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lagrange_Ssim.f90
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lagrange_Ssim.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 lagrange_Ssim()
!*******************************************************************************
!
! This subroutine dynamically calculates Cs_opt2. See Meneveau, Lund, Cabot,
! JFM, 319: 353-385 (1996) DOI: 10.1017/S0022112096007379
!
use types, only : rprec
use param
use sim_param, only : u, v, w
use sgs_param, only : F_LM, F_MM, Beta, Cs_opt2, opftime, lagran_dt
use sgs_param, only : S11, S12, S13, S22, S23, S33, delta, S, ee_now, Tn_all, &
u_bar, v_bar, w_bar, &
L11, L12, L13, L22, L23, L33, M11, M12, M13, M22, M23, M33, &
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
use test_filtermodule
use messages
use string_util, only : string_concat
#ifdef PPLVLSET
use level_set, only : level_set_lag_dyn, level_set_Cs_lag_dyn
#endif
#ifdef PPDYN_TN
use sgs_param, only:F_ee2,F_deedt2,ee_past
#endif
#ifdef PPMPI
use mpi_defs, only:mpi_sync_real_array,MPI_SYNC_DOWNUP
#endif
implicit none
character(*), parameter :: sub_name = 'lagrange_Ssim'
real(rprec), parameter :: eps = 1.e-32_rprec
real(rprec), dimension(ld,ny) :: fourbeta
real(rprec), dimension(ld,ny) :: LM, MM, Tn, epsi, dumfac
real(rprec) :: const
real(rprec) :: opftdelta, powcoeff
integer :: istart, iend, jz, ii, i
logical, save :: F_LM_MM_init = .false.
! Set coefficients
opftdelta = opftime*delta
powcoeff = -1._rprec/8._rprec
const = 2._rprec*delta**2
#ifdef PPLVLSET
call level_set_lag_dyn (S11, S12, S13, S22, S23, S33)
#else
Beta = 1._rprec
#endif
! "Rearrange" F_LM, F_MM, F_ee2, F_deedt2 (running averages) so that
! their new positions (i,j,k) correspond to the current (i,j,k) particle
call interpolag_Ssim()
! For each horizontal level, calculate Lij(:,:) and Mij(:,:). Then update
! the running averages, F_LM(:,:,jz) and F_MM(:,:,jz), which are used to
! calculate Cs_opt2(:,:,jz).
do jz = 1,nz
! Calculate Lij
! Interp u,v,w onto w-nodes and store result as u_bar,v_bar,w_bar
! (except for very first level which should be on uvp-nodes)
if ( ( coord == 0 ) .and. (jz == 1) ) then ! uvp-nodes
u_bar(:,:) = u(:,:,1)
v_bar(:,:) = v(:,:,1)
w_bar(:,:) = .25_rprec*w(:,:,2)
else ! w-nodes
u_bar(:,:) = .5_rprec*(u(:,:,jz) + u(:,:,jz-1))
v_bar(:,:) = .5_rprec*(v(:,:,jz) + v(:,:,jz-1))
w_bar(:,:) = w(:,:,jz)
end if
! First term before filtering (not the final value)
L11 = u_bar*u_bar
L12 = u_bar*v_bar
L13 = u_bar*w_bar
L23 = v_bar*w_bar
L22 = v_bar*v_bar
L33 = w_bar*w_bar
! Filter first term and add the second term to get the final value
call test_filter ( u_bar ) ! in-place filtering
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
! 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)))
! Select Sij for this level for test-filtering, saving results as Sij_bar
! note: Sij is 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)
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 )
! Calculate |S_bar| (the test-filtered Sij)
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)))
! Calculate |S|Sij then test-filter this quantity
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)
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 )
! Calculate Mij
fourbeta=4._rprec*Beta(:,:,jz)
M11 = const*(S_S11_bar - fourbeta*S_bar*S11_bar)
M12 = const*(S_S12_bar - fourbeta*S_bar*S12_bar)
M13 = const*(S_S13_bar - fourbeta*S_bar*S13_bar)
M22 = const*(S_S22_bar - fourbeta*S_bar*S22_bar)
M23 = const*(S_S23_bar - fourbeta*S_bar*S23_bar)
M33 = const*(S_S33_bar - fourbeta*S_bar*S33_bar)
! Calculate LijMij and MijMij for each point in the plane
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)
! Calculate ee_now (the current value of eij*eij)
ee_now(:,:,jz) = L11**2+L22**2+L33**2+2._rprec*(L12**2+L13**2+L23**2) &
-2._rprec*LM*Cs_opt2(:,:,jz) + MM*Cs_opt2(:,:,jz)**2
! Using local time counter to reinitialize SGS quantities when restarting
if (inilag) then
if ((.not. F_LM_MM_init) .and. (jt == cs_count .or. jt == DYN_init)) then
print *,'F_MM and F_LM initialized'
F_MM (:,:,jz) = MM
F_LM (:,:,jz) = 0.025_rprec*MM
F_MM(ld-1:ld,:,jz)=1._rprec
F_LM(ld-1:ld,:,jz)=1._rprec
if (jz == 1) then
if (coord == 0) then
write(*, *) 'LM(1, 1)=', LM(1, 1)
write(*, *) 'MM(1, 1)=', MM(1, 1)
write(*, *) 'M11(1, 1)=', M11(1, 1)
write(*, *) 'S_S11_bar(1, 1)=', S_S11_bar(1, 1)
write(*, *) 'S11(1, 1, 1)=', S11(1, 1, 1)
write(*, *) 'S(1, 1)=', S(1, 1)
write(*, *) 'S11_bar(1, 1)=', S11_bar(1, 1)
write(*, *) 'S_bar(1, 1)=', S_bar(1, 1)
endif
endif
if (jz == nz) F_LM_MM_init = .true.
endif
endif
! Inflow
if (inflow_type > 0) then
iend = floor (fringe_region_end * nx + 1._rprec)
istart = floor ((fringe_region_end - fringe_region_len) * nx + 1._rprec)
Tn = merge(.1_rprec*const*S**2,MM,MM.le..1_rprec*const*S**2)
MM = Tn
if (istart > iend) then
write (*, *) 'lagrange_Ssim: istart > iend'
stop
endif
do i = istart, iend
ii = modulo (i - 1, nx) + 1
LM(ii, :) = 0._rprec
F_LM(ii, :, jz) = 0._rprec
enddo
endif
! Update running averages (F_LM, F_MM, F_ee2, F_deedt2)
! Determine averaging timescale
#ifdef PPDYN_TN
! based on Taylor timescale
Tn = 4._rprec*pi*sqrt(F_ee2(:,:,jz)/F_deedt2(:,:,jz))
#else
! based on Meneveau, Cabot, Lund paper (JFM 1996)
Tn = max (F_LM(:,:,jz) * F_MM(:,:,jz), eps)
Tn = opftdelta*(Tn**powcoeff)
#endif
! Calculate new running average = old*(1-epsi) + instantaneous*epsi
dumfac = lagran_dt/Tn
epsi = dumfac / (1._rprec + dumfac)
F_LM(:,:,jz)=(epsi*LM + (1.0_rprec-epsi)*F_LM(:,:,jz))
F_MM(:,:,jz)=(epsi*MM + (1.0_rprec-epsi)*F_MM(:,:,jz))
! clipping to avoid instability
F_LM(:,:,jz)= max(eps, F_LM(:,:,jz))
#ifdef PPDYN_TN
! note: the instantaneous value of the derivative is a Lagrangian average
F_ee2(:,:,jz) = epsi*ee_now(:,:,jz)**2 + (1._rprec-epsi)*F_ee2(:,:,jz)
F_deedt2(:,:,jz) = epsi*( ((ee_now(:,:,jz)-ee_past(:,:,jz))/lagran_dt)**2 )&
+ (1._rprec-epsi)*F_deedt2(:,:,jz)
ee_past(:,:,jz) = ee_now(:,:,jz)
#endif
! Calculate Cs_opt2 (use only one of the methods below)
! Standard method - LASS
! Added +eps to avoid division by zero
Cs_opt2(:,:,jz) = F_LM(:,:,jz) / (F_MM(:,:,jz) + eps)
Cs_opt2(ld-1:ld,:,jz) = 0._rprec
! 9-point average
!do i=1,nx
!do j=1,ny
! ilo=i-1; ihi=i+1; jlo=j-1; jhi=j+1
! if (ilo.eq.0) ilo=nx
! if (jlo.eq.0) jlo=ny
! if (ihi.eq.nx+1) ihi=1
! if (jhi.eq.ny+1) jhi=1
! Cs_opt2(i,j,jz) = (LM(i,j)+LM(ilo,j)+LM(ihi,j)+LM(ilo,jlo)+&
! LM(ihi,jlo)+LM(i,jlo)+LM(ilo,jhi)+LM(i,jhi)+LM(ihi,jhi))/ &
! (MM(i,j)+MM(ilo,j)+MM(ihi,j)+MM(ilo,jlo)+&
! MM(ihi,jlo)+MM(i,jlo)+MM(ilo,jhi)+MM(i,jhi)+MM(ihi,jhi))
!enddo
!enddo
! Directly
!Cs_opt2(:,:,jz) = LM(:,:)/MM(:,:)
! Clip Cs if necessary
Cs_opt2(:,:,jz)= max (eps, Cs_opt2(:,:,jz))
! Save Tn to 3D array for use with tavg_sgs
Tn_all(:,:,jz) = Tn(:,:)
end do
! Share new data between overlapping nodes
#ifdef PPMPI
call mpi_sync_real_array( F_LM, 0, MPI_SYNC_DOWNUP )
call mpi_sync_real_array( F_MM, 0, MPI_SYNC_DOWNUP )
call mpi_sync_real_array( Tn_all, 0, MPI_SYNC_DOWNUP )
#ifdef PPDYN_TN
call mpi_sync_real_array( F_ee2, 0, MPI_SYNC_DOWNUP )
call mpi_sync_real_array( F_deedt2, 0, MPI_SYNC_DOWNUP )
call mpi_sync_real_array( ee_past, 0, MPI_SYNC_DOWNUP )
#endif
#endif
#ifdef PPLVLSET
call level_set_Cs_lag_dyn ()
#endif
! Reset variable for use during next set of cs_count timesteps
if( use_cfl_dt ) lagran_dt = 0._rprec
end subroutine lagrange_Ssim