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FluidQuantity.py
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FluidQuantity.py
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import taichi as ti
from utils import (
euler,
swap_field,
copy_field,
bilerp,
get_value,
cerp
)
@ti.data_oriented
class FluidQuantity():
def __init__(self, res_x, res_y, ox, oy) -> None:
self.res_x = res_x
self.res_y = res_y
self.ox = ox
self.oy = oy
self.q = ti.field(float, shape=(res_x, res_y)) # q for quantity
self.q_tmp = ti.field(float, shape=(res_x, res_y)) # buffer for the quantity
self.q_forward = ti.field(float, shape=(res_x, res_y)) # buffer for MAC advection
self.q_backward = ti.field(float, shape=(res_x, res_y)) # buffer for MAC advection
@ti.kernel
def reset(self):
self.q.fill(0)
self.q_tmp.fill(0)
# Get the value of the field at arbitrary point
@ti.func
def at(self, x, y):
# Clmap and project to bot-left corner
fx = min(max(x - self.ox, 0.0), self.res_x - 1.001)
fy = min(max(y - self.oy, 0.0), self.res_y - 1.001)
ix = int(fx)
iy = int(fy)
x_weight = fx - ix
y_weight = fy - iy
return bilerp(x_weight, y_weight, self.q[ix, iy], self.q[ix+1, iy], self.q[ix, iy+1], self.q[ix+1, iy+1])
# Get field value at arbitrary point using cubic interpolation
@ti.func
def at_cerp(self, x, y):
# Clmap and project to bot-left corner
fx = min(max(x - self.ox, 0.0), self.res_x - 1.001)
fy = min(max(y - self.oy, 0.0), self.res_y - 1.001)
ix = int(fx)
iy = int(fy)
x_weight = fx - ix
y_weight = fy - iy
#int index for calculating cerp
x0 = max(ix - 1, 0)
x1 = ix
x2 = ix + 1
x3 = min(ix + 2, self.res_x - 1)
y0 = max(iy - 1, 0)
y1 = iy
y2 = iy + 1
y3 = min(iy + 2, self.res_y - 1)
q0 = cerp(self.q[x0,y0], self.q[x1,y0], self.q[x2,y0],self.q[x3,y0], x_weight)
q1 = cerp(self.q[x0,y1], self.q[x1,y1], self.q[x2,y1],self.q[x3,y1], x_weight)
q2 = cerp(self.q[x0,y2], self.q[x1,y2], self.q[x2,y2],self.q[x3,y2], x_weight)
q3 = cerp(self.q[x0,y3], self.q[x1,y3], self.q[x2,y3],self.q[x3,y3], x_weight)
return cerp(q0,q1,q2,q3,y_weight)
@ti.kernel
def flip(self):
swap_field(self.q, self.q_tmp)
@ti.kernel
def advect_SL(self, u: ti.template(), v: ti.template(), dx: float, dt: float):
for iy in range(self.q.shape[1]):
for ix in range(self.q.shape[0]):
# Current position
x = ix + self.ox
y = iy + self.oy
# Last position, in grid units
x_last = euler(x, get_value(u, x, y, 0, 0.5) / dx, -dt)
y_last = euler(y, get_value(v, x, y, 0.5, 0) / dx, -dt)
# x_last = x - self.get_value(x, y) / dx * dt
# y_last = y - self.get_value(x, y) / dx * dt
#at.() can be replaced by higher order lerp method: cerp
self.q_tmp[ix, iy] = self.at(x_last, y_last)
copy_field(self.q_tmp, self.q)
@ti.kernel
def advect_SL_MAC(self, q: ti.template(), q_tmp: ti.template() ,u: ti.template(), v: ti.template(),dx: float, dt: float):
for iy in range(q.shape[1]):
for ix in range(q.shape[0]):
# Current position
x = ix + self.ox
y = iy + self.oy
# Last position, in grid units
x_last = euler(x, get_value(u, x, y, 0, 0.5) / dx, -dt)
y_last = euler(y, get_value(v, x, y, 0.5, 0) / dx, -dt)
# x_last = x - self.get_value(x, y) / dx * dt
# y_last = y - self.get_value(x, y) / dx * dt
#at.() can be replaced by higher order lerp method: cerp
q_tmp[ix, iy] = self.at(x_last, y_last)
copy_field(q_tmp, q)
#high order backtrace time integration step with third order RungeKutta
@ti.kernel
def advect_SL_RK3(self, u: ti.template(), v: ti.template(), dx: float, dt: float):
for iy in range(self.q.shape[1]):
for ix in range(self.q.shape[0]):
x = ix + self.ox
y = iy + self.oy
firstU = get_value(u, x, y, 0, 0.5) / dx
firstV = get_value(v, x, y, 0.5, 0) / dx
midX = x - 0.5 * dt * firstU
midY = y - 0.5 * dt * firstV
midU = get_value(u, midX, midY, 0, 0.5) / dx
midV = get_value(v, midX, midY, 0.5, 0) / dx
lastX = x - 0.75 * dt * midU
lastY = y - 0.75 * dt * midV
lastU = get_value(u, lastX, lastY, 0, 0.5) / dx
lastV = get_value(v, lastX, lastY, 0.5, 0) / dx
x_last = x - dt * ((2.0/9.0) * firstU + (1.0 / 3.0) * midU + (4.0 / 9.0) * lastU)
y_last = y - dt * ((2.0/9.0) * firstV + (1.0 / 3.0) * midV + (4.0 / 9.0) * lastV)
self.q_tmp[ix,iy] = self.at_cerp(x_last,y_last) #self.at(x_last,y_last)
copy_field(self.q_tmp, self.q)
@ti.kernel
def copy_to(self, tmp: ti.template(), v: ti.template()):
copy_field(tmp, v)
@ti.kernel
def MC_correct(self):
qmin = 1e-10
qmax = 1e10
for x, y in self.q:
self.q_tmp[x, y] = self.q_forward[x, y] - 0.5 * (self.q_backward[x, y] - self.q[x, y])
copy_field(self.q_tmp, self.q)
def advect_MC(self, u: ti.template(), v: ti.template(), dx: float, dt: float):
self.copy_to(self.q, self.q_forward)
self.copy_to(self.q, self.q_backward)
self.advect_SL_MAC(self.q_forward,self.q_tmp,u, v, dx, dt)
dt *= -1
self.advect_SL_MAC(self.q_backward, self.q_tmp, u, v, dx, dt)
dt *= -1
self.MC_correct()