def sod():
tend = 0.1
fig, ax = plt.subplots(1, 1, figsize=(13, 11))
r_min = 0.1
r_max = 1.
r = [
np.linspace(r_min, r_max, N),
np.logspace(np.log(r_min), np.log(r_max), N, base=np.exp(1))
]
y = 0
order = ['First Order', 'Higher Order']
linny = [':', '--']
for i in [True, False]:
# Object used for the linearly spaced grid
sedov = Hydro(gamma=gamma,
initial_state=((1.0, 1.0, 0.0), (0.1, 0.125, 0.0)),
Npts=N,
geometry=(r_min, r_max, 0.5),
n_vars=3)
s = sedov.simulate(tend=tend,
first_order=i,
dt=dt,
CFL=0.4,
linspace=False,
coordinates=b'spherical')
ax.plot(r[1], s[0], linestyle=linny[y], label=order[y])
y ^= 1
# Make the plot pretty
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.set_xlim(r_min, r_max)
ax.set_xlabel("R", fontsize=15)
ax.set_ylabel("Density", fontsize=15)
ax.set_title("1D Sod after t={:.1f}s with N = {}".format(tend, N),
fontsize=20)
ax.legend(fontsize=15)
fig.savefig('sod.pdf')
plt.show()
def plot_logvlin():
fig, ax = plt.subplots(1, 1, figsize=(13, 11))
y = 0
tend = 0.05
for i in [True, False]:
sedov = Hydro(gamma=gamma,
initial_state=(rho, p, v),
Npts=N,
geometry=(r_min, r_max),
n_vars=3)
u = sedov.simulate(tend=tend, first_order=True, dt=dt, linspace=i)
r = [
np.linspace(r_min, r_max, N),
np.logspace(np.log(r_min), np.log(r_max), N, base=np.exp(1))
]
linny = [':', '--']
label = ['linspace', 'logspace']
ax.plot(r[y], u[0], linestyle=linny[y], label=label[y])
# Make the plot pretty
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.set_xlim(r_min, r_max)
ax.set_xlabel("R", fontsize=15)
ax.set_ylabel("Density", fontsize=15)
ax.set_title("1D Sedov after t={:.3f} s at N = {}".format(tend, N),
fontsize=20)
ax.legend(fontsize=15)
y ^= 1
rs = (epsilon * tend**2 / rho0)**(1 / 5)
ax.axvline(rs)
plt.setp(ax.get_xticklabels(), fontsize=15)
plt.setp(ax.get_yticklabels(), fontsize=15)
fig.savefig('Log_v_linear.pdf')
plt.show()
gamma = 4/3
tend = 1.0
N = 100
dt = 1.e-4
stationary = ((1.4, 1.0, 0.0), (1.0, 1.0, 0.0))
hydro2 = Hydro(gamma=gamma, initial_state = stationary,
Npts=N, geometry=(0.0,1.0,0.5), n_vars=3, regime="relativistic")
hydro = Hydro(gamma=gamma, initial_state = stationary,
Npts=N, geometry=(0.0,1.0,0.5), n_vars=3, regime="relativistic")
h = hydro2.simulate(tend=tend, first_order=False, CFL=0.4, hllc=True)
u = hydro.simulate(tend=tend, first_order=False, CFL=0.4, hllc=False)
x = np.linspace(0, 1, N)
fig, ax = plt.subplots(1, 1, figsize=(15, 11))
# print("RHLLC Density: {}", h[0])
ax.plot(x, u[0], 'o', fillstyle='none', label='RHLLE')
ax.plot(x, h[0], label='RHLLC')
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.set_ylabel('Density', fontsize=20)
vx[:, :] = v_init
vy[:, :] = v_init
tend = 0.2
dt = 1.e-5
sedov = Hydro(gamma=gamma,
initial_state=(rho, p, vx, vy),
Npts=(N + 1, N + 1),
geometry=((rmin, rmax), (0., np.pi)),
n_vars=4)
t1 = (time.time() * u.s).to(u.min)
sol = sedov.simulate(tend=tend,
first_order=False,
dt=dt,
coordinates=b"spherical",
hllc=True)
print("The 2D Sedov Simulation for N = {} took {:.3f}".format(
N, (time.time() * u.s).to(u.min) - t1))
density = sedov.cons2prim(sol)[0]
rr, tt = np.meshgrid(r, theta)
rr, t2 = np.meshgrid(r, theta_mirror)
fig, ax = plt.subplots(1,
1,
figsize=(15, 10),
subplot_kw=dict(projection='polar'))
c1 = ax.contourf(tt, rr, density, cmap='plasma')
tend = 0.1
#print('End Time:', tend)
first_o = Hydro(gamma,
initial_state=(r, p, v),
Npts=npts,
geometry=(0, 1.0),
regime="relativistic")
second_o = Hydro(gamma,
initial_state=(r, p, v),
Npts=npts,
geometry=(0, 1.0),
regime="relativistic")
results[npts] = first_o.simulate(tend=tend, dt=dt, periodic=True)
sims[npts] = second_o.simulate(tend=tend,
dt=dt,
first_order=False,
periodic=True)
# f_p = first_o.cons2prim(results[npts])
# s_p = second_o.cons2prim(sims[npts])
#h = 1/npts
#l1 = h*np.sum(np.absolute(sims[npts][1]/(sims[npts][0]**gamma) - K))
#print(l1)
#zzz = input('')
#fig, ax = plt.subplots(1,1, figsize=(15,11))
#
#ax.plot(x, results[npts][1],'rs',fillstyle='none', label='First Order')
tend = 3.0
r = np.logspace(np.log10(rmin), np.log10(rmax), n)
n_exp = 2
dr = r[n_exp]
p_exp = (gamma - 1.0) * energy / (4 * np.pi * dr**3)
print(p_exp)
rho = 10 * np.ones(n) * r**(-omega)
v = np.zeros(n)
p = np.ones(n)
p[:n_exp] = p_exp
p[n_exp:] = p_amb
sedov = Hydro(gamma, (rho, p, v), n, (rmin, rmax), 3, "spherical")
solution = sedov.simulate(first_order=False, tend=tend, linspace=False)
rho = solution[0]
m = solution[1]
e = solution[2]
fig, ax = plt.subplots(1, 1, figsize=(10, 10))
ax.loglog(r, rho)
ax.set_title("1D Sedov Sherical Explosion at t={:.1f}".format(tend),
fontsize=30)
ax.set_xlabel("r", fontsize=20)
ax.set_ylabel("rho", fontsize=20)
plt.show()
fig, axs = plt.subplots(1, 2, figsize=(20, 10), sharex=True)
hydro = Hydro(gamma=1.4,
initial_state=stationary,
Npts=N,
geometry=(0.0, 1.0, 0.5),
n_vars=3)
hydro2 = Hydro(gamma=1.4,
initial_state=stationary,
Npts=N,
geometry=(0.0, 1.0, 0.5),
n_vars=3)
t1 = time.time()
poll = hydro.simulate(tend=tend, dt=dt, first_order=False, hllc=False)
print("Time for HLLE Simulation: {} sec".format(time.time() - t1))
t2 = time.time()
bar = hydro2.simulate(tend=tend, dt=dt, first_order=False, hllc=True)
print("Time for HLLC Simulation: {} sec".format(time.time() - t2))
u = bar[1] / bar[0]
v = poll[1] / poll[0]
#print(bar[0])
x = np.linspace(0, 1, N)
fig.suptitle("Stationary Wave Problem at t = {} with N = {}".format(tend, N))
axs[0].plot(x[::], poll[0][::], 'r--', fillstyle='none', label='HLLE')
axs[0].plot(x, bar[0], 'b', label='HLLC')
axs[0].set_xlabel('X', fontsize=20)
xx, yy = np.meshgrid(x, y)
fig, ax = plt.subplots(1, 1, figsize=(8, 10), constrained_layout=False)
# HLLC Simulation
SodHLLC = Hydro(gamma=gamma,
initial_state=(rho, p, vx, vy),
Npts=(xnpts, ynpts),
geometry=((xmin, xmax), (ymin, ymax)),
n_vars=4)
t1 = (time.time() * u.s).to(u.min)
hllc_result = SodHLLC.simulate(tend=tend,
first_order=False,
dt=dt,
linspace=True,
CFL=0.8,
hllc=True,
periodic=True)
print("The 2D KH Simulation for ({}, {}) grid took {:.3f}".format(
xnpts, ynpts, (time.time() * u.s).to(u.min) - t1))
rho, mx, my, E = hllc_result
print(rho)
rnorm = colors.LogNorm(vmin=0.9, vmax=2.1)
c1 = ax.pcolormesh(xx,
yy,
rho,
def plot_rho_vs_xi(omega=0, spacing='linspace', dt=1.e-6):
def R(epsilon, t, alpha, rho0=1., nu=3, omega=0):
return (epsilon * t**2 / (alpha * rho0))**(1 / (nu + 2 - omega))
def Rdot(epsilon, t, Rs):
return (2 * Rs / ((nu + 2 - omega) * t))
def D(gamma, rho, rho0):
return ((gamma - 1.) / (gamma + 1.)) * (rho / rho0)
def V(gamma, v, Rdot):
return ((gamma + 1) / 2) * (v / Rdot)
def P(gamma, p, rho0, Rdot):
return ((gamma + 1) / 2) * (p / (rho0 * Rdot**2))
if spacing == 'linspace':
r = np.linspace(r_min, r_max, N)
space = True
else:
r = np.logspace(np.log(r_min), np.log(r_max), N, base=np.exp(1))
space = False
N_exp = 5
dr = r[N_exp]
p_exp = init_pressure(gamma, epsilon, nu, dr)
delta_r = dr - r_min
p_zones = find_nearest(r, (r_min + dr))[0]
p_zones = int(p_zones / 2.5)
print(p_zones)
#zzz = input('')
p = np.zeros(N, float)
p[:p_zones] = p_exp
p[p_zones:] = p_amb
rho = rho0 * r**(-omega)
v = np.zeros(N, float)
alph = alpha(nu, omega, gamma)
re = 1.0
rsedov = 10 * (r_min + dr)
tend = calc_t(alph, rho0, epsilon, re, nu, omega)
tmin = calc_t(alph, rho0, epsilon, rsedov, nu, omega)
ts = np.array([tmin, 2 * tmin, tend])
# Plot stuff
fig = plt.figure(figsize=(15, 9))
for idx, t in enumerate(ts):
ax = fig.add_subplot(1, 3, idx + 1)
sedov = Hydro(gamma=gamma,
initial_state=(rho, p, v),
Npts=N,
geometry=(r_min, r_max),
n_vars=3)
t1 = (time.time() * u.s).to(u.min)
us = sedov.simulate(tend=t,
first_order=False,
CFL=0.4,
dt=dt,
linspace=space,
coordinates=b'spherical')
print("Simulation for t={} took {:.3f}".format(
t, (time.time() * u.s).to(u.min) - t1))
pressure, vel = sedov.cons2prim(us)[1:]
rs = R(epsilon, t, alpha=alph, nu=nu, omega=omega)
rdot = Rdot(epsilon, t, rs)
d = D(gamma, us[0], rho)
vx = V(gamma, vel, rdot)
px = P(gamma, pressure, rho, rdot)
xi = r / (rs)
max_idx = find_nearest(xi, 1)[0]
print("R Max: {} at idx {}".format(r[np.argmax(us[0])],
np.argmax(us[0])))
print("R Shock: {} at idx {}".format(rs, max_idx))
#zzz = input('')
ax.plot(xi[:max_idx], d[:max_idx], ':', label=r'$D(\xi)$'.format(t))
ax.plot(xi[:max_idx], vx[:max_idx], '.', label=r'$V(\xi)$'.format(t))
ax.plot(xi[:max_idx], px[:max_idx], '--', label=r'$P(\xi)$'.format(t))
# Make the plot pretty
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.set_title("t = {:.3f}".format(t), fontsize=12)
ax.set_xlim(xi[0], 1)
ax.set_xlabel(r"$ \xi $", fontsize=15)
#ax.set_xlim(0, 1)
#plt.setp(ax.get_xticklabels(), fontsize=15)
plt.suptitle(
"1D Sedov Self Similarity with N = {}, $\omega = {:.3f}, \gamma = {:.3f} $"
.format(N, omega, gamma),
fontsize=20)
ax.legend(fontsize=15)
fig.savefig("Sedov_densty_xi_linspace.pdf")
plt.show()
vx = np.zeros((N, N), np.double)
vy = np.zeros((N, N), np.double)
vx[:, :] = v_init
vy[:, :] = v_init
tend = 0.01
sedov = Hydro(gamma=gamma,
initial_state=(rho, pr, vx, vy),
Npts=(N, N),
geometry=((-1., 1.), (-1., 1.)),
n_vars=4)
t1 = (time.time() * u.s).to(u.min)
sol = sedov.simulate(tend=tend, first_order=False, dt=1.e-5, hllc=True)
print("The 2D Sedov Simulation for N = {} took {:.3f}".format(
N, (time.time() * u.s).to(u.min) - t1))
rho = sol[0]
x = np.linspace(-1., 1, N)
y = np.linspace(-1., 1, N)
xx, yy = np.meshgrid(x, y)
fig, ax = plt.subplots(1, 1, figsize=(15, 10))
c1 = ax.pcolormesh(xx, yy, rho, cmap='plasma', shading='auto')
ax.set_title('Density at t={} s on {} x {} grid'.format(tend, N, N),
fontsize=20)
cbar = fig.colorbar(c1)
tend = 0.5
dt = 1.e-8
# with PackageResource() as bm:
# bm.Hydro()
bm = Hydro(gamma=gamma,
initial_state=(rho, p, vx, vy),
Npts=(nr, ntheta),
geometry=((rmin, rmax), (theta_min, theta_max)),
n_vars=4,
regime="relativistic")
t1 = (time.time() * u.s).to(u.min)
sol = bm.simulate(tend=tend,
first_order=False,
dt=dt,
coordinates="spherical",
CFL=0.4,
hllc=False,
linspace=False)
print("The 2D BM Simulation for N = {} took {:.3f}".format(
ntheta, (time.time() * u.s).to(u.min) - t1))
#density = b.cons2prim(sol)[0]
W = 1 / np.sqrt(1 - sol[1]**2 + sol[2]**2)
print(sol[1].max())
rr, tt = np.meshgrid(r, theta)
rr, t2 = np.meshgrid(r, theta_mirror)
fig, ax = plt.subplots(1,
print("Rmin: {}".format(rmin))
print("Dim: {}x{}".format(ynpts, xnpts))
S = np.zeros(shape=rho.shape)
SodHLLE = Hydro(gamma=gamma,
initial_state=(rho, p, vr, vt),
Npts=(xnpts, ynpts),
geometry=((rmin, rmax), (theta_min, theta_max)),
n_vars=4)
t1 = (time.time() * u.s).to(u.min)
hlle_result = SodHLLE.simulate(tend=tend,
first_order=False,
dt=dt,
coordinates="spherical",
linspace=False,
CFL=0.4,
hllc=False)
# HLLC Simulation
SodHLLC = Hydro(gamma=gamma,
initial_state=(rho, p, vr, vt),
Npts=(xnpts, ynpts),
geometry=((rmin, rmax), (theta_min, theta_max)),
n_vars=4)
t1 = (time.time() * u.s).to(u.min)
hllc_result = SodHLLC.simulate(tend=tend,
first_order=False,
dt=dt,