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# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
###########################################################################
# Example Fluid
#
# Shows how to implement a simple 2D Stable Fluids solver using
# multidimensional arrays and launches.
#
###########################################################################
import math
import warp as wp
import warp.render
wp.init()
grid_width = wp.constant(256)
grid_height = wp.constant(128)
@wp.func
def lookup_float(f: wp.array2d(dtype=float), x: int, y: int):
x = wp.clamp(x, 0, grid_width - 1)
y = wp.clamp(y, 0, grid_height - 1)
return f[x, y]
@wp.func
def sample_float(f: wp.array2d(dtype=float), x: float, y: float):
lx = int(wp.floor(x))
ly = int(wp.floor(y))
tx = x - float(lx)
ty = y - float(ly)
s0 = wp.lerp(lookup_float(f, lx, ly), lookup_float(f, lx + 1, ly), tx)
s1 = wp.lerp(lookup_float(f, lx, ly + 1), lookup_float(f, lx + 1, ly + 1), tx)
s = wp.lerp(s0, s1, ty)
return s
@wp.func
def lookup_vel(f: wp.array2d(dtype=wp.vec2), x: int, y: int):
if x < 0 or x >= grid_width:
return wp.vec2()
if y < 0 or y >= grid_height:
return wp.vec2()
return f[x, y]
@wp.func
def sample_vel(f: wp.array2d(dtype=wp.vec2), x: float, y: float):
lx = int(wp.floor(x))
ly = int(wp.floor(y))
tx = x - float(lx)
ty = y - float(ly)
s0 = wp.lerp(lookup_vel(f, lx, ly), lookup_vel(f, lx + 1, ly), tx)
s1 = wp.lerp(lookup_vel(f, lx, ly + 1), lookup_vel(f, lx + 1, ly + 1), tx)
s = wp.lerp(s0, s1, ty)
return s
@wp.kernel
def advect(
u0: wp.array2d(dtype=wp.vec2),
u1: wp.array2d(dtype=wp.vec2),
rho0: wp.array2d(dtype=float),
rho1: wp.array2d(dtype=float),
dt: float,
):
i, j = wp.tid()
u = u0[i, j]
# trace backward
p = wp.vec2(float(i), float(j))
p = p - u * dt
# advect
u1[i, j] = sample_vel(u0, p[0], p[1])
rho1[i, j] = sample_float(rho0, p[0], p[1])
@wp.kernel
def divergence(u: wp.array2d(dtype=wp.vec2), div: wp.array2d(dtype=float)):
i, j = wp.tid()
if i == grid_width - 1:
return
if j == grid_height - 1:
return
dx = (u[i + 1, j][0] - u[i, j][0]) * 0.5
dy = (u[i, j + 1][1] - u[i, j][1]) * 0.5
div[i, j] = dx + dy
@wp.kernel
def pressure_solve(p0: wp.array2d(dtype=float), p1: wp.array2d(dtype=float), div: wp.array2d(dtype=float)):
i, j = wp.tid()
s1 = lookup_float(p0, i - 1, j)
s2 = lookup_float(p0, i + 1, j)
s3 = lookup_float(p0, i, j - 1)
s4 = lookup_float(p0, i, j + 1)
# Jacobi update
err = s1 + s2 + s3 + s4 - div[i, j]
p1[i, j] = err * 0.25
@wp.kernel
def pressure_apply(p: wp.array2d(dtype=float), u: wp.array2d(dtype=wp.vec2)):
i, j = wp.tid()
if i == 0 or i == grid_width - 1:
return
if j == 0 or j == grid_height - 1:
return
# pressure gradient
f_p = wp.vec2(p[i + 1, j] - p[i - 1, j], p[i, j + 1] - p[i, j - 1]) * 0.5
u[i, j] = u[i, j] - f_p
@wp.kernel
def integrate(u: wp.array2d(dtype=wp.vec2), rho: wp.array2d(dtype=float), dt: float):
i, j = wp.tid()
# gravity
f_g = wp.vec2(-90.8, 0.0) * rho[i, j]
# integrate
u[i, j] = u[i, j] + dt * f_g
# fade
rho[i, j] = rho[i, j] * (1.0 - 0.1 * dt)
@wp.kernel
def init(rho: wp.array2d(dtype=float), u: wp.array2d(dtype=wp.vec2), radius: int, dir: wp.vec2):
i, j = wp.tid()
d = wp.length(wp.vec2(float(i - grid_width / 2), float(j - grid_height / 2)))
if d < radius:
rho[i, j] = 1.0
u[i, j] = dir
class Example:
def __init__(self, **kwargs):
self.device = wp.get_device()
self.sim_fps = 60.0
self.sim_substeps = 2
self.iterations = 100
self.sim_dt = (1.0 / self.sim_fps) / self.sim_substeps
self.sim_time = 0.0
self.device = wp.get_device()
shape = (grid_width, grid_height)
self.u0 = wp.zeros(shape, dtype=wp.vec2)
self.u1 = wp.zeros(shape, dtype=wp.vec2)
self.rho0 = wp.zeros(shape, dtype=float)
self.rho1 = wp.zeros(shape, dtype=float)
self.p0 = wp.zeros(shape, dtype=float)
self.p1 = wp.zeros(shape, dtype=float)
self.div = wp.zeros(shape, dtype=float)
# capture pressure solve as a CUDA graph
if self.device.is_cuda:
wp.capture_begin(self.device)
try:
self.pressure_iterations()
finally:
self.graph = wp.capture_end(self.device)
def update(self):
with wp.ScopedTimer("update"):
for _ in range(self.sim_substeps):
shape = (grid_width, grid_height)
dt = self.sim_dt
speed = 400.0
angle = math.sin(self.sim_time * 4.0) * 1.5
vel = wp.vec2(math.cos(angle) * speed, math.sin(angle) * speed)
# update emitters
wp.launch(init, dim=shape, inputs=[self.rho0, self.u0, 5, vel])
# force integrate
wp.launch(integrate, dim=shape, inputs=[self.u0, self.rho0, dt])
wp.launch(divergence, dim=shape, inputs=[self.u0, self.div])
# pressure solve
self.p0.zero_()
self.p1.zero_()
if self.device.is_cuda:
wp.capture_launch(self.graph)
else:
self.pressure_iterations()
# velocity update
wp.launch(pressure_apply, dim=shape, inputs=[self.p0, self.u0])
# semi-Lagrangian advection
wp.launch(advect, dim=shape, inputs=[self.u0, self.u1, self.rho0, self.rho1, dt])
# swap buffers
(self.u0, self.u1) = (self.u1, self.u0)
(self.rho0, self.rho1) = (self.rho1, self.rho0)
self.sim_time += dt
def render(self):
pass
def pressure_iterations(self):
for _ in range(self.iterations):
wp.launch(pressure_solve, dim=self.p0.shape, inputs=[self.p0, self.p1, self.div])
# swap pressure fields
(self.p0, self.p1) = (self.p1, self.p0)
def update_and_render_frame(self, frame_num=None, img=None):
self.update()
with wp.ScopedTimer("render"):
if img:
img.set_array(self.rho0.numpy())
return (img,)
if __name__ == "__main__":
import matplotlib
import matplotlib.animation as anim
import matplotlib.pyplot as plt
example = Example()
fig = plt.figure()
img = plt.imshow(example.rho0.numpy(), origin="lower", animated=True, interpolation="antialiased")
img.set_norm(matplotlib.colors.Normalize(0.0, 1.0))
seq = anim.FuncAnimation(
fig, example.update_and_render_frame, fargs=(img,), frames=100000, blit=True, interval=8, repeat=False
)
plt.show()
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