def plot_trajectories(q_l, q_r, ax=None, t=None, xmax=None):
states, speeds, reval, wave_types = exact_riemann_solution(q_l, q_r)
def reval_with_speed(xi):
q = reval(xi)
u = q
qu = np.vstack((q, u))
return qu
# density of particles for trajectories:
rho_left = q_l / 3.
rho_right = q_r / 3.
# compute trajectories:
x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(
states,
speeds,
reval_with_speed,
wave_types,
xmax=xmax,
rho_left=rho_left,
rho_right=rho_right)
# plot trajectories along with waves in the x-t plane:
riemann_tools.plot_riemann_trajectories(x_traj,
t_traj,
speeds,
wave_types,
xmax=xmax,
ax=ax,
t=t)
ax.set_title('Particle trajectories')
def plot_riemann_trajectories(q_l, q_r, gamma=1.4, primitive=False):
if primitive:
q_left = euler.primitive_to_conservative(*q_l)
q_right = euler.primitive_to_conservative(*q_r)
else:
q_left = q_l
q_right = q_r
ex_states, ex_speeds, reval, wave_types = exact_riemann_solution(
q_left, q_right, gamma=gamma)
def reval_rho_u(x):
q = reval(x)
rho = q[0]
u = q[1] / q[0]
rho_u = np.vstack((rho, u))
return rho_u
# Specify density of trajectories to left and right:
rho_l = q_left[0] / 10.
rho_r = q_right[0] / 10.
x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(
ex_states,
ex_speeds,
reval_rho_u,
wave_types,
i_vel=1,
rho_left=rho_l,
rho_right=rho_r)
riemann_tools.plot_riemann_trajectories(x_traj, t_traj, ex_speeds,
wave_types)
def plot_car_trajectories(q_l, q_r, D, axes=None, t=None, xmax=None):
states, speeds, reval, wave_types = exact_riemann_solution(q_l, q_r, D)
def reval_with_speed(xi):
q = reval(xi)
u = 1 - q
qu = np.vstack((q, u))
return qu
# density of particles for trajectories:
rho_left = q_l / 2.
rho_right = q_r / 2.
# compute trajectories:
x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(
states,
speeds,
reval_with_speed,
wave_types,
xmax=xmax,
rho_left=rho_left,
rho_right=rho_right)
# plot trajectories along with waves in the x-t plane:
axes = riemann_tools.plot_riemann_trajectories(x_traj,
t_traj,
speeds,
wave_types,
xmax=xmax,
ax=axes,
t=t)
axes.set_title('Vehicle trajectories')
axes.set_xlabel('$x$', fontsize=15)
axes.set_ylabel('$t$', fontsize=15)
def plot_car_trajectories(q_l,q_r,ax=None,t=None,xmax=None):
states, speeds, reval, wave_types = riemann_traffic_exact(q_l,q_r)
def reval_with_speed(xi):
q = reval(xi)
u = 1-q
qu = np.vstack((q,u))
return qu
# density of particles for trajectories:
rho_left = q_l / 3.
rho_right = q_r / 3.
# compute trajectories:
x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(states,
speeds, reval_with_speed, wave_types,
xmax=xmax,rho_left=rho_left, rho_right=rho_right)
# plot trajectories along with waves in the x-t plane:
riemann_tools.plot_riemann_trajectories(x_traj, t_traj, speeds, wave_types,
xmax=xmax, ax=ax, t=t)
ax.set_title('Vehicle trajectories')
def make_demo_plot_function(h_l=3.,
h_r=1.,
u_l=0.,
u_r=0,
figsize=(10, 3),
hlim=(0, 3.5),
ulim=(-1, 1),
force_waves=None,
stripes=True):
from matplotlib.mlab import find
g = 1.
q_l = primitive_to_conservative(h_l, u_l)
q_r = primitive_to_conservative(h_r, u_r)
x = np.linspace(-1., 1., 1000)
states, speeds, reval, wave_types = \
exact_riemann_solution(q_l,q_r,g,force_waves=force_waves)
# compute particle trajectories:
def reval_rho_u(x):
q = reval(x)
rho = q[0]
u = q[1] / q[0]
rho_u = np.vstack((rho, u))
return rho_u
if stripes:
x_traj, t_traj, xmax = \
riemann_tools.compute_riemann_trajectories(states, speeds,
reval_rho_u,
wave_types, i_vel=1,
xmax=2,
rho_left=h_l/4.,
rho_right=h_r/4.)
else:
x_traj, t_traj, xmax = \
riemann_tools.compute_riemann_trajectories(states, speeds,
reval_rho_u,
wave_types, i_vel=1,
xmax=2,
num_left=3,
num_right=3)
num_vars = len(primitive_variables)
def plot_shallow_water_demo(t=0.5, fig=0):
if t == 0:
q = np.zeros((2, len(x)))
q[0, :] = q_l[0] * (x <= 0) + q_r[0] * (x > 0)
q[1, :] = q_l[1] * (x <= 0) + q_r[1] * (x > 0)
else:
q = np.array(reval(x / t))
if t < 0.02:
q[1] = np.where(x < 0, q_l[1], q_r[1])
primitive = conservative_to_primitive(q[0], q[1])
if fig == 0:
fig = plt.figure(figsize=figsize)
show_fig = True
else:
show_fig = False
axes = [0] * num_vars
for i in range(num_vars):
axes[i] = fig.add_subplot(1, num_vars, i + 1)
q = primitive[i]
plt.plot(x, q, '-k', linewidth=3)
plt.title(primitive_variables[i])
if t != 0:
plt.suptitle('Solution at time $t=' + str(t) + '$',
fontsize=12)
else:
plt.suptitle('Initial data', fontsize=12)
axes[i].set_xlim(-1, 1)
if i == 0 and force_waves != 'raref':
# plot stripes only on depth plot
# (and suppress if nonphysical solution plotted)
n = find(t > t_traj)
if len(n) == 0:
n = 0
else:
n = min(n.max(), len(t_traj) - 1)
for j in range(1, x_traj.shape[1] - 1):
j1 = find(x_traj[n, j] > x)
if len(j1) == 0:
j1 = 0
else:
j1 = min(j1.max(), len(x) - 1)
j2 = find(x_traj[n, j + 1] > x)
if len(j2) == 0:
j2 = 0
else:
j2 = min(j2.max(), len(x) - 1)
# set advected color for density plot:
if x_traj[0, j] < 0:
# shades of red for fluid starting from x<0
if np.mod(j, 2) == 0:
c = 'lightblue'
alpha = 1.0
else:
c = 'dodgerblue'
alpha = 1.0
else:
# shades of blue for fluid starting from x<0
if np.mod(j, 2) == 0:
c = 'cornflowerblue'
alpha = 1.0
else:
c = 'blue'
alpha = 1.0
plt.fill_between(x[j1:j2],
q[j1:j2],
0,
color=c,
alpha=alpha)
axes[0].set_ylim(hlim)
axes[1].set_ylim(ulim)
if show_fig:
plt.show()
return plot_shallow_water_demo
def plot_with_stripes(rho_l=3.,
u_l=0.,
p_l=3.,
rho_r=1.,
u_r=0.,
p_r=1.,
gamma=1.4,
t=0.4):
import matplotlib.pyplot as plt
import numpy as np
from exact_solvers import euler
from utils import riemann_tools
q_l = euler.primitive_to_conservative(rho_l, u_l, p_l)
q_r = euler.primitive_to_conservative(rho_r, u_r, p_r)
x = np.linspace(-1., 1., 1000)
states, speeds, reval, wave_types = euler.exact_riemann_solution(
q_l, q_r, gamma=gamma)
if t == 0:
q = np.zeros((3, len(x)))
q[0, :] = q_l[0] * (x <= 0) + q_r[0] * (x > 0)
q[1, :] = q_l[1] * (x <= 0) + q_r[1] * (x > 0)
q[1, :] = q_l[2] * (x <= 0) + q_r[2] * (x > 0)
else:
q = reval(x / t)
primitive = euler.conservative_to_primitive(q[0], q[1], q[2])
# compute particle trajectories:
def reval_rho_u(x):
eps = 1.e-16
q = reval(x)
rho = q[0]
u = q[1] / (q[0] + eps)
rho_u = np.vstack((rho, u))
return rho_u
# Specify density of trajectories to left and right:
num_left = 10
num_right = 10
rho_left = q_l[0] / 10.
rho_right = q_r[0] / 10.
x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(
states,
speeds,
reval_rho_u,
wave_types,
i_vel=1,
xmax=1,
rho_left=rho_left,
rho_right=rho_right)
fig = plt.figure(figsize=(9, 8))
names = ['Density', 'Velocity', 'Pressure']
axes = [0] * 3
for i in range(3):
axes[i] = fig.add_subplot(3, 1, i + 1)
q = primitive[i]
plt.plot(x, q, '-k', linewidth=3)
plt.title(names[i])
qmax = max(q)
qmin = min(q)
qdiff = qmax - qmin
if qdiff == 0: qdiff = qmin * 0.5
axes[i].set_ylim((qmin - 0.1 * qdiff, qmax + 0.1 * qdiff))
axes[i].set_xlim(-xmax, xmax)
if i == 0:
# plot stripes only on density plot
n = np.array([j for j, v in enumerate(t > t_traj) if v])
if len(n) == 0:
n = 0
else:
n = min(n.max(), len(t_traj) - 1)
for i in range(1, x_traj.shape[1] - 1):
j1 = np.array([j for j, v in enumerate(x_traj[n, i] > x) if v])
if len(j1) == 0:
j1 = 0
else:
j1 = min(j1.max(), len(x) - 1)
j2 = np.array(
[j for j, v in enumerate(x_traj[n, i + 1] > x) if v])
if len(j2) == 0:
j2 = 0
else:
j2 = min(j2.max(), len(x) - 1)
# set advected color for density plot:
if x_traj[0, i] < 0:
# shades of red for fluid starting from x<0
if np.mod(i, 2) == 0:
c = [1, 0, 0]
else:
c = [1, 0.8, 0.8]
else:
# shades of blue for fluid starting from x<0
if np.mod(i, 2) == 0:
c = [0, 0, 1]
else:
c = [0.8, 0.8, 1]
plt.fill_between(x[j1:j2], q[j1:j2], 0, color=c)
plt.tight_layout()
plt.show()
def make_demo_plot_function(h_l=3., h_r=1., u_l=0., u_r=0,
figsize=(10,3), hlim=(0,3.5), ulim=(-1,1),
force_waves=None, stripes=True):
from matplotlib.mlab import find
g = 1.
q_l = primitive_to_conservative(h_l,u_l)
q_r = primitive_to_conservative(h_r,u_r)
x = np.linspace(-1.,1.,1000)
states, speeds, reval, wave_types = \
exact_riemann_solution(q_l,q_r,g,force_waves=force_waves)
# compute particle trajectories:
def reval_rho_u(x):
q = reval(x)
rho = q[0]
u = q[1]/q[0]
rho_u = np.vstack((rho,u))
return rho_u
if stripes:
x_traj, t_traj, xmax = \
riemann_tools.compute_riemann_trajectories(states, speeds,
reval_rho_u,
wave_types, i_vel=1,
xmax=2,
rho_left=h_l/4.,
rho_right=h_r/4.)
else:
x_traj, t_traj, xmax = \
riemann_tools.compute_riemann_trajectories(states, speeds,
reval_rho_u,
wave_types, i_vel=1,
xmax=2,
num_left=3,
num_right=3)
num_vars = len(primitive_variables)
def plot_shallow_water_demo(t=0.5, fig=0):
if t == 0:
q = np.zeros((2,len(x)))
q[0,:] = q_l[0]*(x<=0) + q_r[0]*(x>0)
q[1,:] = q_l[1]*(x<=0) + q_r[1]*(x>0)
else:
q = np.array(reval(x/t))
if t<0.02:
q[1] = np.where(x<0, q_l[1], q_r[1])
primitive = conservative_to_primitive(q[0],q[1])
if fig == 0:
fig = plt.figure(figsize=figsize)
show_fig = True
else:
show_fig = False
axes = [0]*num_vars
for i in range(num_vars):
axes[i] = fig.add_subplot(1,num_vars,i+1)
q = primitive[i]
plt.plot(x,q,'-k',linewidth=3)
plt.title(primitive_variables[i])
if t != 0:
plt.suptitle('Solution at time $t='+str(t)+'$',fontsize=12)
else:
plt.suptitle('Initial data',fontsize=12)
axes[i].set_xlim(-1,1)
if i==0 and force_waves != 'raref':
# plot stripes only on depth plot
# (and suppress if nonphysical solution plotted)
n = find(t > t_traj)
if len(n)==0:
n = 0
else:
n = min(n.max(), len(t_traj)-1)
for j in range(1, x_traj.shape[1]-1):
j1 = find(x_traj[n,j] > x)
if len(j1)==0:
j1 = 0
else:
j1 = min(j1.max(), len(x)-1)
j2 = find(x_traj[n,j+1] > x)
if len(j2)==0:
j2 = 0
else:
j2 = min(j2.max(), len(x)-1)
# set advected color for density plot:
if x_traj[0,j]<0:
# shades of red for fluid starting from x<0
if np.mod(j,2)==0:
c = 'lightblue'
alpha = 1.0
else:
c = 'dodgerblue'
alpha = 1.0
else:
# shades of blue for fluid starting from x<0
if np.mod(j,2)==0:
c = 'cornflowerblue'
alpha = 1.0
else:
c = 'blue'
alpha = 1.0
plt.fill_between(x[j1:j2],q[j1:j2],0,color=c,alpha=alpha)
axes[0].set_ylim(hlim)
axes[1].set_ylim(ulim)
if show_fig:
plt.show()
return plot_shallow_water_demo
def make_demo_plot_function(h_l=3.,
h_r=1.,
u_l=0.,
u_r=0,
figsize=(10, 3),
hlim=(0, 3.5),
ulim=(-1, 1),
force_waves=None):
from matplotlib.mlab import find
import matplotlib.pyplot as plt
from exact_solvers import shallow_water
from utils import riemann_tools
#plt.style.use('seaborn-talk')
g = 1.
q_l = shallow_water.primitive_to_conservative(h_l, u_l)
q_r = shallow_water.primitive_to_conservative(h_r, u_r)
x = np.linspace(-1., 1., 1000)
states, speeds, reval, wave_types = \
shallow_water.exact_riemann_solution(q_l,q_r,g,force_waves=force_waves)
# compute particle trajectories:
def reval_rho_u(x):
q = reval(x)
rho = q[0]
u = q[1] / q[0]
rho_u = np.vstack((rho, u))
return rho_u
x_traj, t_traj, xmax = \
riemann_tools.compute_riemann_trajectories(states, speeds, reval_rho_u,
wave_types, i_vel=1, xmax=2,
rho_left=h_l/4.,
rho_right=h_r/4.)
num_vars = len(primitive_variables)
def plot_shallow_water_demo(t=0.5, fig=0):
if t == 0:
q = np.zeros((2, len(x)))
q[0, :] = q_l[0] * (x <= 0) + q_r[0] * (x > 0)
q[1, :] = q_l[1] * (x <= 0) + q_r[1] * (x > 0)
else:
q = np.array(reval(x / t))
if t < 0.02:
q[1] = np.where(x < 0, q_l[1], q_r[1])
primitive = shallow_water.conservative_to_primitive(q[0], q[1])
if fig == 0:
fig = plt.figure(figsize=figsize)
show_fig = True
else:
show_fig = False
axes = [0] * num_vars
for i in range(num_vars):
axes[i] = fig.add_subplot(1, num_vars, i + 1)
q = primitive[i]
plt.plot(x, q, '-k', linewidth=3)
plt.title(primitive_variables[i])
axes[i].set_xlim(-1, 1)
if i == 0:
# plot stripes only on depth plot
n = find(t > t_traj)
if len(n) == 0:
n = 0
else:
n = min(n.max(), len(t_traj) - 1)
for i in range(1, x_traj.shape[1] - 1):
j1 = find(x_traj[n, i] > x)
if len(j1) == 0:
j1 = 0
else:
j1 = min(j1.max(), len(x) - 1)
j2 = find(x_traj[n, i + 1] > x)
if len(j2) == 0:
j2 = 0
else:
j2 = min(j2.max(), len(x) - 1)
# set advected color for density plot:
if x_traj[0, i] < 0:
# shades of red for fluid starting from x<0
if np.mod(i, 2) == 0:
c = [1, 0, 0]
else:
c = [1, 0.8, 0.8]
else:
# shades of blue for fluid starting from x<0
if np.mod(i, 2) == 0:
c = [0, 0, 1]
else:
c = [0.8, 0.8, 1]
plt.fill_between(x[j1:j2], q[j1:j2], 0, color=c)
axes[0].set_ylim(hlim)
axes[1].set_ylim(ulim)
if show_fig:
plt.show()
return plot_shallow_water_demo
