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cfd.py
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#
# cfd.py
# tf-cfd
#
# Created by Jean Flaherty on 7/1/17.
# Copyright © 2017 kobejean. All rights reserved.
#
"""
script that runs cfd and produces a sequence of images animating the simulation
"""
import tensorflow as tf
import numpy as np
import math, os
from threading import Thread
# create output directory
if not os.path.exists("output"):
os.makedirs("output")
LOGGING = False
PERIOD = 100
# # Dimensions (height x width)
DIM = (240, 600)
# DIM = (480, 1200)
# DIM = (1600, 2560) # Okar dimentions
# DIM = (1024, 2560) # Okar widescreen
# DIM = (2160, 3840) # 4k
# DIM = (1536, 3840) # widescreen 4k
# DIM = (1920, 4800)
velocity = 0.050
viscocity = 0.020
# useful constants
v = velocity # short hand
four9ths = 4.0 / 9.0
one9th = 1.0 / 9.0
one36th = 1.0 / 36.0
zeroes = tf.zeros(shape=DIM)
four9ths = 4.0 / 9.0
one9th = 1.0 / 9.0
one36th = 1.0 / 36.0
# circle barrier in the middle
barrier = np.empty(shape=DIM, dtype=bool)
# fountain = np.empty(shape=DIM, dtype=float)
for i in range(DIM[0]):
for j in range(DIM[1]):
reli = DIM[0]/2.0 - i;
relj = DIM[1]/2.0 - j;
r = math.sqrt(reli*reli + relj*relj)
barrier[i][j] = (r < min(DIM[0], DIM[1]) * 0.2)
# fountain[i][j] = 0.005 if (r < min(DIM[0], DIM[1]) * 0.3 and not barrier[i][j]) else 0.0
with tf.name_scope('variables') as scope:
# variable initial values
n0 = tf.fill(DIM, four9ths * (1.0 - 1.5*v*v) )
nE = tf.fill(DIM, one9th * (1.0 + 3*v + 3*v*v) )
nW = tf.fill(DIM, one9th * (1.0 - 3*v + 3*v*v) )
nN = tf.fill(DIM, one9th * (1.0 - 1.5*v*v) )
nS = tf.fill(DIM, one9th * (1.0 - 1.5*v*v) )
nNE = tf.fill(DIM, one36th * (1.0 + 3*v + 3*v*v) )
nSE = tf.fill(DIM, one36th * (1.0 + 3*v + 3*v*v) )
nNW = tf.fill(DIM, one36th * (1.0 - 3*v + 3*v*v) )
nSW = tf.fill(DIM, one36th * (1.0 - 3*v + 3*v*v) )
# variables (masked with barrier)
n0 = tf.Variable(tf.where(barrier, zeroes, n0) , name="n0" )
nE = tf.Variable(tf.where(barrier, zeroes, nE) , name="nE" )
nW = tf.Variable(tf.where(barrier, zeroes, nW) , name="nW" )
nN = tf.Variable(tf.where(barrier, zeroes, nN) , name="nN" )
nS = tf.Variable(tf.where(barrier, zeroes, nS) , name="nS" )
nNE = tf.Variable(tf.where(barrier, zeroes, nNE) , name="nNE")
nSE = tf.Variable(tf.where(barrier, zeroes, nSE) , name="nSE")
nNW = tf.Variable(tf.where(barrier, zeroes, nNW) , name="nNW")
nSW = tf.Variable(tf.where(barrier, zeroes, nSW) , name="nSW")
with tf.name_scope('computed_variables') as scope:
# computed variables
density = tf.fill(DIM, 1.0 )
xvel = tf.fill(DIM, v )
yvel = tf.fill(DIM, 0.0 )
speed2 = tf.fill(DIM, v*v )
# computer variables (masked with barrier)
density = tf.Variable(tf.where(barrier, zeroes, density) , name="density" )
xvel = tf.Variable(tf.where(barrier, zeroes, xvel) , name="xvel" )
yvel = tf.Variable(tf.where(barrier, zeroes, yvel) , name="yvel" )
speed2 = tf.Variable(tf.where(barrier, zeroes, speed2) , name="speed2" )
with tf.name_scope('image') as scope:
H = tf.fill(DIM, 0.5)
S = tf.fill(DIM, 1.0)
# V = tf.minimum(tf.sqrt(yvel)*6.0, 1.0)
# V = tf.minimum(tf.sqrt(xvel)*6.0, 1.0)
V = tf.minimum(tf.sqrt(speed2)*8.0, 1.0)
HSV = tf.stack([H,S,V], axis=-1)
RGB = tf.image.hsv_to_rgb(HSV, "RGB")*(2**16-1)
RGB = tf.cast(RGB, dtype=tf.uint16)
encoded_image = tf.image.encode_png(RGB)
# distribute the moving densities
def collide():
with tf.name_scope('collide') as scope:
omega = 1 / (3*viscocity + 0.5)
n = n0 + nN + nS + nE + nW + nNW + nNE + nSW + nSE
n = tf.where(barrier, zeroes, n)
one9thn = one9th * n
one36thn = one36th * n
vx = (nE + nNE + nSE - nW - nNW - nSW) / n
vx = tf.where(tf.greater(n, zeroes), vx, zeroes)
vy = (nS + nSE + nSW - nN - nNE - nNW) / n
vy = tf.where(tf.greater(n, zeroes), vy, zeroes)
vx3 = 3 * vx
vy3 = 3 * vy
vx2 = vx * vx
vy2 = vy * vy
vxvy2 = 2 * vx * vy
v2 = vx2 + vy2
v215 = 1.5 * v2
tmp_n0 = omega * (four9ths*n * (1 - v215) - n0 )
tmp_nE = omega * ( one9thn * (1 + vx3 + 4.5*vx2 - v215) - nE )
tmp_nW = omega * ( one9thn * (1 - vx3 + 4.5*vx2 - v215) - nW )
tmp_nN = omega * ( one9thn * (1 - vy3 + 4.5*vy2 - v215) - nN )
tmp_nS = omega * ( one9thn * (1 + vy3 + 4.5*vy2 - v215) - nS )
tmp_nNE = omega * ( one36thn * (1 + vx3 - vy3 + 4.5*(v2-vxvy2) - v215) - nNE)
tmp_nNW = omega * ( one36thn * (1 - vx3 - vy3 + 4.5*(v2+vxvy2) - v215) - nNW)
tmp_nSE = omega * ( one36thn * (1 + vx3 + vy3 + 4.5*(v2+vxvy2) - v215) - nSE)
tmp_nSW = omega * ( one36thn * (1 - vx3 + vy3 + 4.5*(v2-vxvy2) - v215) - nSW)
ops = tf.group( tf.assign(density , n ),
tf.assign(xvel , vx),
tf.assign(yvel , vy),
tf.assign(speed2 , v2),
tf.assign_add(n0 , tmp_n0 ),
tf.assign_add(nE , tmp_nE ),
tf.assign_add(nW , tmp_nW ),
tf.assign_add(nN , tmp_nN ),
tf.assign_add(nS , tmp_nS ),
tf.assign_add(nNE, tmp_nNE),
tf.assign_add(nSE, tmp_nSE),
tf.assign_add(nNW, tmp_nNW),
tf.assign_add(nSW, tmp_nSW))
return ops
# stream densities
def stream():
with tf.name_scope('stream') as scope:
# set all density values at barrier sites to 0 before stream
# density values that flow into the barrier will be used for bounce
tmp_n0 = tf.where(barrier, zeroes, n0 )
tmp_nE = tf.where(barrier, zeroes, nE )
tmp_nW = tf.where(barrier, zeroes, nW )
tmp_nN = tf.where(barrier, zeroes, nN )
tmp_nS = tf.where(barrier, zeroes, nS )
tmp_nNE = tf.where(barrier, zeroes, nNE)
tmp_nSE = tf.where(barrier, zeroes, nSE)
tmp_nNW = tf.where(barrier, zeroes, nNW)
tmp_nSW = tf.where(barrier, zeroes, nSW)
# stream by slicing and padding matrices in appropriate directions
# slice sizes
Sx = (DIM[0] , DIM[1]-1)
Sy = (DIM[0]-2, DIM[1] )
Sxy = (DIM[0]-2, DIM[1]-1)
tmp_n0 = tf.slice(tmp_n0 , [1,0], Sy)
tmp_nE = tf.slice(tmp_nE , [1,0], Sxy)
tmp_nW = tf.slice(tmp_nW , [1,1], Sxy)
tmp_nN = tf.slice(tmp_nN , [2,0], Sy )
tmp_nS = tf.slice(tmp_nS , [0,0], Sy )
tmp_nNE = tf.slice(tmp_nNE, [2,0], Sxy)
tmp_nSE = tf.slice(tmp_nSE, [0,0], Sxy)
tmp_nNW = tf.slice(tmp_nNW, [2,1], Sxy)
tmp_nSW = tf.slice(tmp_nSW, [0,1], Sxy)
# padding
PX = (DIM[0] , 1 )
Px = (DIM[0]-2, 1 )
PY = (1 , DIM[1] )
Py = (1 , DIM[1]-1)
# pad_n0x = tf.fill(Px, four9ths * (1 - 1.5*v*v) )
pad_n0y = tf.fill(PY, four9ths * (1 - 1.5*v*v) )
pad_nEx = tf.fill(Px, one9th * (1 + 3*v + 3*v*v) )
pad_nEy = tf.fill(PY, one9th * (1 + 3*v + 3*v*v) )
pad_nWx = tf.fill(Px, one9th * (1 - 3*v + 3*v*v) )
pad_nWy = tf.fill(PY, one9th * (1 - 3*v + 3*v*v) )
# pad_nNx = tf.fill(Px, one9th * (1 - 1.5*v*v) )
pad_nNy = tf.fill(PY, one9th * (1 - 1.5*v*v) )
# pad_nSx = tf.fill(Px, one9th * (1 - 1.5*v*v) )
pad_nSy = tf.fill(PY, one9th * (1 - 1.5*v*v) )
pad_nNEx = tf.fill(Px, one36th * (1 + 3*v + 3*v*v) )
pad_nNEy = tf.fill(PY, one36th * (1 + 3*v + 3*v*v) )
pad_nSEx = tf.fill(Px, one36th * (1 + 3*v + 3*v*v) )
pad_nSEy = tf.fill(PY, one36th * (1 + 3*v + 3*v*v) )
pad_nNWx = tf.fill(Px, one36th * (1 - 3*v + 3*v*v) )
pad_nNWy = tf.fill(PY, one36th * (1 - 3*v + 3*v*v) )
pad_nSWx = tf.fill(Px, one36th * (1 - 3*v + 3*v*v) )
pad_nSWy = tf.fill(PY, one36th * (1 - 3*v + 3*v*v) )
# tmp_n0 = tf.concat([pad_n0x , tmp_n0 , pad_n0x ], 1)
tmp_n0 = tf.concat([pad_n0y , tmp_n0 , pad_n0y ], 0)
tmp_nE = tf.concat([pad_nEx , tmp_nE ], 1)
tmp_nE = tf.concat([pad_nEy , tmp_nE , pad_nEy ], 0)
tmp_nW = tf.concat([tmp_nW , pad_nWx ], 1)
tmp_nW = tf.concat([pad_nWy , tmp_nW , pad_nWy ], 0)
# tmp_nN = tf.concat([pad_nNx , tmp_nN , pad_nNx ], 1)
tmp_nN = tf.concat([pad_nNy , tmp_nN , pad_nNy ], 0)
# tmp_nS = tf.concat([pad_nSx , tmp_nS , pad_nSx ], 1)
tmp_nS = tf.concat([pad_nSy , tmp_nS , pad_nSy ], 0)
tmp_nNE = tf.concat([pad_nNEx, tmp_nNE ], 1)
tmp_nNE = tf.concat([pad_nNEy, tmp_nNE , pad_nNEy], 0)
tmp_nSE = tf.concat([pad_nSEx, tmp_nSE ], 1)
tmp_nSE = tf.concat([pad_nSEy, tmp_nSE , pad_nSEy], 0)
tmp_nNW = tf.concat([tmp_nNW , pad_nNWx], 1)
tmp_nNW = tf.concat([pad_nNWy, tmp_nNW , pad_nNWy], 0)
tmp_nSW = tf.concat([tmp_nSW , pad_nSWx], 1)
tmp_nSW = tf.concat([pad_nSWy, tmp_nSW , pad_nSWy], 0)
ops = tf.group( tf.assign(n0 , tmp_n0 ),
tf.assign(nE , tmp_nE ),
tf.assign(nW , tmp_nW ),
tf.assign(nN , tmp_nN ),
tf.assign(nS , tmp_nS ),
tf.assign(nNE, tmp_nNE),
tf.assign(nSE, tmp_nSE),
tf.assign(nNW, tmp_nNW),
tf.assign(nSW, tmp_nSW))
return ops
# bounce off the barrier (flip direction)
def bounce():
with tf.name_scope('bounce') as scope:
bool_nW = tf.logical_and(barrier, tf.greater(nW ,zeroes))
bool_nE = tf.logical_and(barrier, tf.greater(nE ,zeroes))
bool_nS = tf.logical_and(barrier, tf.greater(nS ,zeroes))
bool_nN = tf.logical_and(barrier, tf.greater(nN ,zeroes))
bool_nSW = tf.logical_and(barrier, tf.greater(nSW,zeroes))
bool_nNW = tf.logical_and(barrier, tf.greater(nNW,zeroes))
bool_nSE = tf.logical_and(barrier, tf.greater(nSE,zeroes))
bool_nNE = tf.logical_and(barrier, tf.greater(nNE,zeroes))
dif_nE = tf.where(bool_nW , nW , zeroes)
dif_nW = tf.where(bool_nE , nE , zeroes)
dif_nN = tf.where(bool_nS , nS , zeroes)
dif_nS = tf.where(bool_nN , nN , zeroes)
dif_nNE = tf.where(bool_nSW, nSW, zeroes)
dif_nSE = tf.where(bool_nNW, nNW, zeroes)
dif_nNW = tf.where(bool_nSE, nSE, zeroes)
dif_nSW = tf.where(bool_nNE, nNE, zeroes)
# slice sizes
Sx = (DIM[0] , DIM[1]-1)
Sy = (DIM[0]-2, DIM[1] )
Sxy = (DIM[0]-2, DIM[1]-1)
# dif_n0 = tf.slice(n0 , [1,0], Sy)
dif_nE = tf.slice(dif_nE , [1,0], Sxy)
dif_nW = tf.slice(dif_nW , [1,1], Sxy)
dif_nN = tf.slice(dif_nN , [2,0], Sy )
dif_nS = tf.slice(dif_nS , [0,0], Sy )
dif_nNE = tf.slice(dif_nNE, [2,0], Sxy)
dif_nSE = tf.slice(dif_nSE, [0,0], Sxy)
dif_nNW = tf.slice(dif_nNW, [2,1], Sxy)
dif_nSW = tf.slice(dif_nSW, [0,1], Sxy)
# padding
PX = (DIM[0] , 1 )
Px = (DIM[0]-2, 1 )
PY = (1 , DIM[1] )
Py = (1 , DIM[1]-1)
# pad_n0x = tf.fill(Px, 0.0)
# pad_n0y = tf.fill(PY, 0.0)
pad_nEx = tf.fill(Px, 0.0)
pad_nEy = tf.fill(PY, 0.0)
pad_nWx = tf.fill(Px, 0.0)
pad_nWy = tf.fill(PY, 0.0)
# pad_nNx = tf.fill(Px, 0.0)
pad_nNy = tf.fill(PY, 0.0)
# pad_nSx = tf.fill(Px, 0.0)
pad_nSy = tf.fill(PY, 0.0)
pad_nNEx = tf.fill(Px, 0.0)
pad_nNEy = tf.fill(PY, 0.0)
pad_nSEx = tf.fill(Px, 0.0)
pad_nSEy = tf.fill(PY, 0.0)
pad_nNWx = tf.fill(Px, 0.0)
pad_nNWy = tf.fill(PY, 0.0)
pad_nSWx = tf.fill(Px, 0.0)
pad_nSWy = tf.fill(PY, 0.0)
# dif_n0 = tf.concat([pad_n0x , dif_n0 , pad_n0x ], 1)
# dif_n0 = tf.concat([pad_n0y , dif_n0 , pad_n0y ], 0)
dif_nE = tf.concat([pad_nEx , dif_nE ], 1)
dif_nE = tf.concat([pad_nEy , dif_nE , pad_nEy ], 0)
dif_nW = tf.concat([dif_nW , pad_nWx ], 1)
dif_nW = tf.concat([pad_nWy , dif_nW , pad_nWy ], 0)
# dif_nN = tf.concat([pad_nNx , dif_nN , pad_nNx ], 1)
dif_nN = tf.concat([pad_nNy , dif_nN , pad_nNy ], 0)
# dif_nS = tf.concat([pad_nSx , dif_nS , pad_nSx ], 1)
dif_nS = tf.concat([pad_nSy , dif_nS , pad_nSy ], 0)
dif_nNE = tf.concat([pad_nNEx, dif_nNE ], 1)
dif_nNE = tf.concat([pad_nNEy, dif_nNE , pad_nNEy], 0)
dif_nSE = tf.concat([pad_nSEx, dif_nSE ], 1)
dif_nSE = tf.concat([pad_nSEy, dif_nSE , pad_nSEy], 0)
dif_nNW = tf.concat([dif_nNW , pad_nNWx], 1)
dif_nNW = tf.concat([pad_nNWy, dif_nNW , pad_nNWy], 0)
dif_nSW = tf.concat([dif_nSW , pad_nSWx], 1)
dif_nSW = tf.concat([pad_nSWy, dif_nSW , pad_nSWy], 0)
ops = tf.group( tf.assign_add(nE , dif_nE ),
tf.assign_add(nW , dif_nW ),
tf.assign_add(nN , dif_nN ),
tf.assign_add(nS , dif_nS ),
tf.assign_add(nNE, dif_nNE),
tf.assign_add(nSE, dif_nSE),
tf.assign_add(nNW, dif_nNW),
tf.assign_add(nSW, dif_nSW))
return ops
# three steps per time step
collide_step = collide()
stream_step = stream()
bounce_step = bounce()
with tf.Session() as sess:
init = tf.global_variables_initializer()
sess.run(init)
if LOGGING:
writer = tf.summary.FileWriter("log/", sess.graph)
for t in range(10000000000):
print("T: {}".format(t), end="\r")
sess.run(collide_step)
sess.run(stream_step)
sess.run(bounce_step)
if t % PERIOD == 0:
# print(sess.run(RGB))
image = sess.run(encoded_image)
outpath = "output/cfd_{0:0>10}.png".format(t//PERIOD)
def write(image, outpath):
with open(outpath, 'wb') as f:
f.write(image)
worker = Thread(target=write, args=(image, outpath,))
worker.setDaemon(True)
worker.start()