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discretisation_QUICK.f90
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subroutine discretisation_QUICK()
use variables
implicit none
!!! u_star calculation (x component) !!!
!$OMP PARALLEL DO PRIVATE(i,j,k)
do k=1,nz
do j=1,ny
do i=1,nx-1
if (u(i,j,k) > 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) )
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) )
vnu = 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) )
vsu = 0.5*(v(i,j-1,k) + v(i+1,j-1,k)) -0.125*Dxs(i)*Dxs(i)/iDx(i) &
*( (v(i+1,j-1,k) - v(i,j-1,k) ) / Dxs(i) &
- (v(i,j-1,k) - v(i-1,j-1,k)) / Dxs(i-1) )
wfu = 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) )
wbu = 0.5*(w(i,j,k-1) + w(i+1,j,k-1)) -0.125*Dxs(i)*Dxs(i)/iDx(i) &
*( (w(i+1,j,k-1) - w(i,j,k-1) ) / Dxs(i) &
- (w(i,j,k-1) - w(i-1,j,k-1)) / Dxs(i-1) )
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) )
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) )
vnu = 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) )
vsu = 0.5*(v(i,j-1,k) + v(i+1,j-1,k) ) -0.125*Dxs(i)*Dxs(i)/iDx(i+1) &
*( (v(i+2,j-1,k) - v(i+1,j-1,k)) / Dxs(i+1) &
- (v(i+1,j-1,k) - v(i,j-1,k) ) / Dxs(i) )
wfu = 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) )
wbu = 0.5*(w(i,j,k-1) + w(i+1,j,k-1) ) -0.125*Dxs(i)*Dxs(i)/iDx(i+1) &
*( (w(i+2,j,k-1) - w(i+1,j,k-1)) / Dxs(i+1) &
- (w(i+1,j,k-1) - w(i,j,k-1) ) / Dxs(i) )
end if
if (v(i,j,k) > 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))
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
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) )
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(i,j,k) > 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) ) !!!
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
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) )
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
if (Q1 == 1) then
delta = ( Dxs(i)*iDy(j)*iDz(k) ) ** (1./3)
nut = (Cs*delta)**2 * ( 0.5*(1/Dxs(i)/Dxs(i))*((u(i+1,j,k)+u(i,j,k))-(u(i,j,k)+u(i-1,j,k)))**2 + &
0.5*(1/iDy(j)/iDy(j))*((v(i+1,j,k)+v(i,j,k))-(v(i+1,j-1,k)+v(i,j-1,k)))**2 + &
0.5*(1/iDz(k)/iDz(k))*((w(i+1,j,k)+w(i,j,k))-(w(i+1,j,k-1)+w(i,j,k-1)))**2 + &
( 0.5*(1/iDy(j))*((u(i,j+1,k)+u(i,j,k))-(u(i,j,k)+u(i,j-1,k)))+ &
0.5*(1/Dxs(i))*((v(i+1,j,k)+v(i+1,j-1,k))-(v(i,j,k)+v(i,j-1,k))) )**2 + &
( 0.5*(1/iDz(k))*((u(i,j,k+1)+u(i,j,k))-(u(i,j,k)+u(i,j,k-1)))+ &
0.5*(1/Dxs(i))*((w(i+1,j,k)+w(i+1,j,k-1))-(w(i,j,k)+w(i,j,k-1))) )**2 + &
( 0.5*(1/iDz(k))*((v(i+1,j,k+1)+v(i,j-1,k))-(v(i+1,j,k-1)+v(i,j-1,k)))+ &
0.5*(1/iDy(j))*((w(i+1,j+1,k)+w(i,j,k-1))-(w(i+1,j-1,k)+w(i,j,k-1))) )**2 )**0.5
end if
u_star(i,j,k) = u(i,j,k)-dt*(ue*ue-uw*uw) / Dxs(i) &
-dt*(un*vnu-us*vsu) / iDy(j) &
-dt*(uf*wfu-ub*wbu) / iDz(k) &
+(nu+nut*Q1)*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*Q1)*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*Q1)*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
end do
!$OMP END PARALLEL DO
!!! v_star calculation (y component) !!!
!$OMP PARALLEL DO PRIVATE(i,j,k)
do k=1,nz
do j=1,ny-1
do i=1,nx
if (u(i,j,k) > 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) )
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
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) )
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(i,j,k) > 0) then
uev = 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) )
uwv = 0.5*(u(i-1,j,k) + u(i-1,j+1,k) ) -0.125*Dys(j)*Dys(j)/iDy(j) &
*( (u(i-1,j+1,k) - u(i-1,j,k) ) / Dys(j) &
- (u(i-1,j,k) - u(i-1,j-1,k)) / Dys(j-1) )
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) )
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) )
wfv = 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) )
wbv = 0.5*(w(i,j,k-1) + w(i,j+1,k-1) ) -0.125*Dys(j)*Dys(j)/iDy(j) &
*( (w(i,j+1,k-1) - w(i,j,k-1) ) / Dys(j) &
- (w(i,j,k-1) - w(i,j-1,k-1)) / Dys(j-1))
else
uev = 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) )
uwv = 0.5*(u(i-1,j,k) + u(i-1,j+1,k) ) -0.125*Dys(j)*Dys(j)/iDy(j+1) &
*( (u(i-1,j+2,k) - u(i-1,j+1,k)) / Dys(j+1) &
- (u(i-1,j+1,k) - u(i-1,j,k) ) / Dys(j) )
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) )
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) )
wfv = 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) )
wbv = 0.5*(w(i,j,k-1) + w(i,j+1,k-1) ) -0.125*Dys(j)*Dys(j)/iDy(j+1) &
*( (w(i,j+2,k-1) - w(i,j+1,k-1)) / Dys(j+1) &
- (w(i,j+1,k-1) - w(i,j,k-1) ) / Dys(j) )
end if
if (w(i,j,k) > 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) )
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
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) )
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
if (Q1 == 1) then
delta = ( iDx(i)*Dys(j)*iDz(k) ) ** (1./3)
nut = (Cs*delta)**2 * ( 0.5*(1/iDx(i)/iDx(i))*((u(i,j+1,k)+u(i,j,k))-(u(i-1,j+1,k)+u(i-1,j,k)))**2 + &
0.5*(1/Dys(j)/Dys(j))*((v(i,j+1,k)+v(i,j,k))-(v(i,j,k)+v(i,j-1,k)))**2 + &
0.5*(1/iDz(k)/iDz(k))*((w(i,j+1,k)+w(i,j,k))-(w(i,j+1,k-1)+w(i,j,k-1)))**2 + &
( 0.5*(1/Dys(j))*((u(i,j+1,k)+u(i-1,j+1,k))-(u(i,j,k)+u(i-1,j,k)))+ &
0.5*(1/iDx(i))*((v(i+1,j,k)+v(i,j,k))-(v(i,j,k)+v(i-1,j,k))) )**2 + &
( 0.5*(1/iDz(k))*((u(i,j+1,k+1)+u(i-1,j,k))-(u(i,j+1,k-1)+u(i-1,j,k-1)))+ &
0.5*(1/iDx(i))*((w(i+1,j+1,k)+w(i,j,k-1))-(w(i-1,j+1,k)+w(i,j,k-1))) )**2 + &
( 0.5*(1/iDz(k))*((v(i,j,k+1)+v(i,j,k))-(v(i,j,k-1)+v(i,j,k)))+ &
0.5*(1/Dys(j))*((w(i,j+1,k)+w(i,j+1,k-1))-(w(i,j,k)+w(i,j,k-1))) )**2 )**0.5
end if
v_star(i,j,k) = v(i,j,k)-dt*(uev*ve-uwv*vw) / iDx(i) &
-dt*(vn*vn-vs*vs) / Dys(j) &
-dt*(vf*wfv-vb*wbv) / iDz(k) &
+(nu+nut*Q1)*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*Q1)*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*Q1)*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
end do
!$OMP END PARALLEL DO
!!! w_star calculation (z component) !!!
!$OMP PARALLEL DO PRIVATE(i,j,k)
do k=1,nz-1
do j=1,ny
do i=1,nx
if (u(i,j,k) > 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) )
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
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) )
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(i,j,k) > 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) )
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
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) )
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(i,j,k) > 0) then
uew = 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) )
uww = 0.5*(u(i-1,j,k) + u(i-1,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k) &
*( (u(i-1,j,k+1) - u(i-1,j,k) ) / Dzs(k) &
- (u(i-1,j,k) - u(i-1,j,k-1)) / Dzs(k-1) )
vnw = 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) )
vsw = 0.5*(v(i,j-1,k) + v(i,j-1,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k) &
*( (v(i,j-1,k+1) - v(i,j-1,k) ) / Dzs(k) &
- (v(i,j-1,k) - v(i,j-1,k-1)) / Dzs(k-1) )
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) )
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
uew = 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) )
uww = 0.5*(u(i-1,j,k) + u(i-1,j,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k+1) &
*( (u(i-1,j,k+2) - u(i-1,j,k+1)) / Dzs(k+1) &
- (u(i-1,j,k+1) - u(i-1,j,k) ) / Dzs(k) )
vnw = 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) )
vsw = 0.5*(v(i,j-1,k) + v(i,j-1,k+1) ) -0.125*Dzs(k)*Dzs(k)/iDz(k+1) &
*( (v(i,j-1,k+2) - v(i,j-1,k+1)) / Dzs(k+1) &
- (v(i,j-1,k+1) - v(i,j-1,k) ) / Dzs(k) )
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) )
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
if (Q1 == 1) then
delta = ( iDx(i)*iDy(j)*Dzs(k) ) ** (1./3)
nut = (Cs*delta)**2 * ( 0.5*(1/iDx(i)/iDx(i))*((u(i,j,k+1)+u(i,j,k))-(u(i-1,j,k+1)+u(i-1,j,k)))**2 + &
0.5*(1/iDy(j)/iDy(j))*((v(i,j,k+1)+v(i,j,k))-(v(i,j-1,k+1)+v(i,j-1,k)))**2 + &
0.5*(1/Dzs(k)/Dzs(k))*((w(i,j,k+1)+w(i,j,k))-(w(i,j,k)+w(i,j,k-1)))**2 + &
( 0.5*(1/iDy(j))*((u(i,j+1,k)+u(i,j,k))-(u(i,j,k)+u(i,j-1,k)))+ &
0.5*(1/iDx(i))*((v(i+1,j,k+1)+v(i,j-1,k))-(v(i-1,j,k+1)+v(i,j-1,k))) )**2 + &
( 0.5*(1/Dzs(k))*((u(i,j,k+1)+u(i-1,j,k+1))-(u(i,j,k)+u(i-1,j,k)))+ &
0.5*(1/iDx(i))*((w(i+1,j,k)+w(i,j,k))-(w(i-1,j,k)+w(i,j,k))) )**2 + &
( 0.5*(1/Dzs(k))*((v(i,j,k+1)+v(i,j-1,k+1))-(v(i,j,k)+v(i,j-1,k)))+ &
0.5*(1/iDy(j))*((w(i,j+1,k)+w(i,j,k))-(w(i,j-1,k)+w(i,j,k))) )**2 )**0.5
end if
w_star(i,j,k) = w(i,j,k)-dt*(uew*we-uww*ww) / iDx(i) &
-dt*(vnw*wn-vsw*ws) / iDy(j) &
-dt*(wf*wf-wb*wb) / Dzs(k) &
+(nu+nut*Q1)*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*Q1)*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*Q1)*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
end do
!$OMP END PARALLEL DO
end subroutine discretisation_QUICK