &
sum(M11**2 + M22**2 + M33**2 + 2._rprec*(M12**2 + M13**2 + M23**2))
Cs_1D(jz) = max(0._rprec, real(Cs_1D(jz),rprec))
! Calculate ee_now (the current value of eij*eij)
LM = L11*M11+L22*M22+L33*M33+2._rprec*(L12*M12+L13*M13+L23*M23)
MM = M11**2+M22**2+M33**2+2._rprec*(M12**2+M13**2+M23**2)
ee_now(:,:,jz) = L11**2+L22**2+L33**2+2._rprec*(L12**2+L13**2+L23**2) &
-2._rprec*LM*Cs_1D(jz) + MM*Cs_1D(jz)**2
end do
! Nullify pointers
nullify( M11, M12, M13, M22, M23, M33 )
end subroutine scaledep_dynamic