first_o = Hydro(gamma,
initial_state=(r, p, v),
Npts=npts,
geometry=(0, 1.0))
second_o = Hydro(gamma,
initial_state=(r, p, v),
Npts=npts,
geometry=(0, 1.0))
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
# print(f_p[1][3])
# print(p[3])
# l1 = h*np.sum(np.absolute(s_p[1]/(s_p[0]**gamma) - 1.))
# print(l1)
# zzz = input('')
fig, ax = plt.subplots(1, 1, figsize=(15, 11))
ax.plot(x, results[npts][0], 'rs', fillstyle='none', label='First Order')
ax.plot(x, sims[npts][0], 'b-', label='Higher Order')
# ax.plot(x, p/(r**gamma), '.')
# ax.plot(x, r, 'g--', label='Initial')
ax.set_xlim(x[0], x[-1])
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')
c2 = ax.contourf(t2, rr, np.flip(density, axis=0), cmap='plasma')
fig.suptitle('Sedov Explosion at t={} s on {} x {} grid'.format(tend, N, N),
fontsize=20)
ax.set_title(r'$\rho(\theta) = 2.0 + \sin(n \theta)$ with n = {}'.format(n),
fontsize=25)
cbar = fig.colorbar(c1)
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()