def plot_function_xt_phase(plot_1_chars=False, plot_2_chars=False):
plt.figure(figsize=(7, 2))
ax = plt.subplot(121)
riemann_tools.plot_waves(states,
speeds,
reval,
wave_types,
t=0,
ax=ax,
color='multi')
if plot_1_chars:
riemann_tools.plot_characteristics(reval,
shallow_water.lambda_1,
axes=ax,
extra_lines=extra_lines)
if plot_2_chars:
riemann_tools.plot_characteristics(reval,
shallow_water.lambda_2,
axes=ax,
extra_lines=extra_lines)
ax = plt.subplot(122)
shallow_water.phase_plane_plot(q_l,
q_r,
g,
ax=ax,
force_waves=force_waves,
y_axis='u')
plt.title('Phase plane')
plt.show()
def plot_riemann(q_l,q_r,t,x_range=1):
states, speeds, reval, wave_types = exact_riemann_solution(q_l,q_r)
ax = riemann_tools.plot_riemann(states, speeds, reval,
wave_types,t=t,
layout='horizontal',
t_pointer=0,
extra_axes=False,
variable_names=['q'],
xmax=x_range);
riemann_tools.plot_characteristics(reval, speed, axes=ax[0])
ax[1].set_ylim(-0.05,1.05)
for a in ax:
a.set_xlim(-x_range,x_range)
plt.show()
def plot_riemann(q_l,q_r,t,x_range=1):
states, speeds, reval, wave_types = exact_riemann_solution(q_l,q_r)
ax = riemann_tools.plot_riemann(states, speeds, reval,
wave_types,t=t,
layout='horizontal',
t_pointer=0,
extra_axes=False,
variable_names=['q'],
xmax=x_range);
riemann_tools.plot_characteristics(reval, speed, axes=ax[0])
ax[1].set_ylim(-0.05,1.05)
for a in ax:
a.set_xlim(-x_range,x_range)
plt.show()
def plot_riemann_traffic(rho_l,rho_r,t,xrange=1.):
states, speeds, reval, wave_types = \
riemann_traffic_exact(rho_l,rho_r)
ax = riemann_tools.plot_riemann(states,speeds,reval,
wave_types,t=t,
t_pointer=0,extra_axes=True,
variable_names=['Density'],
xmax=xrange)
riemann_tools.plot_characteristics(reval,c,axes=ax[0])
plot_car_trajectories(rho_l,rho_r,ax[2],t=t,xmax=xrange)
ax[1].set_ylim(-0.05,1.05); ax[2].set_ylim(0,1)
for a in ax:
a.set_xlim(-xrange,xrange)
plt.show()
def plot_function_xt_phase(plot_1_chars=False,plot_2_chars=False,plot_tracer_chars=False):
plt.figure(figsize=(7,2))
ax = plt.subplot(121)
riemann_tools.plot_waves(states, speeds, reval, wave_types, t=0,
ax=ax, color='multi')
if plot_1_chars:
riemann_tools.plot_characteristics(reval,lambda_1,
axes=ax,extra_lines=extra_lines)
if plot_2_chars:
riemann_tools.plot_characteristics(reval,lambda_2,
axes=ax,extra_lines=extra_lines)
if plot_tracer_chars:
riemann_tools.plot_characteristics(reval,lambda_tracer,
axes=ax,extra_lines=extra_lines)
ax = plt.subplot(122)
phase_plane_plot(q_l,q_r,g,ax=ax,
force_waves=force_waves,y_axis='u')
plt.title('Phase plane')
plt.show()
def plot_function(t, which_char, xmin=0, xmax=6, ymin=-6, ymax=6):
"Subfunction required for interactive (function of only interactive parameters)."
# Define parameters
pl = ql[0]
ul = ql[1]
pr = qr[0]
ur = qr[1]
dp = pr - pl
du = ur - ul
c = np.sqrt(bulk / rho)
Z = rho * c
# Define eigenvectors and functions
eig1 = np.array([-Z, 1])
eig2 = np.array([Z, 1])
lin1l = lambda p: ul - 1. / Z * (p - pl)
lin2l = lambda p: ul + 1. / Z * (p - pl)
lin1r = lambda p: ur - 1. / Z * (p - pr)
lin2r = lambda p: ur + 1. / Z * (p - pr)
# Solve Riemann problem
aux = [rho, bulk]
states, speeds, riemann_eval = acoustics.exact_riemann_solution(
np.array([pl, ul]), np.array([pr, ur]), aux)
pm = states[0][1]
um = states[1][1]
# Set figure grid
fig = plt.figure(figsize=(10, 5)) #figsize=(11.5, 5.5))
outer_grid = gridspec.GridSpec(1, 2, wspace=0.15, hspace=0.15)
inner_grid = gridspec.GridSpecFromSubplotSpec(
3, 1, subplot_spec=outer_grid[0], wspace=0.0, hspace=0.0)
ax1 = plt.Subplot(fig, inner_grid[0]) # x-t plane
ax2 = plt.Subplot(fig, inner_grid[1]) # x vs pressure
ax3 = plt.Subplot(fig, inner_grid[2]) # x vs velocity
ax4 = plt.Subplot(fig, outer_grid[1]) # phase plane
ax1.set_ylabel("t", fontsize=10)
ax2.set_ylabel("pressure", fontsize=10)
ax3.set_ylabel("velocity", fontsize=10)
ax3.set_xlabel("x", fontsize=10)
ax1.set_xticks([])
ax2.set_xticks([])
# Plot Riemann solution on ax1, ax2 and ax3
ax = np.array([ax1, ax2, ax3])
riemann_tools.plot_riemann(states,
speeds,
riemann_eval,
wave_types=None,
t=t,
ax=ax,
layout='vertical',
variable_names=['pressure', 'velocity'])
# Plot characteristics on ax1 if required
if which_char:
plot_chars = [acoustics.lambda1, acoustics.lambda2]
riemann_tools.plot_characteristics(riemann_eval,
plot_chars[which_char - 1],
aux=(np.array(aux),
np.array(aux)),
axes=ax[0],
speeds=speeds)
# Plot solution in phase plane plot ion ax4
x = (pl, pr, pm)
y = (ul, ur, um)
dx, dy = xmax - xmin, ymax - ymin
ax4.set_xlim(min(0.00000001, xmin), xmax)
ax4.set_ylim(ymin, ymax)
ax4.set_xlabel('Pressure (p)', fontsize=10)
ax4.set_ylabel('Velocity (u)', fontsize=10)
ax4.set_title('Phase plane', fontsize=12)
p = np.linspace(xmin, xmax, 500)
# Plot incorrect solution
ax4.plot(p, lin2l(p), '--k')
ax4.plot(p, lin1r(p), '--k')
# Plot physical solution
ax4.plot(p, lin1l(p), '-k')
ax4.plot(p, lin2r(p), '-k')
if (pm >= 0 and pm <= xmax and um > ymin and um < ymax):
ax4.plot(pm, um, '-ok', markersize=10)
ax4.text(x[2] + 0.03 * dx, y[2] + 0.03 * dy, '$q_m$', fontsize=15)
# Plot initial states and markers
ax4.plot(pl, ul, '-ok', markersize=10)
ax4.plot(pr, ur, '-ok', markersize=10)
for i, label in enumerate(('$q_l$', '$q_r$')):
ax4.text(x[i] + 0.03 * dx, y[i] + 0.03 * dy, label, fontsize=15)
# Add all plots to fig and show
fig.add_subplot(ax1)
fig.add_subplot(ax2)
fig.add_subplot(ax3)
fig.add_subplot(ax4)
plt.show()
def plot_function(t,pl,ul,pr,ur,rho,bulk,which_char,
xmin=0,xmax=6,ymin=-6,ymax=6,show_phys=True,show_unphys=True):
"Subfunction required for interactive (function of only interactive parameters)."
# Define parameters
dp = pr - pl
du = ur - ul
c = np.sqrt(bulk/rho)
Z = rho*c
# Define eigenvectors and functions
eig1 = np.array([-Z, 1])
eig2 = np.array([Z, 1])
lin1l = lambda p: ul - 1./Z*(p-pl)
lin2l = lambda p: ul + 1./Z*(p-pl)
lin1r = lambda p: ur - 1./Z*(p-pr)
lin2r = lambda p: ur + 1./Z*(p-pr)
# Solve Riemann problem
aux = [rho,bulk]
states, speeds, riemann_eval = acoustics.exact_riemann_solution(np.array([pl,ul]), np.array([pr,ur]), aux)
pm = states[0][1]
um = states[1][1]
# Set figure grid
fig = plt.figure(figsize=(10,5)) #figsize=(11.5, 5.5))
outer_grid = gridspec.GridSpec(1, 2, wspace=0.15, hspace=0.15)
inner_grid = gridspec.GridSpecFromSubplotSpec(3, 1, subplot_spec=outer_grid[0], wspace=0.0, hspace=0.0)
ax1 = plt.Subplot(fig, inner_grid[0]) # x-t plane
ax2 = plt.Subplot(fig, inner_grid[1]) # x vs pressure
ax3 = plt.Subplot(fig, inner_grid[2]) # x vs velocity
ax4 = plt.Subplot(fig, outer_grid[1]) # phase plane
ax1.set_ylabel("t", fontsize=10)
ax2.set_ylabel("pressure", fontsize=10)
ax3.set_ylabel("velocity", fontsize=10)
ax3.set_xlabel("x", fontsize=10)
ax1.set_xticks([])
ax2.set_xticks([])
# Plot Riemann solution on ax1, ax2 and ax3
ax = np.array([ax1, ax2, ax3])
riemann_tools.plot_riemann(states, speeds, riemann_eval, wave_types=None, t=t, ax=ax,
layout='vertical', variable_names=['pressure', 'velocity'])
# Plot characteristics on ax1 if required
if which_char:
plot_chars=[acoustics.lambda1, acoustics.lambda2]
riemann_tools.plot_characteristics(riemann_eval, plot_chars[which_char-1],
aux=(np.array(aux),np.array(aux)), axes=ax[0], speeds=speeds)
# Plot solution in phase plane plot ion ax4
x = (pl, pr, pm)
y = (ul, ur, um)
dx, dy = xmax - xmin, ymax - ymin
ax4.set_xlim(min(0.00000001,xmin),xmax)
ax4.set_ylim(ymin,ymax)
ax4.set_xlabel('Pressure (p)', fontsize=10)
ax4.set_ylabel('Velocity (u)', fontsize=10)
ax4.set_title('Phase plane', fontsize=12)
p = np.linspace(xmin,xmax,500)
# Plot unphysical solutions
if show_unphys:
ax4.plot(p,lin2l(p),'--k')
ax4.plot(p,lin1r(p),'--k')
# Plot physical solutions
if show_phys:
ax4.plot(p,lin1l(p),'-k')
ax4.plot(p,lin2r(p),'-k')
if (pm>=0 and pm <= xmax and um > ymin and um < ymax):
ax4.plot(pm, um, '-ok', markersize=10)
ax4.text(x[2] + 0.03*dx,y[2] + 0.03*dy, '$q_m$', fontsize=15)
# Plot initial states and markers
ax4.plot(pl, ul, '-ok', markersize=10)
ax4.plot(pr, ur, '-ok', markersize=10)
for i,label in enumerate(('$q_l$', '$q_r$')):
ax4.text(x[i] + 0.03*dx,y[i] + 0.03*dy,label, fontsize=15)
# Add all plots to fig and show
fig.add_subplot(ax1)
fig.add_subplot(ax2)
fig.add_subplot(ax3)
fig.add_subplot(ax4)
plt.show()
