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subroutines.f90
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subroutines.f90
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module subroutines
use control
use constant
contains
!transmiting arrays Êý×é´«ËÍ
subroutine transmit_arrays(ua,va,za,ub,vb,zb)
real ,intent(in) :: ub(grid%x_grd_num_u ,grid%y_grd_num_u),&
vb(grid%x_grd_num_v ,grid%y_grd_num_v),&
zb(grid%x_grd_num ,grid%y_grd_num)
real ,intent(out):: ua(grid%x_grd_num_u ,grid%y_grd_num_u),&
va(grid%x_grd_num_v ,grid%y_grd_num_v),&
za(grid%x_grd_num ,grid%y_grd_num)
ua=ub
va=vb
za=zb
end subroutine transmit_arrays
!Lateral Boundary Conditions by Davies and Turner (1977) modified by Skamarock(2008)
subroutine WRF_LBC(var_in,var_t,var_BYS,var_BYE,var_BXS,var_BXE,var_BTYS,var_BTYE,var_BTXS,var_BTXE ,&
F1,F2,interval_seconds,integrated_step_num,ts,x_grd_num,y_grd_num ,&
bdy_width,spec_zone,bdy_time_num,bdy_tend_time_num)
implicit none
integer,intent(in)::spec_zone ,&
x_grd_num ,&
y_grd_num ,&
bdy_width ,&
bdy_time_num ,&
bdy_tend_time_num
real ,intent(in)::var_in (x_grd_num,y_grd_num) ,&
var_BYS(x_grd_num,bdy_width,bdy_time_num) ,&
var_BYE(x_grd_num,bdy_width,bdy_time_num) ,&
var_BXS(y_grd_num,bdy_width,bdy_time_num) ,&
var_BXE(y_grd_num,bdy_width,bdy_time_num) ,&
var_BTYS(x_grd_num,bdy_width,bdy_tend_time_num),&
var_BTYE(x_grd_num,bdy_width,bdy_tend_time_num),&
var_BTXS(y_grd_num,bdy_width,bdy_tend_time_num),&
var_BTXE(y_grd_num,bdy_width,bdy_tend_time_num),&
F1(spec_zone+1:bdy_width-1) ,&
F2(spec_zone+1:bdy_width-1) ,&
interval_seconds ,&
integrated_step_num ,&
ts
real ,intent(out)::var_t(x_grd_num,y_grd_num)
real BYS (x_grd_num,bdy_width) ,&
BYE (x_grd_num,bdy_width) ,&
BXS (y_grd_num,bdy_width) ,&
BXE (y_grd_num,bdy_width) ,&
dBYS (x_grd_num,bdy_width) ,&
dBYE (x_grd_num,bdy_width) ,&
dBXS (y_grd_num,bdy_width) ,&
dBXE (y_grd_num,bdy_width)
integer i,j,k,i_inv,j_inv,n
integer bdy_stage,bdy_stage_index
integer jm1,jp1
real ij_angle
var_t = 0.
bdy_stage = int(integrated_step_num*time_step/interval_seconds)+1
bdy_stage_index = min(grid%BDY_TEND_TIME_NUM,bdy_stage)
BYS = var_BYS(:,:,bdy_stage)+dble(integrated_step_num*time_step-(bdy_stage-1)*interval_seconds)*var_BTYS(:,:,bdy_stage_index)/3600.
BYE = var_BYE(:,:,bdy_stage)+dble(integrated_step_num*time_step-(bdy_stage-1)*interval_seconds)*var_BTYE(:,:,bdy_stage_index)/3600.
BXS = var_BXS(:,:,bdy_stage)+dble(integrated_step_num*time_step-(bdy_stage-1)*interval_seconds)*var_BTXS(:,:,bdy_stage_index)/3600.
BXE = var_BXE(:,:,bdy_stage)+dble(integrated_step_num*time_step-(bdy_stage-1)*interval_seconds)*var_BTXE(:,:,bdy_stage_index)/3600.
forall(i=1:x_grd_num,j=1:bdy_width)
dBYS(i,j) = BYS(i,j)-var_in(i,j)
dBYE(i,j) = BYE(i,j)-var_in(i,y_grd_num-j+1)
endforall
forall(i=1:bdy_width,j=1:y_grd_num)
dBXS(j,i) = BXS(j,i)-var_in(i,j)
dBXE(j,i) = BXE(j,i)-var_in(x_grd_num-i+1,j)
endforall
do j=1,x_grd_num
jm1 = max(j-1,1)
jp1 = min(j+1,x_grd_num)
forall(i=spec_zone+1:bdy_width-spec_zone)
var_t(j,i) = F1(i)/ts*dBYS(j,i)-F2(i)/ts*(dBYS(jm1,i)+dBYS(jp1,i)+dBYS(j,i+1)+dBYS(j,i-1)-4.*dBYS(j,i))
var_t(j,y_grd_num-i+1) = F1(i)/ts*dBYE(j,i)-F2(i)/ts*(dBYE(jm1,i)+dBYE(jp1,i)+dBYE(j,i+1)+dBYE(j,i-1)-4.*dBYE(j,i))
endforall
enddo
do j=1,y_grd_num
jm1 = max(j-1,1)
jp1 = min(j+1,y_grd_num)
forall(i=spec_zone+1:bdy_width-spec_zone)
var_t(i,j) = F1(i)/ts*dBXS(j,i)-F2(i)/ts*(dBXS(jm1,i)+dBXS(jp1,i)+dBXS(j,i+1)+dBXS(j,i-1)-4.*dBXS(j,i))
var_t(x_grd_num-i+1,j) = F1(i)/ts*dBXE(j,i)-F2(i)/ts*(dBXE(jm1,i)+dBXE(jp1,i)+dBXE(j,i+1)+dBXE(j,i-1)-4.*dBXE(j,i))
endforall
enddo
do i=spec_zone+1,bdy_width-1
do j=spec_zone+1,bdy_width-1
ij_angle=atan(dble(j)/dble(i))
i_inv=x_grd_num-i+1
j_inv=y_grd_num-j+1
var_t(i,j) = (sin(ij_angle)**2*F1(i)+cos(ij_angle)**2*F1(j))/ts*dBYS(i,j) -(sin(ij_angle)**2*F2(i)+cos(ij_angle)**2*F2(j))/ts*(dBYS(i-1,j) +dBYS(i+1,j) +dBYS(i,j+1) +dBYS(i,j-1) -4.*dBYS(i,j))
var_t(i_inv,j) = (sin(ij_angle)**2*F1(i)+cos(ij_angle)**2*F1(j))/ts*dBXE(j,i) -(sin(ij_angle)**2*F2(i)+cos(ij_angle)**2*F2(j))/ts*(dBXE(j-1,i) +dBXE(j+1,i) +dBXE(j,i+1) +dBXE(j,i-1) -4.*dBXE(j,i))
var_t(i,j_inv) = (sin(ij_angle)**2*F1(i)+cos(ij_angle)**2*F1(j))/ts*dBYE(i,j) -(sin(ij_angle)**2*F2(i)+cos(ij_angle)**2*F2(j))/ts*(dBYE(i-1,j) +dBYE(i+1,j) +dBYE(i,j+1) +dBYE(i,j-1) -4.*dBYE(i,j))
var_t(i_inv,j_inv) = (sin(ij_angle)**2*F1(i)+cos(ij_angle)**2*F1(j))/ts*dBYE(i_inv,j)-(sin(ij_angle)**2*F2(i)+cos(ij_angle)**2*F2(j))/ts*(dBYE(i_inv-1,j)+dBYE(i_inv+1,j)+dBYE(i_inv,j+1)+dBYE(i_inv,j-1)-4.*dBYE(i_inv,j))
enddo
enddo
forall (i=1:spec_zone,j=1:x_grd_num)
var_t(j,i) = dBYS(j,i)/ts
var_t(j,y_grd_num-i+1) = dBYE(j,i)/ts
endforall
forall (i=1:spec_zone,j=1:y_grd_num)
var_t(i,j) = dBXS(j,i)/ts
var_t(x_grd_num-i+1,j) = dBXE(j,i)/ts
endforall
end subroutine WRF_LBC
! Calculate Lateral Boundary Condition Weight Function Coefficients
subroutine LBC_WFC(F1,F2,bdy_width,spec_zone,RelaxZone,dx)
implicit none
integer,intent(in) :: bdy_width,spec_zone,RelaxZone
real,intent(in) :: dx
real,intent(out) :: F1(spec_zone+1:bdy_width-1),&
F2(spec_zone+1:bdy_width-1)
integer n
forall (n=spec_zone+1:bdy_width-1)
F1(n)= 0.1d0*dble(bdy_width-n)/dble(RelaxZone-1.d0)*exp(-dble(n-spec_zone-1.d0)*spec_exp) !spec_exp is a parameter defined by user, 0 for linear ramp, 0.33 =~ 3*dx exp decay factor
F2(n)=0.02d0*dble(bdy_width-n)/dble(RelaxZone-1.d0)*exp(-dble(n-spec_zone-1.d0)*spec_exp) !spec_exp is a parameter defined by user, 0 for linear ramp, 0.33 =~ 3*dx exp decay factor
endforall
end subroutine LBC_WFC
!Update Lateral Boundary Conditions by using WRF scheme
subroutine ULBC_WRF(u,v,z,integerated_step_num,ts)
implicit none
real ,intent(inout)::u(grid%x_grd_num_u,grid%y_grd_num_u),&
v(grid%x_grd_num_v,grid%y_grd_num_v),&
z(grid%x_grd_num ,grid%y_grd_num )
real ,intent(in):: integerated_step_num
real ,intent(in):: ts !time_step used by updating lbc
real u_bdy_temp(grid%x_grd_num_u,grid%y_grd_num_u),&
v_bdy_temp(grid%x_grd_num_v,grid%y_grd_num_v),&
z_bdy_temp(grid%x_grd_num ,grid%y_grd_num )
integer iubs,iube,jubs,jube,iuts,iute,juts,jute,iuls,iule,juls,jule,iurs,iure,jurs,jure,&
ivbs,ivbe,jvbs,jvbe,ivts,ivte,jvts,jvte,ivls,ivle,jvls,jvle,ivrs,ivre,jvrs,jvre,&
izbs,izbe,jzbs,jzbe,izts,izte,jzts,jzte,izls,izle,jzls,jzle,izrs,izre,jzrs,jzre
!$omp parallel
!$omp sections
!$omp section
!u bottom bdy
iubs=1
iube=grid%x_grd_num_u
jubs=1
jube=grid%bdy_width
!$omp section
!u top bdy
iuts=1
iute=grid%x_grd_num_u
juts=grid%y_grd_num_u-grid%bdy_width+1
jute=grid%y_grd_num_u
!$omp section
!u left bdy
iuls=1
iule=grid%bdy_width
juls=1
jule=grid%y_grd_num_u
!$omp section
!u right bdy
iurs=grid%x_grd_num_u-grid%bdy_width+1
iure=grid%x_grd_num_u
jurs=1
jure=grid%y_grd_num_u
!$omp section
!v bottom bdy
ivbs=1
ivbe=grid%x_grd_num_v
jvbs=1
jvbe=grid%bdy_width
!$omp section
!v top bdy
ivts=1
ivte=grid%x_grd_num_v
jvts=grid%y_grd_num_v-grid%bdy_width+1
jvte=grid%y_grd_num_v
!$omp section
!v left bdy
ivls=1
ivle=grid%bdy_width
jvls=1
jvle=grid%y_grd_num_v
!$omp section
!v right bdy
ivrs=grid%x_grd_num_v-grid%bdy_width+1
ivre=grid%x_grd_num_v
jvrs=1
jvre=grid%y_grd_num_v
!$omp section
!z bottom bdy
izbs=1
izbe=grid%x_grd_num
jzbs=1
jzbe=grid%bdy_width
!$omp section
!z top bdy
izts=1
izte=grid%x_grd_num
jzts=grid%y_grd_num-grid%bdy_width+1
jzte=grid%y_grd_num
!$omp section
!z left bdy
izls=1
izle=grid%bdy_width
jzls=1
jzle=grid%y_grd_num
!$omp section
!z right bdy
izrs=grid%x_grd_num-grid%bdy_width+1
izre=grid%x_grd_num
jzrs=1
jzre=grid%y_grd_num
!$omp end sections
!$omp end parallel
!$omp parallel
!$omp sections
!$omp section
call WRF_LBC(u,u_bdy_temp,grid%U_BYS,grid%U_BYE,grid%U_BXS,grid%U_BXE,grid%U_BTYS,grid%U_BTYE,grid%U_BTXS,grid%U_BTXE ,&
grid%F1,grid%F2,grid%interval_seconds,integerated_step_num,ts,grid%x_grd_num_u,grid%y_grd_num_u ,&
grid%bdy_width,grid%Spec_Zone,grid%bdy_time_num,grid%bdy_tend_time_num)
!$omp section
call WRF_LBC(v,v_bdy_temp,grid%V_BYS,grid%V_BYE,grid%V_BXS,grid%V_BXE,grid%V_BTYS,grid%V_BTYE,grid%V_BTXS,grid%V_BTXE ,&
grid%F1,grid%F2,grid%interval_seconds,integerated_step_num,ts,grid%x_grd_num_v,grid%y_grd_num_v ,&
grid%bdy_width,grid%Spec_Zone,grid%bdy_time_num,grid%bdy_tend_time_num)
!$omp section
call WRF_LBC(z,z_bdy_temp,grid%Z_BYS,grid%Z_BYE,grid%Z_BXS,grid%Z_BXE,grid%Z_BTYS,grid%Z_BTYE,grid%Z_BTXS,grid%Z_BTXE ,&
grid%F1,grid%F2,grid%interval_seconds,integerated_step_num,ts,grid%x_grd_num,grid%y_grd_num ,&
grid%bdy_width,grid%spec_zone,grid%bdy_time_num,grid%bdy_tend_time_num)
!$omp end sections
!$omp end parallel
!$omp parallel
!$omp sections
!$omp section
!u bottom bound
u(iubs:iube,jubs:jube)=u(iubs:iube,jubs:jube)+ts*u_bdy_temp(iubs:iube,jubs:jube)
!$omp section
!u top bound
u(iuts:iute,juts:jute)=u(iuts:iute,juts:jute)+ts*u_bdy_temp(iuts:iute,juts:jute)
!$omp section
!u left bound
u(iuls:iule,juls:jule)=u(iuls:iule,juls:jule)+ts*u_bdy_temp(iuls:iule,juls:jule)
!$omp section
!u right bound
u(iurs:iure,jurs:jure)=u(iurs:iure,jurs:jure)+ts*u_bdy_temp(iurs:iure,jurs:jure)
!$omp section
!v bottom bound
v(ivbs:ivbe,jvbs:jvbe)=v(ivbs:ivbe,jvbs:jvbe)+ts*v_bdy_temp(ivbs:ivbe,jvbs:jvbe)
!$omp section
!v top bound
v(ivts:ivte,jvts:jvte)=v(ivts:ivte,jvts:jvte)+ts*v_bdy_temp(ivts:ivte,jvts:jvte)
!$omp section
!v left bound
v(ivls:ivle,jvls:jvle)=v(ivls:ivle,jvls:jvle)+ts*v_bdy_temp(ivls:ivle,jvls:jvle)
!$omp section
!v right bound
v(ivrs:ivre,jvrs:jvre)=v(ivrs:ivre,jvrs:jvre)+ts*v_bdy_temp(ivrs:ivre,jvrs:jvre)
!$omp section
!z bottom bound
z(izbs:izbe,jzbs:jzbe)=z(izbs:izbe,jzbs:jzbe)+ts*z_bdy_temp(izbs:izbe,jzbs:jzbe)
!$omp section
!z top bound
z(izts:izte,jzts:jzte)=z(izts:izte,jzts:jzte)+ts*z_bdy_temp(izts:izte,jzts:jzte)
!$omp section
!z left bound
z(izls:izle,jzls:jzle)=z(izls:izle,jzls:jzle)+ts*z_bdy_temp(izls:izle,jzls:jzle)
!$omp section
!z right bound
z(izrs:izre,jzrs:jzre)=z(izrs:izre,jzrs:jzre)+ts*z_bdy_temp(izrs:izre,jzrs:jzre)
!$omp end sections
!$omp end parallel
end subroutine ULBC_WRF
subroutine diffusion(var,x_grd_num,y_grd_num)
implicit none
!ts is the time step
integer ,intent(in):: x_grd_num,y_grd_num
real ,intent(inout):: var(x_grd_num,y_grd_num)
real diffusion_term(x_grd_num,y_grd_num)
real k2
integer i,j
diffusion_term=0.d0
!2nd order
forall(i=2:2,j=2:y_grd_num-1)
diffusion_term(i,j)=0.125*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1)-4*var(i,j))
endforall
forall(i=grid%bdy_width+1:x_grd_num-1,j=2:2)
diffusion_term(i,j)=0.125*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1)-4*var(i,j))
endforall
forall(i=x_grd_num-1:x_grd_num-1,j=grid%bdy_width+1:y_grd_num-1)
diffusion_term(i,j)=0.125*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1)-4*var(i,j))
endforall
forall(i=grid%bdy_width+1:x_grd_num-grid%bdy_width,j=y_grd_num-1:y_grd_num-1)
diffusion_term(i,j)=0.125*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1)-4*var(i,j))
endforall
!4th order
forall(i=3:3,j=3:y_grd_num-2)
diffusion_term(i,j)=-0.03125*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2)-4*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+12*var(i,j))
endforall
forall(i=3:x_grd_num-2,j=3:3)
diffusion_term(i,j)=-0.03125*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2)-4*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+12*var(i,j))
endforall
forall(i=x_grd_num-2:x_grd_num-2,j=3:y_grd_num-2)
diffusion_term(i,j)=-0.03125*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2)-4*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+12*var(i,j))
endforall
forall(i=3:x_grd_num-2,j=y_grd_num-2:y_grd_num-2)
diffusion_term(i,j)=-0.03125*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2)-4*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+12*var(i,j))
endforall
!6th order
forall(i=4:grid%bdy_width,j=4:y_grd_num-3)
diffusion_term(i,j)=0.0078125*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3)-6*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))+15*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))-40*var(i,j))
endforall
forall(i=grid%bdy_width+1:x_grd_num-3,j=4:grid%bdy_width)
diffusion_term(i,j)=0.0078125*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3)-6*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))+15*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))-40*var(i,j))
endforall
forall(i=x_grd_num-grid%bdy_width+1:x_grd_num-3,j=grid%bdy_width+1:y_grd_num-3)
diffusion_term(i,j)=0.0078125*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3)-6*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))+15*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))-40*var(i,j))
endforall
forall(i=grid%bdy_width+1:x_grd_num-grid%bdy_width,j=y_grd_num-grid%bdy_width+1:y_grd_num-3)
diffusion_term(i,j)=0.0078125*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3)-6*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))+15*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))-40*var(i,j))
endforall
!Diffusion cases
if(diff_order==0)then
!No diffusion
!2th order diffusion full field
elseif(diff_order==2)then
forall(i=5:x_grd_num-4,j=5:y_grd_num-4)
diffusion_term(i,j)=0.125*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1)-4*var(i,j))
endforall
!4th order diffusion full field
elseif(diff_order==4)then
forall(i=5:x_grd_num-4,j=5:y_grd_num-4)
diffusion_term(i,j)=-0.03125*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2)-4*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+12*var(i,j))
endforall
!6th order diffusion full field
elseif(diff_order==6)then
forall(i=5:x_grd_num-4,j=5:y_grd_num-4)
diffusion_term(i,j)=0.0078125*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3)-6*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))+15*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))-40*var(i,j))
endforall
!8th order diffusion full field
elseif(diff_order==8)then
forall(i=5:x_grd_num-4,j=5:y_grd_num-4)
diffusion_term(i,j)=-0.001953125*(var(i+4,j)+var(i-4,j)+var(i,j+4)+var(i,j-4)-8*(var(i+3,j)+var(i-3,j)+var(i,j+3)+var(i,j-3))+28*(var(i+2,j)+var(i-2,j)+var(i,j+2)+var(i,j-2))-56*(var(i+1,j)+var(i-1,j)+var(i,j+1)+var(i,j-1))+140*var(i,j))
endforall
endif
var=var+diffusion_term
end subroutine diffusion
end module subroutines