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particles.py
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from grid import Grid3D
import numpy as np
from utils import *
np.seterr(divide='ignore', invalid='ignore')
class Particles(object):
def __init__(self, grid, simType):
self.grid = grid
self.particles = []
self.n = 0
self.x = []
self.u = []
self.cx = []
self.cy = []
self.cz = []
self.simType = simType
self.n_sum = np.zeros((self.grid.nx+1, self.grid.ny+1, self.grid.nz+1))
def add_particle(self, px, pu):
"""
:param px: position (x,y,z) of each particle
:param pu: velocity (u,v,w) of each particle
:return: None
"""
self.x.append(px)
self.u.append(pu)
self.cx.append(np.zeros(3))
self.cy.append(np.zeros(3))
self.cz.append(np.zeros(3))
self.n += 1
def accumulate(self, accum, q, i, j, k, fx, fy, fz):
diffx = 1-fx
diffy = 1-fy
diffz = 1-fz
weight = diffx * diffy * diffz
accum[i,j,k] += weight * q
self.n_sum[i,j,k] += weight
weight = fx * diffy * diffz
accum[i+1,j,k] += weight * q
self.n_sum[i+1,j,k] += weight
weight = diffx * fy * diffz
accum[i,j+1,k] += weight * q
self.n_sum[i,j+1,k] += weight
weight = fx * fy * diffz
accum[i+1,j+1,k] += weight * q
self.n_sum[i+1,j+1,k] += weight
weight = diffx * diffy * fz
accum[i,j,k+1] += weight * q
self.n_sum[i,j,k+1] += weight
weight = fx * diffy * fz
accum[i+1,j,k+1] += weight * q
self.n_sum[i+1,j,k+1] += weight
weight = diffx * fy * fz
accum[i,j+1,k+1] += weight * q
self.n_sum[i,j+1,k+1] += weight
weight = fx * fy * fz
accum[i+1, j+1, k+1] += weight * q
self.n_sum[i+1, j+1, k+1] += weight
return accum
def affineFix(self, accum, c, i, j, k, fx, fy, fz):
diffx = 1 - fx
diffy = 1 - fy
diffz = 1 - fz
weight = diffx * diffy * diffz
accum[i,j,k] += weight * np.dot(c, (np.array([-fx,-fy,-fz]) * self.grid.h))
weight = fx * diffy * diffz
accum[i+1,j,k] += weight * np.dot(c, (np.array([diffx, -fy, -fz]) * self.grid.h))
weight = diffx * fy * diffz
accum[i,j+1,k] += weight * np.dot(c, (np.array([-fx, diffy, -fz]) * self.grid.h))
weight = fx * fy * diffz
accum[i+1, j+1, k] += weight * np.dot(c, (np.array([diffx, diffy, -fz]) * self.grid.h))
weight = diffx * diffy * fz
accum[i, j, k+1] += weight * np.dot(c, (np.array([-fx, -fy, diffz]) * self.grid.h))
weight = fx * diffy * fz
accum[i+1, j, k+1] += weight * np.dot(c, (np.array([diffx, -fy, diffz]) * self.grid.h))
weight = diffx * fy * fz
accum[i, j+1, k+1] += weight * np.dot(c, (np.array([-fx, diffy, diffz]) * self.grid.h))
weight = fx * fy * fz
accum[i+1, j+1, k+1] += weight * np.dot(c, (np.array([diffx, diffy, diffz]) * self.grid.h))
return accum
def transfer_to_grid(self):
self.grid.u = np.zeros((self.grid.nx+1, self.grid.ny, self.grid.nz))
self.n_sum = np.zeros(self.grid.u.shape)
for p in range(self.n):
ui, ufx = bary_x(self.x[p][0], self.grid.h)
j, fy = bary_y_center(self.x[p][1], self.grid.h, self.grid.ny)
k, fz = bary_z_center(self.x[p][2], self.grid.h, self.grid.nz)
self.grid.u = self.accumulate(self.grid.u, self.u[p][0], ui, j, k, ufx, fy, fz)
if (self.simType == "APIC"):
self.grid.u = self.affineFix(self.grid.u, self.cx[p], ui, j, k, ufx, fy, fz)
self.grid.u[np.where(self.n_sum != 0)] /= self.n_sum[np.where(self.n_sum != 0)]
self.grid.v = np.zeros((self.grid.nx, self.grid.ny+1, self.grid.nz))
self.n_sum = np.zeros(self.grid.v.shape)
for p in range(self.n):
i, fx = bary_x_center(self.x[p][0], self.grid.h, self.grid.nx)
vj, vfy = bary_y(self.x[p][1], self.grid.h)
k, fz = bary_z_center(self.x[p][2], self.grid.h, self.grid.nz)
self.grid.v = self.accumulate(self.grid.v, self.u[p][1], i, vj, k, fx, vfy, fz)
if (self.simType == "APIC"):
self.grid.v = self.affineFix(self.grid.v, self.cy[p], i, vj, k, fx, vfy, fz)
self.grid.v[np.where(self.n_sum != 0)] /= self.n_sum[np.where(self.n_sum != 0)]
# for j in range(self.grid.ny):
# for i in range(self.grid.nx):
# for k in range(self.grid.nz):
# if self.n_sum[i,j,k] != 0:
# self.grid.v[i,j,k] /= self.n_sum[i,j,k]
self.grid.w = np.zeros((self.grid.nx, self.grid.ny, self.grid.nz+1))
self.n_sum = np.zeros(self.grid.w.shape)
for p in range(self.n):
i, fx = bary_x_center(self.x[p][0], self.grid.h, self.grid.nx)
j, fy = bary_y_center(self.x[p][1], self.grid.h, self.grid.ny)
wk, wfz = bary_z(self.x[p][2], self.grid.h)
self.grid.w = self.accumulate(self.grid.w, self.u[p][2], i, j, wk, fx, fy, wfz)
if (self.simType == "APIC"):
self.grid.w = self.affineFix(self.grid.w, self.cz[p], i, j, wk, fx, fy, wfz)
self.grid.w[np.where(self.n_sum != 0)] /= self.n_sum[np.where(self.n_sum != 0)]
# for j in range(self.grid.ny):
# for i in range(self.grid.nx):
# for k in range(self.grid.nz):
# if self.n_sum[i,j,k] != 0:
# self.grid.w[i,j,k] /= self.n_sum[i,j,k]
self.grid.marker = np.zeros(self.grid.size, dtype = int) #dim
for p in range(self.n):
i, fx = bary_x(self.x[p][0], self.grid.h)
j, fy = bary_y(self.x[p][1], self.grid.h)
k, fz = bary_z(self.x[p][2], self.grid.h)
self.grid.marker[i, j, k] = 1
def computeC(self, ufield, i, j, k, fx, fy, fz):
diff_z = 1 - fz
diff_y = 1 - fy
diff_x = 1 - fx
newC = np.zeros(3)
#i, j, k
weight = diff_x * diff_y * diff_z
weight_prime = np.array([-fx, -fy, -fz]) * self.grid.h
newC += weight * weight_prime * ufield[i, j, k]
#i + 1, j, k
weight = fx * diff_y * diff_z
weight_prime = np.array([diff_x, -fy, -fz]) * self.grid.h
newC += weight * weight_prime * ufield[i + 1, j, k]
#i, j + 1, k
weight = diff_x * fy * diff_z
weight_prime = np.array([-fx, diff_y, -fz]) * self.grid.h
newC += weight * weight_prime * ufield[i, j + 1, k]
#i + 1, j + 1, k
weight = fx * fy * diff_z
weight_prime = np.array([diff_x, diff_y, -fz]) * self.grid.h
newC += weight * weight_prime * ufield[i + 1, j + 1, k]
# i, j, k + 1
weight = diff_x * diff_y * fz
weight_prime = np.array([-fx, -fy, diff_z]) * self.grid.h
newC += weight * weight_prime * ufield[i, j, k + 1]
# i + 1, j, k
weight = fx * diff_y * fz
weight_prime = np.array([diff_x, -fy, diff_z]) * self.grid.h
newC += weight * weight_prime * ufield[i + 1, j, k + 1]
# i, j + 1, k
weight = diff_x * fy * fz
weight_prime = np.array([-fx, diff_y, diff_z]) * self.grid.h
newC += weight * weight_prime * ufield[i, j + 1, k + 1]
# i + 1, j + 1, k
weight = fx * fy * fz
weight_prime = np.array([diff_x, diff_y, diff_z]) * self.grid.h
newC += weight * weight_prime * ufield[i + 1, j + 1, k + 1]
return newC
def update_from_grid(self):
for p in range(self.n):
ui, ufx = bary_x(self.x[p][0], self.grid.h)
i, fx = bary_x_center(self.x[p][0], self.grid.h, self.grid.nx)
vj, vfy = bary_y(self.x[p][1], self.grid.h)
j, fy = bary_y_center(self.x[p][1], self.grid.h, self.grid.ny)
wk, wfz = bary_z(self.x[p][2], self.grid.h)
k, fz = bary_z_center(self.x[p][2], self.grid.h, self.grid.nz)
if self.simType == "FLIP":
self. u[p] += np.array([trilerp(self.grid.du, ui, j, k, ufx, fy, fz),
trilerp(self.grid.dv, i, vj, k, fx, vfy, fz),
trilerp(self.grid.dw, i, j, wk, fx, fy, wfz)]) #FLIP
else:
self.u[p]= np.array([trilerp(self.grid.u, ui, j, k, ufx, fy, fz),
trilerp(self.grid.v, i, vj, k, fx, vfy, fz),
trilerp(self.grid.w, i, j, wk, fx, fy, wfz)]) #PIC and APIC
if self.simType == "APIC":
self.cx[p] = self.computeC(self.grid.u, ui, j, k, ufx, fy, fz)
self.cy[p] = self.computeC(self.grid.v, i, vj, k, fx, vfy, fz)
self.cz[p] = self.computeC(self.grid.w, i, j, wk, fx, fy, wfz)
def move_particles_in_grid(self, dt):
gu = np.zeros(3)
x_min, x_max = 1.001 * self.grid.h, self.grid.lx - 1.001 * self.grid.h
y_min, y_max = 1.001 * self.grid.h, self.grid.ly - 1.001 * self.grid.h
z_min, z_max = 1.001 * self.grid.h, self.grid.lz - 1.001 * self.grid.h
for p in range(self.n): # Runge-Kutta 2
gu[0], gu[1], gu[2] = self.grid.trilerp_uvw(self.x[p][0], self.x[p][1], self.x[p][2])
midx = self.x[p] + 0.5 * dt * gu
np.clip(midx[0], x_min, x_max)
np.clip(midx[1], y_min, y_max)
np.clip(midx[2], z_min, z_max)
#second stage of Runge - Kutta2
if np.isnan(midx[0]):
print(self.x[p], midx, gu)
gu[0], gu[1], gu[2] = self.grid.trilerp_uvw(midx[0], midx[1], self.x[p][2]) #should it be this or midx[2]
self.x[p] += dt * gu
np.clip(self.x[p][0], x_min, x_max)
np.clip(self.x[p][1], y_min, y_max)
np.clip(self.x[p][2], z_min, z_max)
def write_to_file(self, filename):
'''
create a new file where each particle's position is
stored. This method will first create a new file specify
how many particles there are and then, for each particle,
specify the x y z coordinates of the particle
Input:
filename: name of file where the particle coordinates are written to
Output:
None. Will have a file created with the particle coordinates
'''
f = open(filename, "w+")
f.write(str(self.n) + '\n')
for p in range(0, self.n):
particle_coor = str(self.x[p][0]) + " " + str(self.x[p][1]) + " " + str(self.x[p][2]) + "\n"
f.write(particle_coor)
f.close()