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Gen_IC.py
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Gen_IC.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import numpy as np
from numpy import linalg as LA
import sys
import os
from scipy import io
from numpy.fft import fftfreq, fft, ifft, irfft2, rfft2
from mpi4py import MPI
try:
from pyfftw.interfaces.numpy_fft import fft, ifft, irfft2, rfft2
import pyfftw
pyfftw.interfaces.cache.enable()
except ImportError:
pass
# %%##########################################################################
sim_in = sys.argv[1]
N_in = sys.argv[2]
N = int(N_in)
Kf_in = sys.argv[3]
kf = float(Kf_in)
nproc_in = sys.argv[4]
nproc = int(nproc_in)
dirpath = os.path.join(os.getcwd(),'N_'+N_in+'-Kf_'+Kf_in+'-num_'+sim_in)
os.mkdir(dirpath)
os.chdir(dirpath)
# %%##########################################################################
comm = MPI.COMM_WORLD
n_proc = comm.Get_size()
rank = comm.Get_rank()
Np = N//n_proc
N2 = N//2+1
NN = Np*N**2
U = np.empty((3, Np, N, N))
dUdX = np.empty((9, Np, N, N))
U_hat = np.empty((3, N, Np, N2), dtype=complex)
dU = np.empty((3, N, Np, N2), dtype=complex)
Uc_hat = np.empty((N, Np, N2), dtype=complex)
Uc_hatT = np.empty((Np, N, N2), dtype=complex)
# %%##########################################################################
kx = fftfreq(N, 1./N)
kz = kx[:N2].copy()
kz[-1] *= -1
K = np.array(np.meshgrid(kx, kx[rank*Np:(rank+1)*Np], kz, indexing='ij'),
dtype=int)
K2 = np.sum(K*K, 0, dtype=int)
K_over_K2 = K.astype(float) / np.where(K2 == 0, 1, K2).astype(float)
# %%##########################################################################
def fftn_mpi(u, fu):
Uc_hatT[:] = rfft2(u, axes=(1, 2))
fu[:] = np.rollaxis(Uc_hatT.reshape(Np, n_proc, Np, N2),
1).reshape(fu.shape)
comm.Alltoall(MPI.IN_PLACE, [fu, MPI.DOUBLE_COMPLEX])
fu[:] = fft(fu, axis=0)
return fu
def ifftn_mpi(fu, u):
Uc_hat[:] = ifft(fu, axis=0)
comm.Alltoall(MPI.IN_PLACE, [Uc_hat, MPI.DOUBLE_COMPLEX])
Uc_hatT[:] = np.rollaxis(Uc_hat.reshape((n_proc, Np, Np, N2)),
1).reshape(Uc_hatT.shape)
u[:] = irfft2(Uc_hatT, axes=(1, 2))
return u
#%%###########################################################################
def gen_IC(res,Kf):
PI=np.pi
u_w=np.zeros((res**3,3),dtype=complex)
wave_n=np.array([0.0,0.0,0.0])
max_wave=int(res/2)
ndx=0
for k in range(0,res):
for j in range(0,res):
for i in range(0,res):
wave_n[0]=i
if i > max_wave:
wave_n[0]=i-res
wave_n[1]=j
if j > max_wave:
wave_n[1]=j-res
wave_n[2]=k
if k > max_wave:
wave_n[2]=k-res
k_tmp=LA.norm(wave_n, ord=2)
Esp=k_tmp
theta=np.random.uniform(0.0,2*PI,2)
psi=np.random.uniform(0.0,2*PI)
phs1=np.exp(1j*theta[0])
phs2=np.exp(1j*theta[1])
Amp=1.0/(4.0*PI)
if Esp <= Kf:
A1=np.sqrt(Amp/Kf**3)
alpha=A1*np.cos(psi)*phs1
beta=A1*np.sin(psi)*phs2
else:
A1=np.sqrt(Amp*(Kf**2/Esp**11)**(1.0/3.0))
alpha=A1*np.cos(psi)*phs1
beta=A1*np.sin(psi)*phs2
den12=Esp*np.sqrt(wave_n[0]**2+wave_n[1]**2)
den3=Esp
if den3 == 0.0:
den3 = 1.0
if den12 == 0.0:
den12 = 1.0
u_w[ndx,0]=(alpha*Esp*wave_n[1]+alpha*wave_n[0]*wave_n[2])/den12
u_w[ndx,1]=(beta*wave_n[1]*wave_n[2]-alpha*Esp*wave_n[0])/den12
u_w[ndx,2]=beta*np.sqrt(wave_n[0]**2+wave_n[1]**2)/den3
ndx +=1
u1_w=u_w[:,0].reshape(res,res,res)
u2_w=u_w[:,1].reshape(res,res,res)
u3_w=u_w[:,2].reshape(res,res,res)
u=np.real(np.fft.ifftn(u1_w,axes=(0,1,2)))
v=np.real(np.fft.ifftn(u2_w,axes=(0,1,2)))
w=np.real(np.fft.ifftn(u3_w,axes=(0,1,2)))
return u,v,w
# %%##########################################################################
U[0], U[1], U[2] = gen_IC(N,kf)
U *= N**3
for i in range(3):
U_hat[i] = fftn_mpi(U[i], U_hat[i])
U_hat[:] -= (K[0]*U_hat[0]+K[1]*U_hat[1]+K[2]*U_hat[2])*K_over_K2
if rank == 0:
U_hat[:, 0, 0, 0] = 0.0
for i in range(3):
U[i] = ifftn_mpi(U_hat[i], U[i])
# %%##########################################################################
TKE = 0.5*np.mean(U[0]**2+U[1]**2+U[2]**2)
dUdX[0] = ifftn_mpi(1j*K[0]*U_hat[0],dUdX[0])
dUdX[1] = ifftn_mpi(1j*K[1]*U_hat[0],dUdX[1])
dUdX[2] = ifftn_mpi(1j*K[2]*U_hat[0],dUdX[2])
dUdX[3] = ifftn_mpi(1j*K[0]*U_hat[1],dUdX[3])
dUdX[4] = ifftn_mpi(1j*K[1]*U_hat[1],dUdX[4])
dUdX[5] = ifftn_mpi(1j*K[2]*U_hat[1],dUdX[5])
dUdX[6] = ifftn_mpi(1j*K[0]*U_hat[2],dUdX[6])
dUdX[7] = ifftn_mpi(1j*K[1]*U_hat[2],dUdX[7])
dUdX[8] = ifftn_mpi(1j*K[2]*U_hat[2],dUdX[8])
Sk = np.zeros(3)
Fl = np.zeros(3)
Sk[0] = np.mean(dUdX[0]**3)/np.mean(dUdX[0]**2)**1.5
Sk[1] = np.mean(dUdX[4]**3)/np.mean(dUdX[4]**2)**1.5
Sk[2] = np.mean(dUdX[8]**3)/np.mean(dUdX[8]**2)**1.5
Fl[0] = np.mean(dUdX[0]**4)/np.mean(dUdX[0]**2)**2
Fl[1] = np.mean(dUdX[4]**4)/np.mean(dUdX[4]**2)**2
Fl[2] = np.mean(dUdX[8]**4)/np.mean(dUdX[8]**2)**2
f1 = open('Turb_Stats.txt', 'a')
print(format(TKE, 'g'),
format(np.mean(U[0]), 'g'),
format(np.mean(U[1]), 'g'),
format(np.mean(U[2]), 'g'),
format(np.mean(U[0]**3)/np.mean(U[0]**2)**1.5, 'g'),
format(np.mean(U[1]**3)/np.mean(U[1]**2)**1.5, 'g'),
format(np.mean(U[2]**3)/np.mean(U[2]**2)**1.5, 'g'),
format(np.mean(U[0]**4)/np.mean(U[0]**2)**2, 'g'),
format(np.mean(U[1]**4)/np.mean(U[1]**2)**2, 'g'),
format(np.mean(U[2]**4)/np.mean(U[2]**2)**2, 'g'),
sep=" ", end='\n', file = f1, flush=False)
f1.close()
f2 = open('VGT_Moments.txt', 'a')
print(format(Sk[0], 'g'), format(Sk[1], 'g'), format(Sk[2], 'g'),
format(Fl[0], 'g'), format(Fl[1], 'g'), format(Fl[2], 'g'),
sep=" ", end='\n', file = f2, flush=False)
f2.close()
# %%##########################################################################
Np = N//nproc
for i in range(nproc):
io.savemat('Vel'+str(N)+'-p_'+str(i)+'.mat', {
'u1': np.reshape(U[0,i*Np:(i+1)*Np,:,:], NN),
'u2': np.reshape(U[1,i*Np:(i+1)*Np,:,:], NN),
'u3': np.reshape(U[2,i*Np:(i+1)*Np,:,:], NN)})