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discrete_operator_verification.py
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import taichi as ti
import numpy as np
from fluid_simulator import ImcompressibleFlowSimulation
mx = 2
my = 4
@ti.data_oriented
class DiscreteOperatorTester():
def __init__(self, Lx, Ly, nx, ny) -> None:
self.simulator = ImcompressibleFlowSimulation(Lx, Ly, nx, ny, 1)
self.error_gradp_x = ti.field(dtype=float, shape=())
self.error_gradp_y = ti.field(dtype=float, shape=())
self.error_div_v = ti.field(dtype=float, shape=())
self.error_laplacian_vx = ti.field(dtype=float, shape=())
self.error_laplacian_vy = ti.field(dtype=float, shape=())
self.error_advect_vx = ti.field(dtype=float, shape=())
self.error_advect_vy = ti.field(dtype=float, shape=())
@ti.func
def analytical_vx(self, x, y):
return ti.sin(mx * np.pi * x) * ti.cos(my * np.pi * y)
@ti.func
def analytical_vy(self, x, y):
return ti.cos(mx * np.pi * x) * ti.sin(my * np.pi * y)
@ti.func
def analytical_pressure(self, x, y):
return ti.sin(mx * np.pi * x) * ti.cos(mx * np.pi * y)
@ti.func
def analytical_pressure_grad_x(self, x, y):
return mx * np.pi * ti.cos(mx * np.pi * x) * ti.cos(mx * np.pi * y)
@ti.func
def analytical_pressure_grad_y(self, x, y):
return -mx * np.pi * ti.sin(mx * np.pi * x) * ti.sin(mx * np.pi * y)
@ti.func
def analytical_div_v(self, x, y):
grad_vx_x = mx * np.pi * ti.cos(mx * np.pi * x) * ti.cos(my * np.pi * y)
grad_vy_y = my * np.pi * ti.cos(mx * np.pi * x) * ti.cos(my * np.pi * y)
return grad_vx_x + grad_vy_y
@ti.func
def analytical_laplacian_v(self, x, y):
laplacian_vx = -(mx * mx + my * my) * np.pi * np.pi * ti.sin(mx * np.pi * x) * ti.cos(my * np.pi * y)
laplacian_vy = -(mx * mx + my * my) * np.pi * np.pi * ti.cos(mx * np.pi * x) * ti.sin(my * np.pi * y)
return ti.Vector([laplacian_vx, laplacian_vy], float)
@ti.func
def analytical_advection(self, x, y):
duu_dx = np.pi * mx * ti.sin(2 * mx * np.pi * x) * (ti.cos(my * np.pi * y) ** 2)
duv_dy = 0.5 * np.pi * my * ti.sin(2 * mx * np.pi * x) * ti.cos(2 * my * np.pi * y)
duv_dx = 0.5 * np.pi * mx * ti.cos(2 * mx * np.pi * x) * ti.sin(2 * my * np.pi * y)
dvv_dy = np.pi * my * (ti.cos(mx * np.pi * x) ** 2) * ti.sin(2 * my * np.pi * y)
return ti.Vector([duu_dx + duv_dy, duv_dx + dvv_dy], float)
@ti.kernel
def fill_data(self):
for I in ti.grouped(self.simulator.vx):
x = I[0] * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
self.simulator.vx[I] = self.analytical_vx(x, y)
for I in ti.grouped(self.simulator.vy):
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy
self.simulator.vy[I] = self.analytical_vy(x, y)
for I in ti.grouped(self.simulator.pressure):
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
self.simulator.pressure[I] = self.analytical_pressure(x, y)
@ti.kernel
def compute_error(self):
self.error_div_v[None] = 0.0
self.error_gradp_x[None] = 0.0
self.error_gradp_y[None] = 0.0
self.error_laplacian_vx[None] = 0.0
self.error_laplacian_vy[None] = 0.0
for I in ti.grouped(self.simulator.gradp_x):
if I[0] == 0 or I[0] == self.simulator.nx:
continue
x = I[0] * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
self.error_gradp_x[None] += (self.analytical_pressure_grad_x(x, y) - self.simulator.gradp_x[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.gradp_y):
if I[1] == 0 or I[1] == self.simulator.ny:
continue
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy
self.error_gradp_y[None] += (self.analytical_pressure_grad_y(x, y) - self.simulator.gradp_y[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.div_v):
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
self.error_div_v[None] += (self.analytical_div_v(x, y) - self.simulator.div_v[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.laplacian_vx):
if I[0] == 0 or I[0] == self.simulator.nx or I[1] == 0 or I[1] == self.simulator.ny-1:
continue
x = I[0] * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
lap_vec = self.analytical_laplacian_v(x, y)
self.error_laplacian_vx[None] += (lap_vec[0] - self.simulator.laplacian_vx[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.laplacian_vy):
if I[1] == 0 or I[1] == self.simulator.ny or I[0] == 0 or I[0] == self.simulator.nx-1:
continue
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy
lap_vec = self.analytical_laplacian_v(x, y)
self.error_laplacian_vy[None] += (lap_vec[1] - self.simulator.laplacian_vy[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.advect_vx):
if I[0] == 0 or I[0] == self.simulator.nx:
continue
x = I[0] * self.simulator.dx
y = I[1] * self.simulator.dy + 0.5 * self.simulator.dy
self.error_advect_vx[None] += (self.analytical_advection(x, y)[0] - self.simulator.advect_vx[I]) ** 2 * self.simulator.dx * self.simulator.dy
for I in ti.grouped(self.simulator.advect_vy):
if I[1] == 0 or I[1] == self.simulator.ny:
continue
x = I[0] * self.simulator.dx + 0.5 * self.simulator.dx
y = I[1] * self.simulator.dy
self.error_advect_vy[None] += (self.analytical_advection(x, y)[1] - self.simulator.advect_vy[I]) ** 2 * self.simulator.dx * self.simulator.dy
print("dx: ", self.simulator.dx)
print("Error gradp_x: ", ti.sqrt(self.error_gradp_x[None]))
print("Error gradp_y: ", ti.sqrt(self.error_gradp_y[None]))
print("Error div_v: ", ti.sqrt(self.error_div_v[None]))
print("Error laplacian_vx: ", ti.sqrt(self.error_laplacian_vx[None]))
print("Error laplacian_vy: ", ti.sqrt(self.error_laplacian_vy[None]))
print("Error advect_vx: ", ti.sqrt(self.error_advect_vx[None]))
print("Error advect_vy: ", ti.sqrt(self.error_advect_vy[None]))
if __name__ == '__main__':
ti.init(default_fp=ti.f64, arch=ti.cuda)
import sys
N = int(sys.argv[1])
tester = DiscreteOperatorTester(1.0, 1.0, N, N)
tester.fill_data()
tester.simulator.compute_div_v()
tester.simulator.compute_gradp()
tester.simulator.compute_laplacian_v()
tester.simulator.compute_advection()
tester.compute_error()