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diffuse_explicit_2.py
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import taichi as ti
ti.init(arch = ti.cpu)
# control
paused = True
save_images = False
# problem setting
n = 64
scatter = 8
res = n * scatter
# physical parameters
# time-integration related
h = 1e-3 # time-step size
substep = 1 # number of substeps
dx = 1 # finite difference step size (in space)
# heat-source related
t_max = 300 # max temperature (in Celsius)
t_min = 0 # min temperature
heat_center = (n//2, n//2)
heat_radius = 5.1
k = 50.0 # rate of heat diffusion
# visualization
pixels = ti.Vector.field(3, ti.f32, shape = (res, res))
# diffuse matrix
n2 = n**2
D_builder = ti.linalg.SparseMatrixBuilder(n2, n2, max_num_triplets=n2*5)
I_builder = ti.linalg.SparseMatrixBuilder(n2, n2, max_num_triplets=n2)
# temperature now and temperature next_time
t_n = ti.field(ti.f32, shape = n2) # unrolled to 1-d array
t_np1 = ti.field(ti.f32, shape = n2) # unrolled to 1-d array
ind = lambda i, j: i*n+j
@ti.kernel
def fillDiffusionMatrixBuilder(A: ti.linalg.sparse_matrix_builder()):
for i,j in ti.ndrange(n, n):
count = 0
if i-1 >= 0:
A[ind(i,j), ind(i-1,j)] += 1
count += 1
if i+1 < n:
A[ind(i,j), ind(i+1,j)] += 1
count += 1
if j-1 >= 0:
A[ind(i,j), ind(i,j-1)] += 1
count += 1
if j+1 < n:
A[ind(i,j), ind(i,j+1)] += 1
count += 1
A[ind(i,j), ind(i,j)] += -count
@ti.kernel
def fillEyeMatrixBuilder(A: ti.linalg.sparse_matrix_builder()):
for i,j in ti.ndrange(n, n):
A[ind(i,j), ind(i,j)] += 1
def buildMatrices():
fillDiffusionMatrixBuilder(D_builder)
fillEyeMatrixBuilder(I_builder)
D = D_builder.build()
I = I_builder.build()
return D, I
@ti.kernel
def init():
for i,j in ti.ndrange(n, n):
if (float(i)-heat_center[0])**2 + (float(j)-heat_center[1])**2 <= heat_radius**2:
t_n[ind(i, j)] = t_max # source
t_np1[ind(i, j)] = t_max # source
else:
t_n[ind(i, j)] = t_min
t_np1[ind(i, j)] = t_min
@ti.kernel
def update_source():
for i,j in ti.ndrange(n, n):
if (float(i)-heat_center[0])**2 + (float(j)-heat_center[1])**2 <= heat_radius**2:
t_np1[ind(i, j)] = t_max
def diffuse(dt: ti.f32):
c = dt * k / dx**2
IpcD = I + c*D
t_np1.from_numpy(IpcD@t_n.to_numpy()) # t_np1 = t_n + c*D*t_n
def update_source_and_commit():
update_source()
t_n.copy_from(t_np1)
@ti.func
def get_color(v, vmin, vmax):
c = ti.Vector([1.0, 1.0, 1.0]) # white
if v < vmin:
v = vmin
if v > vmax:
v = vmax
dv = vmax - vmin
if v < (vmin + 0.25 * dv):
c[0] = 0
c[1] = 4 * (v-vmin) / dv
elif v < (vmin + 0.5 * dv):
c[0] = 0
c[2] = 1 + 4 * (vmin + 0.25*dv -v) / dv
elif v < (vmin + 0.75*dv):
c[0] = 4 * (v - vmin -0.5 * dv) / dv
c[2] = 0
else:
c[1] = 1 + 4 * (vmin + 0.75 * dv - v) / dv
c[2] = 0
return c
@ti.kernel
def temperature_to_color(t: ti.template(), color: ti.template(), tmin: ti.f32, tmax: ti.f32):
for i,j in ti.ndrange(n, n):
for k,l in ti.ndrange(scatter, scatter):
color[i*scatter+k,j*scatter+l] = get_color(t[ind(i,j)], tmin, tmax)
# GUI
my_gui = ti.GUI("Diffuse", (res, res))
my_gui.show()
init()
D,I = buildMatrices()
i = 0
while my_gui.running:
for e in my_gui.get_events(ti.GUI.PRESS):
if e.key == ti.GUI.ESCAPE:
exit()
elif e.key == ti.GUI.SPACE:
paused = not paused
elif e.key == 'i':
save_images = not save_images
print(f"Exporting images to images\output_{i:05}.png")
elif e.key == 'r':
init()
i = 0
if not paused:
for sub in range(substep):
diffuse(h/substep)
update_source_and_commit()
temperature_to_color(t_np1, pixels, t_min, t_max)
my_gui.set_image(pixels)
if save_images and not paused:
my_gui.show(f"images\output_{i:05}.png")
i += 1
else:
my_gui.show()