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advect_functions.py
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advect_functions.py
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import numpy as np
from intergrid import Intergrid
import scipy.ndimage.interpolation
import csv
def interp(x0,y0,z0,lo,hi,maps,U0,ord):
query_points = np.zeros((len(x0),3)) # lo + np.random.uniform( size=(xp*yp*zp, 3) ) * (hi - lo)
query_points[:,0] = x0
query_points[:,1] = y0
query_points[:,2] = z0
if_U = Intergrid(U0, lo=lo, hi=hi, order=ord, maps=maps, verbose=1)
# query_points[:,0] = np.interp(query_points[:,0], Xlist, range(len(Xlist)))
# query_points[:,1] = np.interp(query_points[:,1], Ylist, range(len(Ylist)))
# query_points[:,2] = np.interp(query_points[:,2], Zlist, range(len(Zlist)))
Ui = if_U.at( query_points )
return Ui
def interp2D(x0,y0,lo,hi,maps,U0,ord):
query_points = np.zeros((len(x0),2)) # lo + np.random.uniform( size=(xp*yp*zp, 3) ) * (hi - lo)
query_points[:,0] = x0
query_points[:,1] = y0
if_U = Intergrid(U0, lo=lo, hi=hi, order=ord, maps=maps, verbose=1)
# query_points[:,0] = np.interp(query_points[:,0], Xlist, range(len(Xlist)))
# query_points[:,1] = np.interp(query_points[:,1], Ylist, range(len(Ylist)))
# query_points[:,2] = np.interp(query_points[:,2], Zlist, range(len(Zlist)))
Ui = if_U.at( query_points )
return Ui
def interp2(x0,y0,z0,limit,U0):
#U0 = Ut0
#xp,yp,zp = x0.shape
# x = 1.*np.reshape(x0, (np.size(x0),))
# y = 1.*np.reshape(y0, (np.size(y0),))
# z = 1.*np.reshape(z0, (np.size(z0),))
x = (1.*x0-np.min(limit[0]))/np.max(limit[0])*xn
y = (1.*y0-np.min(limit[1]))/np.max(limit[1])*yn
z = (1.*z0-np.max(limit[2]))/np.min(limit[2])*zn
# print min(x), max(x), min(y), max(y), min(z), max(z)
t = scipy.ndimage.interpolation.map_coordinates(U0, np.array([x,y,z]), output=None, order=3, mode='constant', cval=0.0, prefilter=True)
return t #np.reshape(t,(xp,yp,zp))
import scipy.interpolate
def interp3(x0,y0,z0,U0):
points = np.array([np.reshape(X, (np.size(X),)),np.reshape(Y, (np.size(Y),)),np.reshape(Z, (np.size(Z),))])
t = scipy.interpolate.griddata(np.transpose(points), np.reshape(U0,(np.size(U0),)), (x0,y0,z0), method='linear')
return t
def RK4(x0,y0,z0,Ut0,Vt0,Wt0,Ut1,Vt1,Wt1,lo,hi,maps,dt,ord):
h2 = dt/2.0
h6 = dt/6.0
# linear time interpolation at t = t0 + 0.5dt
Ut05 = (Ut0 + Ut1)*0.5
Vt05 = (Vt0 + Vt1)*0.5
Wt05 = (Wt0 + Wt1)*0.5
U1 = interp(x0,y0,z0,lo,hi,maps,Ut0,ord)
V1 = interp(x0,y0,z0,lo,hi,maps,Vt0,ord)
W1 = interp(x0,y0,z0,lo,hi,maps,Wt0,ord)
x1 = x0 + h2*U1
y1 = y0 + h2*V1
z1 = z0 + h2*W1
U2 = interp(x1,y1,z1,lo,hi,maps,Ut05,ord)
V2 = interp(x1,y1,z1,lo,hi,maps,Vt05,ord)
W2 = interp(x1,y1,z1,lo,hi,maps,Wt05,ord)
x1 = x0 + h2*U2
y1 = y0 + h2*V2
z1 = z0 + h2*W2
U3 = interp(x1,y1,z1,lo,hi,maps,Ut05,ord)
V3 = interp(x1,y1,z1,lo,hi,maps,Vt05,ord)
W3 = interp(x1,y1,z1,lo,hi,maps,Wt05,ord)
x1 = x0 + dt*U3
y1 = y0 + dt*V3
z1 = z0 + dt*W3
U4 = interp(x1,y1,z1,lo,hi,maps,Ut1,ord)
V4 = interp(x1,y1,z1,lo,hi,maps,Vt1,ord)
W4 = interp(x1,y1,z1,lo,hi,maps,Wt1,ord)
x0 = x0 + h6 * (U1 + 2.*U2 + 2.*U3 + U4)
y0 = y0 + h6 * (V1 + 2.*V2 + 2.*V3 + V4)
z0 = z0 + h6 * (W1 + 2.*W2 + 2.*W3 + W4)
return x0,y0,z0
def RK4_zyx(z0,y0,x0,Ut0,Vt0,Wt0,Ut1,Vt1,Wt1,lo,hi,maps,dt,ord):
h2 = dt/2.0
h6 = dt/6.0
# linear time interpolation at t = t0 + 0.5dt
Ut05 = (Ut0 + Ut1)*0.5
Vt05 = (Vt0 + Vt1)*0.5
Wt05 = (Wt0 + Wt1)*0.5
U1 = interp(z0,y0,x0,lo,hi,maps,Ut0,ord)
V1 = interp(z0,y0,x0,lo,hi,maps,Vt0,ord)
W1 = interp(z0,y0,x0,lo,hi,maps,Wt0,ord)
x1 = x0 + h2*U1
y1 = y0 + h2*V1
z1 = z0 + h2*W1
U2 = interp(z1,y1,x1,lo,hi,maps,Ut05,ord)
V2 = interp(z1,y1,x1,lo,hi,maps,Vt05,ord)
W2 = interp(z1,y1,x1,lo,hi,maps,Wt05,ord)
x1 = x0 + h2*U2
y1 = y0 + h2*V2
z1 = z0 + h2*W2
U3 = interp(z1,y1,x1,lo,hi,maps,Ut05,ord)
V3 = interp(z1,y1,x1,lo,hi,maps,Vt05,ord)
W3 = interp(z1,y1,x1,lo,hi,maps,Wt05,ord)
x1 = x0 + dt*U3
y1 = y0 + dt*V3
z1 = z0 + dt*W3
U4 = interp(z1,y1,x1,lo,hi,maps,Ut1,ord)
V4 = interp(z1,y1,x1,lo,hi,maps,Vt1,ord)
W4 = interp(z1,y1,x1,lo,hi,maps,Wt1,ord)
x0 = x0 + h6 * (U1 + 2.*U2 + 2.*U3 + U4)
y0 = y0 + h6 * (V1 + 2.*V2 + 2.*V3 + V4)
z0 = z0 + h6 * (W1 + 2.*W2 + 2.*W3 + W4)
return x0,y0,z0
def EULER(x0,y0,z0,Ut0,Vt0,Wt0,lo,hi,maps,dt):
U1 = interp(x0,y0,z0,lo,hi,maps,Ut0)
V1 = interp(x0,y0,z0,lo,hi,maps,Vt0)
W1 = interp(x0,y0,z0,lo,hi,maps,Wt0)
x = x0 + U1*dt
y = y0 + V1*dt
z = z0 + W1*dt
return x,y,z
def cBC(x0,y0,z0,lo,hi):
# applies periodic boundaries
x0[np.where(x0 > hi[0])] = hi[0]
x0[np.where(x0 < lo[0])] = lo[0]
y0[np.where(y0 > hi[1])] = hi[1]
y0[np.where(y0 < lo[1])] = lo[1]
z0[np.where(z0 > hi[2])] = hi[2]
z0[np.where(z0 < lo[2])] = lo[2]
return x0,y0,z0
def pBC(x0,y0,z0,lo,hi):
# applies periodic boundaries
x0[np.where(x0 > hi[0])] = x0[np.where(x0 > hi[0])] - hi[0]
x0[np.where(x0 < lo[0])] = x0[np.where(x0 < lo[0])] + hi[0]
y0[np.where(y0 > hi[1])] = y0[np.where(y0 > hi[1])] - hi[1]
y0[np.where(y0 < lo[1])] = y0[np.where(y0 < lo[1])] + hi[1]
z0[np.where(z0 > hi[2])] = hi[2]
z0[np.where(z0 < lo[2])] = lo[2]
return x0,y0,z0
def read_particles_csv(filename,pt,tt):
time = []
par = np.zeros((pt,3,tt))
f = open(filename,'r')
reader = csv.reader(f)
j = 0
k = 0
for row in reader:
if k == 0: time.append(float(row[3]));
if k == pt: j = j + 1; k = 0; print j; time.append(float(row[3]));
i = 0
for item in row[0:3]: # new line character !!
par[k,i,j] = float(item)
i = i + 1
k = k + 1
time.append(float(row[3]))
f.close()
return np.asarray(time), np.asarray(par)