def test_drag_velocity_implicit_explicit(self):
""" Tests simulated terminal velocity against a calculated value using implicit and explicit integration. """
v = 5 # Fluid speed
def get_vel_fluid(self):
return [v, 0, 0]
data = []
tau = None
for timestep in [1]:
p_implicit = Particle(0, [0, 0, 0], [0, 0, 0], get_vel_fluid=get_vel_fluid,
get_gravity=lambda dummy: [0, 0, 0], diameter=0.001)
p_explicit = Particle(1, [0, 0, 0], [0, 0, 0], get_vel_fluid=get_vel_fluid,
get_gravity=lambda dummy: [0, 0, 0], diameter=0.001)
times = []
explicit = []
implicit = []
analytic = []
last_time = 0
for time in np.arange(0, 40, timestep):
p_explicit.iterate(time - last_time, implicit=False)
p_implicit.iterate(time - last_time, implicit=True)
times.append(time)
explicit.append(vect.mag(p_explicit.vel))
implicit.append(vect.mag(p_implicit.vel))
tau = p_explicit.get_tau()
analytic.append(v * (1 - math.exp(- time / tau)))
last_time = time
data.append([times, explicit])
data.append([times, implicit])
data.append([times, analytic])
fig = plt.figure()
fig.patch.set_facecolor('white')
ax = fig.gca()
plots = []
for i in range(len(data[0][0])):
data[0][0][i] /= tau
for d in data:
for j in range(len(d[1])):
d[1][j] = d[1][j] / v
plots.append(ax.plot(d[0], d[1])[0])
ax.set_xlabel(r'$t/\tau$')
ax.set_ylabel(r'Speed / Max Speed')
plt.legend(plots, ['Explicit', 'Implicit', 'Analytic'], loc=4)
plt.show()
print("Explicit terminal velocity = {0}".format(data[0][1][-1]))
print("Implicit terminal velocity = {0}".format(data[1][1][-1]))
# Test if terminal velocity is within 0.1% of a calculated value.
explicit_diff_sum = 0
implicit_diff_sum = 0
length = len(data[0][0])
for i in range(1, length): # Start at 1 to avoid division by zero at the initial conditions.
explicit_diff_sum += (data[0][1][i] - data[2][1][i]) / data[2][1][i]
implicit_diff_sum += (data[1][1][i] - data[2][1][i]) / data[2][1][i]
explicit_avg = 100 * np.abs(explicit_diff_sum / length)
print("Explicit average percentage difference = {0}".format(explicit_avg))
implicit_avg = 100 * np.abs(implicit_diff_sum / length)
print("Implicit average percentage difference = {0}".format(implicit_avg))
def test_bouncing_collision_timesteps(self):
p1 = Particle(1, [0, 0.5, 0], [0, 0, 0], 0.1)
p2 = Particle(2, [0, 0, 0], [0, 0, 0], 0.1, density=1e99, get_gravity=lambda dummy: [0, 0, 0])
col = Collision(p1, p2, 1e5, restitution=0.8)
tau = p1.get_tau()
timesteps = np.arange(0.0005, 0.001, 0.00001)
overlap_errors = []
for timestep in timesteps:
last_time = 0
for time in np.arange(0, 10, timestep):
delta_t = time - last_time
col.calculate(delta_t)
p1.iterate(delta_t)
p2.iterate(delta_t)
last_time = time
predicted_overlap = p1.get_mass() * vect.mag(p1.get_gravity(p1)) / col.stiffness
percent_dif = 100 * np.abs(col.get_particle_overlap() / predicted_overlap) - 100
overlap_errors.append(percent_dif)
for i in range(len(timesteps)):
timesteps[i] /= tau
fig = plt.figure()
fig.patch.set_facecolor('white')
ax = fig.add_subplot(111)
# ax.set_title('Percentage error against timestep')
ax.set_ylabel('Percentage error (%)')
ax.set_xlabel('Timestep (seconds)')
ax.plot(timesteps, overlap_errors)
plt.show()
def test_get_collision_normal(self):
p1 = Particle(1, [0, 0, 0], [0, 0, 0])
p2 = Particle(2, [1, 1, 1], [0, 0, 0])
col = Collision(p1, p2)
TestCase.assertAlmostEquals(self,
vect.mag(
col.get_collision_normal() - (np.array([1, 1, 1]) / vect.mag([1, 1, 1]))),
0)
def calculate_tangential_friction_force(self, normal_force, delta_t):
f_dyn = -self.friction_coefficient * vect.mag(
normal_force) * self.get_collision_tangent()
f_static = -self.friction_stiffness * self.get_tangential_displacement(
delta_t) * self.get_collision_tangent()
if vect.mag_squared(f_dyn) < vect.mag_squared(f_static):
return f_dyn
else:
return f_static
def get_percent_dif(particle1, particle2, delta_t):
print(" Testing " + str(delta_t))
last_time = 0
for time in np.arange(0, 10, delta_t):
delta_t = time - last_time
col.calculate(delta_t)
particle1.iterate(delta_t)
particle2.iterate(delta_t)
last_time = time
predicted_overlap = particle1.get_mass() * vect.mag(particle1.get_gravity(particle1)) / col.stiffness
percent_dif = 100 * np.abs(col.get_particle_overlap() / predicted_overlap) - 100
return percent_dif
def test_terminal_velocity(self):
""" Tests simulated terminal velocity against a calculated value. """
data = []
for timestep in [0.1, 1, 2, 3, 4, 5, 6]:
p = Particle(1, [0, 0, 0], [0, 0, 0])
times = []
speeds = []
last_time = 0
for time in np.arange(0, 40, timestep):
p.iterate(time - last_time)
times.append(time)
speeds.append(vect.mag(p.vel))
last_time = time
data.append([times, speeds])
fig = plt.figure()
fig.patch.set_facecolor('white')
ax = fig.gca()
for d in data:
ax.plot(d[0], d[1])
plt.show()
# Test if terminal velocity is within 0.1% of a calculated value.
self.assertLess(np.abs(vect.mag(data[0][1][-1]) / 56.442091968912 - 1), 0.001)
def test_bouncing_collision(self):
p1 = Particle(1, [0, 0.5, 0], [0, 0, 0], 0.1)
p2 = Particle(2, [0, 0, 0], [0, 0, 0], 0.1, density=1e99, get_gravity=lambda dummy: [0, 0, 0])
col = Collision(p1, p2, 1e5, restitution=0.8)
timestep = 0.0005
last_time = 0
for time in np.arange(0, 10, timestep):
delta_t = time - last_time
col.calculate(delta_t)
p1.iterate(delta_t)
p2.iterate(delta_t)
last_time = time
predicted_overlap = p1.get_mass() * vect.mag(p1.get_gravity(p1)) / col.stiffness
print("Predicted overlap = {0}".format(predicted_overlap))
print("Calculated overlap = {0}".format(col.get_particle_overlap()))
print("Percentage difference = {0}".format(100 * predicted_overlap / col.get_particle_overlap() - 100))
TestCase.assertAlmostEqual(self, predicted_overlap, col.get_particle_overlap())
particles_to_paraview([p1, p2], "bounce_col", "../../run/bounce_collision/")
def test_low_mem_logging(self):
p1 = Particle(1, [0, 0.5, 0], [0, 0, 0], 0.1)
p2 = Particle(2, [0, 0, 0], [0, 0, 0], 0.1, density=1e99, get_gravity=lambda dummy: [0, 0, 0])
col = Collision(p1, p2, 1e5, restitution=0.8)
timestep = 0.0005
logger = Logger([p1, p2], "low_mem_logging", "../../run/low_mem_logging/")
logger.log(0)
last_time = 0
for time in np.arange(0, 10, timestep):
delta_t = time - last_time
col.calculate(delta_t)
p1.iterate(delta_t)
p2.iterate(delta_t)
last_time = time
logger.log(time)
predicted_overlap = p1.get_mass() * vect.mag(p1.get_gravity(p1)) / col.stiffness
print("Predicted overlap = {0}".format(predicted_overlap))
print("Calculated overlap = {0}".format(col.get_particle_overlap()))
print("Percentage difference = {0}".format(100 * predicted_overlap / col.get_particle_overlap() - 100))
def get_speed_at_time(self, time):
try:
index = self.times.index(time)
return vect.mag(self.vel_history[index])
except ValueError:
return 0
def get_speed(self):
return vect.mag(self.vel)
def get_speed_at_index(self, index):
return vect.mag(self.vel_history[index])
def get_tangential_displacement(self, delta_t):
# TODO: Investigate more accurate methods of numerically integrating this.
return vect.mag(
(self.get_relative_velocity() - self.get_normal_velocity()) *
math.pi *
math.sqrt(self.get_reduced_particle_mass() / self.stiffness))
def get_particle_centre_separation(self):
return vect.mag(self.p2.pos - self.p1.pos)
def get_tangential_displacement(self, vel, delta_t):
# TODO: Investigate more accurate methods of numerically integrating this.
return vect.mag(vel * math.pi *
math.sqrt(self.p.get_mass() / self.stiffness))
def test_drag_velocity_implicit_explicit_timestep(self):
""" Tests simulated terminal velocity against a calculated value using implicit and explicit integration. """
v = 5 # Fluid speed
def get_vel_fluid(self):
return [v, 0, 0]
timesteps = np.arange(0.01, 5, 0.01)
explicit_avgs = []
implicit_avgs = []
tau = None
for timestep in timesteps:
p_implicit = Particle(0, [0, 0, 0], [0, 0, 0], get_vel_fluid=get_vel_fluid,
get_gravity=lambda dummy: [0, 0, 0], diameter=0.001)
p_explicit = Particle(1, [0, 0, 0], [0, 0, 0], get_vel_fluid=get_vel_fluid,
get_gravity=lambda dummy: [0, 0, 0], diameter=0.001)
times = []
explicit = []
implicit = []
analytic = []
last_time = 0
data = []
duration = 40
for time in np.arange(0, duration, timestep):
p_explicit.iterate(time - last_time, implicit=False)
p_implicit.iterate(time - last_time, implicit=True)
times.append(time)
explicit.append(vect.mag(p_explicit.vel))
implicit.append(vect.mag(p_implicit.vel))
tau = p_explicit.get_tau()
analytic.append(v * (1 - math.exp(- time / tau)))
last_time = time
data.append([times, explicit])
data.append([times, implicit])
data.append([times, analytic])
# fig = plt.figure()
# ax = fig.gca()
# plots = []
# for d in data:
# plots.append(ax.plot(d[0], d[1])[0])
# ax.set_xlabel('Time ($s$)')
# ax.set_ylabel(r'Speed ($ms^{-1}$)')
# plt.legend(plots, ['Explicit', 'Implicit', 'Analytic'], loc=4)
# plt.show()
explicit_dif_sum = 0
implicit_dif_sum = 0
for i in range(1, len(times)): # Start at 1 to avoid division by zero at the initial conditions.
explicit_dif = (explicit[i] - analytic[i]) / analytic[i]
explicit_dif_sum += timestep * explicit_dif
implicit_dif = (implicit[i] - analytic[i]) / analytic[i]
implicit_dif_sum += timestep * implicit_dif
explicit_avg = 100 * np.abs(explicit_dif_sum / duration)
# print("Explicit average percentage difference = {0}".format(explicit_avg))
implicit_avg = 100 * np.abs(implicit_dif_sum / duration)
# print("Implicit average percentage difference = {0}".format(implicit_avg))
explicit_avgs.append(explicit_avg)
implicit_avgs.append(implicit_avg)
for i in range(len(timesteps)):
timesteps[i] /= tau
fig = plt.figure()
fig.patch.set_facecolor('white')
ax = fig.gca()
explicit_avgs_plot, = ax.plot(timesteps, explicit_avgs)
implicit_avgs_plot, = ax.plot(timesteps, implicit_avgs)
ax.set_xlabel(r'$timestep/\tau$')
ax.set_ylabel(r'Average percentage difference')
plt.legend([explicit_avgs_plot, implicit_avgs_plot], ['Explicit', 'Implicit'], loc=4)
plt.show()