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discretisation_QUICK_centre.f90
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discretisation_QUICK_centre.f90
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subroutine discretisation_QUICK_centre()
use variables
implicit none
!!! u_star calculation (x component) !!!
do k=istart,iend
!$OMP PARALLEL DO PRIVATE(i)
do j=1,ny; do i=1,nx
u_tilde_x1 = 0.5 * (u(i+1,j,k)+u(i,j,k))
u_tilde_x2 = 0.5 * (u(i-1,j,k)+u(i,j,k))
v_tilde_x1 = 0.5 * (v(i,j,k)+v(i+1,j,k))
v_tilde_x2 = 0.5 * (v(i,j-1,k)+v(i+1,j-1,k))
w_tilde_x1 = 0.5 * (w(i+1,j,k)+w(i,j,k))
w_tilde_x2 = 0.5 * (w(i,j,k-1)+w(i+1,j,k-1))
if (u_tilde_x1 > 0) then
ue = 0.5*(u(i,j,k) + u(i+1,j,k) ) -0.125*iDx(i+1)*iDx(i+1)/Dxs(i)* &
( (u(i+1,j,k) - u(i,j,k) ) / iDx(i+1) &
- (u(i,j,k) - u(i-1,j,k) ) / iDx(i) )
else
ue = 0.5*(u(i,j,k) + u(i+1,j,k) ) -0.125*iDx(i+1)*iDx(i+1)/Dxs(i+1)* &
( (u(i+2,j,k) - u(i+1,j,k) ) / iDx(i+2) &
- (u(i+1,j,k) - u(i,j,k) ) / iDx(i+1) )
end if
if (u_tilde_x2 > 0) then
uw = 0.5*(u(i-1,j,k) + u(i,j,k) ) -0.125*iDx(i)*iDx(i)/Dxs(i-1)* &
( (u(i,j,k) - u(i-1,j,k) ) / iDx(i) &
- (u(i-1,j,k) - u(i-2,j,k) ) / iDx(i-1) )
else
uw = 0.5*(u(i-1,j,k) + u(i,j,k) ) -0.125*iDx(i)*iDx(i)/Dxs(i)* &
( (u(i+1,j,k) - u(i,j,k) ) / iDx(i+1) &
- (u(i,j,k) - u(i-1,j,k) ) / iDx(i) )
end if
if (v_tilde_x1 > 0) then
un = 0.5*(u(i,j,k) + u(i,j+1,k) ) -0.125*Dys(j)*Dys(j)/iDy(j)* &
( (u(i,j+1,k) - u(i,j,k) ) / Dys(j) &
- (u(i,j,k) - u(i,j-1,k) ) / Dys(j-1))
else
un = 0.5*(u(i,j,k) + u(i,j+1,k) )-0.125*Dys(j)*Dys(j)/iDy(j+1)* &
( (u(i,j+2,k) - u(i,j+1,k) ) / Dys(j+1)&
- (u(i,j+1,k) - u(i,j,k) ) / Dys(j) )
end if
if (v_tilde_x2 > 0) then
us = 0.5*(u(i,j-1,k) + u(i,j,k) ) -0.125*Dys(j-1)*Dys(j-1)/iDy(j-1)* &
( (u(i,j,k) - u(i,j-1,k) ) / Dys(j-1)&
- (u(i,j-1,k) - u(i,j-2,k) ) / Dys(j-2))
else
us = 0.5*(u(i,j-1,k) + u(i,j,k) ) -0.125*Dys(j-1)*Dys(j-1)/iDy(j)* &
( (u(i,j+1,k) - u(i,j,k) ) / Dys(j) &
- (u(i,j,k) - u(i,j-1,k) ) / Dys(j-1))
end if
if (w_tilde_x1 > 0) then
uf = 0.5*(u(i,j,k) + u(i,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k)* &
( (u(i,j,k+1) - u(i,j,k) ) / Dzs(k) &
- (u(i,j,k) - u(i,j,k-1) ) / Dzs(k-1))
else
uf = 0.5*(u(i,j,k) + u(i,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k+1)* &
( (u(i,j,k+2) - u(i,j,k+1) ) / Dzs(k+1)&
- (u(i,j,k+1) - u(i,j,k) ) / Dzs(k) )
end if
if (w_tilde_x2 > 0) then
ub = 0.5*(u(i,j,k-1) + u(i,j,k) ) -0.125*Dzs(k-1)*Dzs(k-1)/iDz(k-1)* &
( (u(i,j,k) - u(i,j,k-1) ) / Dzs(k-1)&
- (u(i,j,k-1) - u(i,j,k-2) ) / Dzs(k-2))
else
ub = 0.5*(u(i,j,k-1) + u(i,j,k) ) -0.125*Dzs(k-1)*Dzs(k-1)/iDz(k)* &
( (u(i,j,k+1) - u(i,j,k) ) / Dzs(k) &
- (u(i,j,k) - u(i,j,k-1) ) / Dzs(k-1))
end if
nut = Viseff(i,j,k)
u_star(i,j,k) = u(i,j,k)-dt*(u_tilde_x1*ue-u_tilde_x2*uw) / Dxs(i) &
-dt*(v_tilde_x1*un-v_tilde_x2*us) / iDy(j) &
-dt*(w_tilde_x1*uf-w_tilde_x2*ub) / iDz(k) &
+(nu+nut*LES)*dt*( (u(i+1,j,k)-u(i,j,k)) / iDx(i+1) - (u(i,j,k)-u(i-1,j,k)) / iDx(i) ) / Dxs(i) &
+(nu+nut*LES)*dt*( (u(i,j+1,k)-u(i,j,k)) / Dys(j) - (u(i,j,k)-u(i,j-1,k)) / Dys(j-1) ) / iDy(j) &
+(nu+nut*LES)*dt*( (u(i,j,k+1)-u(i,j,k)) / Dzs(k) - (u(i,j,k)-u(i,j,k-1)) / Dzs(k-1) ) / iDz(k)
end do;end do
!$OMP END PARALLEL DO
end do
!!! v_star calculation (y component) !!!
do k=istart,iend
!$OMP PARALLEL DO PRIVATE(i)
do j=1,ny;do i=1,nx
u_tilde_y1 = 0.5 * (u(i,j,k)+u(i,j+1,k))
u_tilde_y2 = 0.5 * (u(i-1,j,k)+u(i-1,j+1,k))
v_tilde_y1 = 0.5 * (v(i,j,k)+v(i,j+1,k))
v_tilde_y2 = 0.5 * (v(i,j-1,k)+v(i,j,k))
w_tilde_y1 = 0.5 * (w(i,j,k)+w(i,j+1,k))
w_tilde_y2 = 0.5 * (w(i,j,k-1)+w(i,j+1,k-1))
if (u_tilde_y1 > 0) then
ve = 0.5*(v(i,j,k) + v(i+1,j,k) ) -0.125*Dxs(i)*Dxs(i)/iDx(i)* &
( (v(i+1,j,k) - v(i,j,k) ) / Dxs(i) &
- (v(i,j,k) - v(i-1,j,k) ) / Dxs(i-1))
else
ve = 0.5*(v(i,j,k) + v(i+1,j,k) ) -0.125*Dxs(i)*Dxs(i)/iDx(i+1)* &
( (v(i+2,j,k) - v(i+1,j,k) ) / Dxs(i+1)&
- (v(i+1,j,k) - v(i,j,k) ) / Dxs(i) )
end if
if (u_tilde_y2 > 0) then
vw = 0.5*(v(i-1,j,k) + v(i,j,k) ) -0.125*Dxs(i-1)*Dxs(i-1)/iDx(i-1)* &
( (v(i,j,k) - v(i-1,j,k) ) / Dxs(i-1)&
- (v(i-1,j,k) - v(i-2,j,k) ) / Dxs(i-2))
else
vw = 0.5*(v(i-1,j,k) + v(i,j,k) ) -0.125*Dxs(i-1)*Dxs(i-1)/iDx(i)* &
( (v(i+1,j,k) - v(i,j,k) ) / Dxs(i) &
- (v(i,j,k) - v(i-1,j,k) ) / Dxs(i-1))
end if
if (v_tilde_y1 > 0) then
vn = 0.5*(v(i,j,k) + v(i,j+1,k) ) -0.125*iDy(j+1)*iDy(j+1)/Dys(j)* &
( (v(i,j+1,k) - v(i,j,k) ) / iDy(j+1) &
- (v(i,j,k) - v(i,j-1,k) ) / iDy(j) )
else
vn = 0.5*(v(i,j,k) + v(i,j+1,k) ) -0.125*iDy(j+1)*iDy(j+1)/Dys(j+1)* &
( (v(i,j+2,k) - v(i,j+1,k) ) / iDy(j+2) &
- (v(i,j+1,k) - v(i,j,k) ) / iDy(j+1) )
end if
if (v_tilde_y2 > 0) then
vs = 0.5*(v(i,j-1,k) + v(i,j,k) ) -0.125*iDy(j)*iDy(j)/Dys(j-1)* &
( (v(i,j,k) - v(i,j-1,k) ) / iDy(j) &
- (v(i,j-1,k) - v(i,j-2,k) ) / iDy(j-1) )
else
vs = 0.5*(v(i,j-1,k) + v(i,j,k) ) -0.125*iDy(j)*iDy(j)/Dys(j)* &
( (v(i,j+1,k) - v(i,j,k) ) / iDy(j+1)&
- (v(i,j,k) - v(i,j-1,k) ) / iDy(j) )
end if
if (w_tilde_y1 > 0) then
vf = 0.5*(v(i,j,k) + v(i,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k)* &
( (v(i,j,k+1) - v(i,j,k) ) / Dzs(k) &
- (v(i,j,k) - v(i,j,k-1) ) / Dzs(k-1))
else
vf = 0.5*(v(i,j,k) + v(i,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k+1)* &
( (v(i,j,k+2) - v(i,j,k+1) ) / Dzs(k+1)&
- (v(i,j,k+1) - v(i,j,k) ) / Dzs(k) )
end if
if (w_tilde_y2 > 0) then
vb = 0.5*(v(i,j,k-1) + v(i,j,k) ) -0.125*Dzs(k-1)*Dzs(k-1)/iDz(k-1)* &
( (v(i,j,k) - v(i,j,k-1) ) / Dzs(k-1)&
- (v(i,j,k-1) - v(i,j,k-2) ) / Dzs(k-2))
else
vb = 0.5*(v(i,j,k-1) + v(i,j,k) ) -0.125*Dzs(k-1)*Dzs(k-1)/iDz(k)* &
( (v(i,j,k+1) - v(i,j,k) ) / Dzs(k) &
- (v(i,j,k) - v(i,j,k-1) ) / Dzs(k-1))
end if
nut = Viseff(i,j,k)
v_star(i,j,k) = v(i,j,k)-dt*(u_tilde_y1*ve-u_tilde_y2*vw) / iDx(i) &
-dt*(v_tilde_y1*vn-v_tilde_y2*vs) / Dys(j) &
-dt*(w_tilde_y1*vf-w_tilde_y2*vb) / iDz(k) &
+(nu+nut*LES)*dt*( (v(i+1,j,k)-v(i,j,k)) / Dxs(i) - (v(i,j,k) - v(i-1,j,k)) / Dxs(i-1) ) / iDx(i) &
+(nu+nut*LES)*dt*( (v(i,j+1,k)-v(i,j,k)) / iDy(j+1) - (v(i,j,k) - v(i,j-1,k)) / iDy(j) ) / Dys(j) &
+(nu+nut*LES)*dt*( (v(i,j,k+1)-v(i,j,k)) / Dzs(k) - (v(i,j,k) - v(i,j,k-1)) / Dzs(k-1) ) / iDz(k)
end do;end do
!$OMP END PARALLEL DO
end do
!!! w_star calculation (z component) !!!
do k=istart,iend
!$OMP PARALLEL DO PRIVATE(i)
do j=1,ny;do i=1,nx
u_tilde_z1 = 0.5 * (u(i,j,k+1)+u(i,j,k))
u_tilde_z2 = 0.5 * (u(i-1,j,k+1)+u(i-1,j,k))
v_tilde_z1 = 0.5 * (v(i,j,k)+v(i,j,k+1))
v_tilde_z2 = 0.5 * (v(i,j-1,k+1)+v(i,j-1,k))
w_tilde_z1 = 0.5 * (w(i,j,k+1)+w(i,j,k))
w_tilde_z2 = 0.5 * (w(i,j,k)+w(i,j,k-1))
if (u_tilde_z1 > 0) then
we = 0.5*(w(i,j,k) + w(i+1,j,k) ) -0.125*Dxs(i)*Dxs(i)/iDx(i)* &
( (w(i+1,j,k) - w(i,j,k) ) / Dxs(i) &
- (w(i,j,k) - w(i-1,j,k) ) / Dxs(i-1))
else
we = 0.5*(w(i,j,k) + w(i+1,j,k) ) -0.125*Dxs(i)*Dxs(i)/iDx(i+1)* &
( (w(i+2,j,k) - w(i+1,j,k) ) / Dxs(i+1) &
- (w(i+1,j,k) - w(i,j,k) ) / Dxs(i) )
end if
if (u_tilde_z2 > 0) then
ww = 0.5*(w(i-1,j,k) + w(i,j,k) ) -0.125*Dxs(i-1)*Dxs(i-1)/iDx(i-1)* &
( (w(i,j,k) - w(i-1,j,k) ) / Dxs(i-1) &
- (w(i-1,j,k) - w(i-2,j,k) ) / Dxs(i-2) )
else
ww = 0.5*(w(i-1,j,k) + w(i,j,k) ) -0.125*Dxs(i-1)*Dxs(i-1)/iDx(i)* &
( (w(i+1,j,k) - w(i,j,k) ) / Dxs(i) &
- (W(i,j,k) - w(i-1,j,k) ) / Dxs(i-1))
end if
if (v_tilde_z1 > 0) then
wn = 0.5*(w(i,j,k) + w(i,j+1,k) ) -0.125*Dys(j)*Dys(j)/iDy(j)* &
( (w(i,j+1,k) - w(i,j,k) ) / Dys(j) &
- (w(i,j,k) - w(i,j-1,k) ) / Dys(j-1))
else
wn = 0.5*(w(i,j,k) + w(i,j+1,k) ) -0.125*Dys(j)*Dys(j)/iDy(j+1)* &
( (w(i,j+2,k) - w(i,j+1,k) ) / Dys(j+1)&
- (w(i,j+1,k) - w(i,j,k) ) / Dys(j) )
end if
if (v_tilde_z2 > 0) then
ws = 0.5*(w(i,j-1,k) + w(i,j,k) ) -0.125*Dys(j-1)*Dys(j-1)/iDy(j-1)* &
( (w(i,j,k) - w(i,j-1,k) ) / Dys(j-1)&
- (w(i,j-1,k) - w(i,j-2,k) ) / Dys(j-2))
else
ws = 0.5*(w(i,j-1,k) + w(i,j,k) ) -0.125*Dys(j-1)*Dys(j-1)/iDy(j)* &
( (w(i,j+1,k) - w(i,j,k) ) / Dys(j) &
- (w(i,j,k) - w(i,j-1,k) ) / Dys(j-1))
end if
if (w_tilde_z1 > 0) then
wf = 0.5*(w(i,j,k) + w(i,j,k+1) ) -0.125*iDz(k+1)*iDz(k+1)/Dzs(k)* &
( (w(i,j,k+1) - w(i,j,k) ) / iDz(k+1)&
- (w(i,j,k) - w(i,j,k-1) ) / iDz(k) )
else
wf = 0.5*(w(i,j,k) + w(i,j,k+1) ) -0.125*iDz(k+1)*iDz(k+1)/Dzs(k+1)* &
( (w(i,j,k+2) - w(i,j,k+1) ) / iDz(k+2)&
- (w(i,j,k+1) - w(i,j,k) ) / iDz(k+1))
end if
if (w_tilde_z2 > 0) then
wb = 0.5*(w(i,j,k-1) + w(i,j,k) ) -0.125*iDz(k)*iDz(k)/Dzs(k-1)* &
( (w(i,j,k) - w(i,j,k-1) ) / iDz(k) &
- (w(i,j,k-1) - w(i,j,k-2) ) / iDz(k-1))
else
wb = 0.5*(w(i,j,k-1) + w(i,j,k) ) -0.125*iDz(k)*iDz(k)/Dzs(k)* &
( (w(i,j,k+1) - w(i,j,k) ) / iDz(k+1)&
- ( w(i,j,k) - w(i,j,k-1) ) / iDz(k) )
end if
nut = Viseff(i,j,k)
w_star(i,j,k) = w(i,j,k)-dt*(u_tilde_z1*we-u_tilde_z2*ww) / iDx(i) &
-dt*(v_tilde_z1*wn-v_tilde_z2*ws) / iDy(j) &
-dt*(w_tilde_z1*wf-w_tilde_z2*wb) / Dzs(k) &
+(nu+nut*LES)*dt*( ( w(i+1,j,k)-w(i,j,k) ) / Dxs(i) - ( w(i,j,k)-w(i-1,j,k) ) / Dxs(i-1) ) / iDx(i) &
+(nu+nut*LES)*dt*( ( w(i,j+1,k)-w(i,j,k) ) / Dys(j) - ( w(i,j,k)-w(i,j-1,k) ) / Dys(j-1) ) / iDy(j) &
+(nu+nut*LES)*dt*( ( w(i,j,k+1)-w(i,j,k) ) / iDz(k+1) - ( w(i,j,k)-w(i,j,k-1) ) / iDz(k) ) / Dzs(k)
end do;end do
!$OMP END PARALLEL DO
end do
end subroutine discretisation_QUICK_centre