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StableFluid3D_taichi.py
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StableFluid3D_taichi.py
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# References:
# https://github.com/taichi-dev/taichi/blob/master/python/taichi/examples/simulation/stable_fluid.py
# Joe Stam's legendary paper
import argparse
import vedo
import numpy as np
from vedo import Volume, show, Plotter
from vedo.applications import RayCastPlotter
import taichi as ti
res = 64
dt = 0.03
p_jacobi_iters = 500 # 40 for a quicker but less accurate result
f_strength = 20000.0
curl_strength = 0
time_c = 2
maxfps = 60
dye_decay = 1 - 1 / (maxfps * time_c)
force_radius = res / 12
gravity = True
debug = False
paused = False
frame = 0
target_frame = 30000
ti.init(arch=ti.gpu)
# ti.init(device_memory_GB=4)
print('Using jacobi iteration')
_velocities = ti.Vector.field(3, float, shape=(res, res, res))
_new_velocities = ti.Vector.field(3, float, shape=(res, res, res))
velocity_divs = ti.field(float, shape=(res, res, res))
_pressures = ti.field(float, shape=(res, res, res))
_new_pressures = ti.field(float, shape=(res, res, res))
_dye_buffer = ti.Vector.field(3, float, shape=(res, res, res))
_new_dye_buffer = ti.Vector.field(3, float, shape=(res, res, res))
_density_color = ti.field(float, shape=(res, res, res))
src = ti.Vector([res / 2, 5, 5])
dir = ti.Vector([0, 1, 1])
class TexPair:
def __init__(self, cur, nxt):
self.cur = cur
self.nxt = nxt
def swap(self):
self.cur, self.nxt = self.nxt, self.cur
velocities_pair = TexPair(_velocities, _new_velocities)
pressures_pair = TexPair(_pressures, _new_pressures)
dyes_pair = TexPair(_dye_buffer, _new_dye_buffer)
@ti.func
def sample(qf, u, v, w):
I = ti.Vector([int(u), int(v), int(w)])
I = max(0, min(res - 1, I))
return qf[I]
@ti.func
def lerp(vl, vr, frac):
# frac: [0.0, 1.0]
return vl + frac * (vr - vl)
@ti.func
def bilerp(vf, p):
u, v, w = p
s, t, q = u - 0.5, v - 0.5, w - 0.5
# floor
iu, iv, iw = ti.floor(s), ti.floor(t), ti.floor(q)
# fract
fu, fv, fw = s - iu, t - iv, q - iw
a = sample(vf, iu, iv, iw)
b = sample(vf, iu + 1, iv, iw)
c = sample(vf, iu, iv + 1, iw)
d = sample(vf, iu + 1, iv + 1, iw)
e = sample(vf, iu, iv, iw + 1)
f = sample(vf, iu + 1, iv, iw + 1)
g = sample(vf, iu, iv + 1, iw + 1)
h = sample(vf, iu + 1, iv + 1, iw + 1)
return lerp(lerp(lerp(a, b, fu), lerp(c, d, fu), fv), lerp(lerp(e, f, fu), lerp(g, h, fu), fv), fw)
# 3rd order Runge-Kutta
@ti.func
def backtrace(vf: ti.template(), p, dt: ti.template()):
v1 = bilerp(vf, p)
p1 = p - 0.5 * dt * v1
v2 = bilerp(vf, p1)
p2 = p - 0.75 * dt * v2
v3 = bilerp(vf, p2)
p -= dt * ((2 / 9) * v1 + (1 / 3) * v2 + (4 / 9) * v3)
return p
@ti.kernel
def advect(vf: ti.template(), qf: ti.template(), new_qf: ti.template()):
for i, j, k in vf:
p = ti.Vector([i, j, k]) + 0.5
p = backtrace(vf, p, dt)
new_qf[i, j, k] = bilerp(qf, p) * dye_decay
@ti.kernel
def apply_impulse(vf: ti.template(), dyef: ti.template()):
g_dir = -ti.Vector([0, -9.8, 0]) * 300
for i, j, k in vf:
omx, omy, omz = src
mdir = dir
dx, dy, dz = (i + 0.5 - omx), (j + 0.5 - omy), (k + 0.5 - omz)
d2 = dx * dx + dy * dy + dz * dz
# dv = F * dt
factor = ti.exp(-d2 / force_radius)
dc = dyef[i, j, k]
a = dc.norm()
momentum = (mdir * f_strength * factor + g_dir * a / (1 + a)) * dt
v = vf[i, j, k]
vf[i, j, k] = v + momentum
# add dye
if mdir.norm() > 0.5:
dc += ti.exp(-d2 * (4 / (res / 15) ** 2)) * ti.Vector(
[0.8, 0.8, 0.8])
dyef[i, j, k] = dc
_density_color[i, j, k] = dc[0]
@ti.kernel
def divergence(vf: ti.template()):
for i, j, k in vf:
vl = sample(vf, i - 1, j, k)
vr = sample(vf, i + 1, j, k)
vb = sample(vf, i, j - 1, k)
vt = sample(vf, i, j + 1, k)
vc = sample(vf, i, j, k)
vzf = sample(vf, i, j, k + 1)
vzb = sample(vf, i, j, k - 1)
if i == 0:
vl.x = -vc.x
if i == res - 1:
vr.x = -vc.x
if j == 0:
vb.y = -vc.y
if j == res - 1:
vt.y = -vc.y
if k == 0:
vzb.z = -vc.z
if k == res - 1:
vzf.z = -vc.z
velocity_divs[i, j, k] = (vr.x - vl.x + vt.y - vb.y + vzf.z - vzb.z) * 0.5
@ti.kernel
def pressure_jacobi(pf: ti.template(), new_pf: ti.template()):
for i, j, k in pf:
pl = sample(pf, i - 1, j, k)
pr = sample(pf, i + 1, j, k)
pb = sample(pf, i, j - 1, k)
pt = sample(pf, i, j + 1, k)
pzf = sample(pf, i, j, k + 1)
pzb = sample(pf, i, j, k - 1)
div = velocity_divs[i, j, k]
new_pf[i, j, k] = (pl + pr + pb + pt + pzf + pzb - div) * (1 / 6)
# print(new_pf[i, j, k], velocity_divs[i, j, k])
@ti.kernel
def subtract_gradient(vf: ti.template(), pf: ti.template()):
for i, j, k in vf:
pl = sample(pf, i - 1, j, k)
pr = sample(pf, i + 1, j, k)
pb = sample(pf, i, j - 1, k)
pt = sample(pf, i, j + 1, k)
pzf = sample(pf, i, j, k + 1)
pzb = sample(pf, i, j, k - 1)
vf[i, j, k] -= 0.5 * ti.Vector([pr - pl, pt - pb, pzf - pzb])
@ti.kernel
def copy_divergence(div_in: ti.template(), div_out: ti.template()):
for I in ti.grouped(div_in):
div_out[I[0] * res + I[1]] = -div_in[I]
@ti.kernel
def apply_pressure(p_in: ti.types.ndarray(), p_out: ti.template()):
for I in ti.grouped(p_out):
p_out[I] = p_in[I[0] * res + I[1]]
def solve_pressure_jacobi():
for _ in range(p_jacobi_iters):
pressure_jacobi(pressures_pair.cur, pressures_pair.nxt)
pressures_pair.swap()
def step():
# replace_velocity_field()
advect(velocities_pair.cur, velocities_pair.cur, velocities_pair.nxt)
advect(velocities_pair.cur, dyes_pair.cur, dyes_pair.nxt)
velocities_pair.swap()
dyes_pair.swap()
apply_impulse(velocities_pair.cur, dyes_pair.cur)
divergence(velocities_pair.cur)
solve_pressure_jacobi()
subtract_gradient(velocities_pair.cur, pressures_pair.cur)
def reset():
velocities_pair.cur.fill(0)
pressures_pair.cur.fill(0)
dyes_pair.cur.fill(0)
_density_color.fill(0)
def fillnumpy():
arr = vol.tonumpy()
arr[:] = _density_color.to_numpy()
vol.mode(0).c('cool').alpha(0.015)
vol.imagedata().GetPointData().GetScalars().Modified()
def step_one_frame(evt):
global frame
print("step: ", frame)
step()
ti.sync()
fillnumpy()
plt.render()
frame += 1
reset()
vol = Volume(np.zeros_like(_density_color.to_numpy())).mode(0).c('cool').alpha(0.02) # change properties
plt = RayCastPlotter(vol, bg='white', bg2='blackboard', screensize=[1920, 1920], axes=7) # Plotter instance
plt.add_callback("timer", step_one_frame)
plt.timer_callback("start")
plt.show(viewup="z")
plt.interactive().close()