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init_velocity.f90
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subroutine init_velocity
use m_openmpi
use m_parameters
use m_io
use m_fields
use m_work
use x_fftw
use m_rand_knuth
use RANDu
implicit none
integer :: i, j, k, n
integer*8 :: seed1, seed2, i8, j8, k8
integer :: time_array(8)
real, allocatable :: rr(:)
real*8, allocatable :: e_spec(:), e_spec1(:)
integer *8, allocatable :: hits(:), hits1(:)
integer :: n_shell
real*8 :: sc_rad1, sc_rad2
real*8 :: wmag, wmag2, ratio, fac, fac2
!--------------------------------------------------------------------------------
! First, if it's a Taylor-Green vortex, then initialize and quit
!--------------------------------------------------------------------------------
if (isp_type .eq. -1) then
call init_velocity_taylor_green
return
end if
!================================================================================
allocate( e_spec(kmax), e_spec1(kmax), rr(nx+2), hits(kmax), hits1(kmax), stat=ierr)
if (ierr.ne.0) stop "cannot allocate the init_velocity arrays"
write(out,*) 'generating random velocities'
call flush(out)
!-------------------------------------------------------------------------------
! Generate the velocities
!-------------------------------------------------------------------------------
! initialize the random number sequence by the seed from the first processor
if (myid.eq.0) call system_clock(seed1,seed2)
if (myid.eq.0) then
call date_and_time(values=time_array)
seed1 = time_array(8)
end if
count = 1
call MPI_BCAST(seed1,count,MPI_INTEGER8,0,MPI_COMM_TASK,mpi_err)
!!$ seed1 = 23498675
!!$ call rand_knuth_init(seed1)
!!$ write(out,*) 'seed1 = ',seed1
!!$ call flush(out)
seed1 = RN1
write(out,*) "RANDOM SEED FOR VELOCITIES = ", seed1
call flush(out)
rseed = real(seed1,8)
fac = random(-rseed)
! bringing the processors to their own places in the random sequence
! ("6" is there because we're generating six fields
! using seed1 because it's int*8
!!$ write(out,*) "Will scroll down to my initial position", myid*ny*nz*6
!!$ call flush(out)
!!$ do i = 1,myid*ny*nz*6
!!$ call rand_knuth(rr,nx+2)
!!$ end do
do i8 = 1,myid*(nx+2)*ny*nz*6
fac = random(rseed)
end do
!!$ write(out,*) "Scrolled."
!!$ call flush(out)
! now filling the arrays wrk1...wrk6
do n = 1,6
do k = 1,nz
do j = 1,ny
do i = 1,nx+2
wrk(i,j,k,n) = random(rseed)
end do
end do
end do
end do
! just in case, bringing the random numbers to the same
! point in the sequence again
do seed1 = 1,int((numprocs-myid-1)*(nx+2)*ny*nz*6,8)
fac = random(rseed)
end do
! making three random arrays with Gaussian PDF
! out of the six arrays that we generated
wrk(:,:,:,1:3) = sqrt(-two*log(wrk(:,:,:,1:3))) * sin(TWO_PI*wrk(:,:,:,4:6))
! --- Making three arrays that have Gaussian PDF and the incompressibility property
! go to Fourier space
do n = 1,3
call xFFT3d(1,n)
end do
! assemble the arrays in wrk4..6, only the wavenumbers below kmax
do k = 1,nz
do j = 1,ny
do i = 1,nx+1,2
n_shell = nint(sqrt(akx(i)**2 + aky(k)**2 + akz(j)**2))
if (n_shell .gt. 0 .and. n_shell .le. kmax) then
wrk(i ,j,k,4) = - (aky(k)*wrk(i+1,j,k,3) - akz(j)*wrk(i+1,j,k,2))
wrk(i+1,j,k,4) = aky(k)*wrk(i ,j,k,3) - akz(j)*wrk(i ,j,k,2)
wrk(i ,j,k,5) = - (akz(j)*wrk(i+1,j,k,1) - akx(i+1)*wrk(i+1,j,k,3))
wrk(i+1,j,k,5) = akz(j)*wrk(i ,j,k,1) - akx(i )*wrk(i ,j,k,3)
wrk(i ,j,k,6) = - (akx(i+1)*wrk(i+1,j,k,2) - aky(k)*wrk(i+1,j,k,1))
wrk(i+1,j,k,6) = akx(i )*wrk(i ,j,k,2) - aky(k)*wrk(i ,j,k,1)
else
wrk(i:i+1,j,k,4:6) = zip
end if
end do
end do
end do
fields(:,:,:,1:3) = wrk(:,:,:,4:6)
!-------------------------------------------------------------------------------
! Making the spectrum to be what it should
!-------------------------------------------------------------------------------
! --- first get the energy spectrum (copied from m_stat.f90)
! need this normalization factor because the FFT is unnormalized
fac = one / real(nx*ny*nz_all)**2
e_spec1 = zip
e_spec = zip
hits = 0
hits1 = 0
! assembling the total energy in each shell and number of hits in each shell
do k = 1,nz
do j = 1,ny
do i = 1,nx
n_shell = nint(sqrt(real(akx(i)**2 + aky(k)**2 + akz(j)**2, 4)))
if (n_shell .gt. 0 .and. n_shell .le. kmax) then
fac2 = fac * (fields(i,j,k,1)**2 + fields(i,j,k,2)**2 + fields(i,j,k,3)**2)
if (akx(i).eq.0.d0) fac2 = fac2 * 0.5d0
e_spec1(n_shell) = e_spec1(n_shell) + fac2
end if
end do
end do
end do
! reducing the number of hits and energy to two arrays on master node
count = kmax
call MPI_REDUCE(e_spec1,e_spec,count,MPI_REAL8,MPI_SUM,0,MPI_COMM_TASK,mpi_err)
count = kmax
call MPI_BCAST(e_spec,count,MPI_REAL8,0,MPI_COMM_TASK,mpi_err)
!-------------------------------------------------------------------------------
! Now make the spectrum to be as desired
!-------------------------------------------------------------------------------
! first, define the desired spectrum
do k = 1,kmax
wmag = real(k, 8)
ratio = wmag / peak_wavenum
if (isp_type.eq.0) then
! Plain Kolmogorov spectrum
e_spec1(k) = wmag**(-5.d0/3.d0)
else if (isp_type.eq.1) then
! Exponential spectrum
e_spec1(k) = ratio**3 / peak_wavenum * exp(-3.0D0*ratio)
else if (isp_type.eq.3) then
! Von Karman spectrum
fac = two * PI * ratio
e_spec1(k) = fac**4 / (one + fac**2)**3
else
write(out,*) "ERROR: WRONG INITIAL SPECTRUM TYPE: ",isp_type
call flush(out)
stop
end if
end do
! normalize it so it has the unit total energy
e_spec1 = e_spec1 / sum(e_spec1(1:kmax))
! now go over all Fourier shells and multiply the velocities in a shell by
! the sqrt of ratio of the resired to the current spectrum
do k = 1,nz
do j = 1,ny
do i = 1,nx+2
n_shell = nint(sqrt(real(akx(i)**2 + aky(k)**2 + akz(j)**2, 4)))
if (n_shell .gt. 0 .and. n_shell .le. kmax .and. e_spec(n_shell) .gt. zip) then
fields(i,j,k,1:3) = fields(i,j,k,1:3) * sqrt(e_spec1(n_shell)/e_spec(n_shell))
else
fields(i,j,k,1:3) = zip
end if
end do
end do
end do
write(out,*) "Generated the velocities."
call flush(out)
! deallocate work arrays
deallocate(e_spec, e_spec1, rr, hits, hits1, stat=ierr)
return
end subroutine init_velocity
!================================================================================
! Initialize the velocities with Taylor-Green vortex
!================================================================================
subroutine init_velocity_taylor_green
use m_openmpi
use m_parameters
use m_io
use m_fields
use m_work
use x_fftw
implicit none
logical :: verbose = .true.
integer :: i, j, k, n
real*8 :: xx, yy, zz
if (verbose) write(out,*) " --- Initial velocity field is Taylor-Green vortex"
if (verbose) call flush(out)
do k = 1, nz
zz = real(nz*myid + k - 1, 8) * dz
do j = 1, ny
yy = real(j-1, 8) * dy
do i = 1, nx
xx = real(i-1,8) *dx
wrk(i,j,k,1) = sin(xx) * cos(yy) * cos(zz)
wrk(i,j,k,2) = - cos(xx) * sin(yy) * cos(zz)
wrk(i,j,k,3) = zip
end do
end do
end do
call xFFT3D(1, 1)
call xFFT3D(1, 2)
call xFFT3D(1, 3)
fields(:,:,:,1:3) = wrk(:,:,:,1:3)
if (verbose) write(out,*) " --- initialized."
if (verbose) call flush(out)
return
end subroutine init_velocity_taylor_green