def test_sedov_timmes_vs_kamm(self):
r"""Checks Timmes' against Kamm's Sedov solver. Expected to fail because
Kamm solver does not return correct values at shock for this choice of
parameters.
"""
# construct spatial grid and choose time
nmax = 11
rmin = 0.95
rmax = 1.05
r = np.linspace(rmin, rmax, nmax)
t = 1.
solvertimmes = SedovTimmes(geometry=3, eblast=0.851072)
solutiontimmes = solvertimmes(r, t)
solverkamm = SedovKamm(geometry=3, eblast=0.851072)
solutionkamm = solverkamm(r, t)
tolerance = 4.e-4
for i in range(nmax):
self.assertAlmostEqual(solutiontimmes.density[i],
solutionkamm.density[i],
delta=tolerance)
self.assertAlmostEqual(solutiontimmes.velocity[i],
solutionkamm.velocity[i],
delta=tolerance)
self.assertAlmostEqual(solutiontimmes.pressure[i],
solutionkamm.pressure[i],
delta=tolerance)
def test_interpolate(self):
r"""Sedov test: interpolation to large number of points.
"""
# construct spatial grid and choose time
rmax = 1.2
t = 1.
solver = SedovTimmes(eblast=0.851072, gamma=1.4)
#
# Solve for small number of points
r_small = np.linspace(0.0, rmax, 501)
solution_small = solver(r_small, t)
#
# Solve for large number of points
r_big = np.linspace(0.0, rmax, 6001)
solution_big = solver(r_big, t)
# Interpolate small to big
from scipy.interpolate import interp1d
interpfcn = interp1d(r_small, solution_small.density)
solution_big_interp = interpfcn(r_big)
err = np.linalg.norm((solution_big_interp - solution_big.density), 1)
self.assertTrue(err < 16.0)
def test_sedov_timmes_vs_kamm(self):
r"""Checks Timmes' against Kamm's Sedov solver.
"""
# construct spatial grid and choose time
nmax = 101
rmin = 0.6
rmax = 1.0
r = np.linspace(rmin, rmax, nmax)
t = 1.
solvertimmes = SedovTimmes(geometry=3, eblast=0.851072)
solutiontimmes = solvertimmes(r, t)
solverkamm = SedovKamm(geometry=3, eblast=0.851072)
solutionkamm = solverkamm(r, t)
tolerance = 4.e-4
for i in range(
nmax - 1
): # note: there is disagreement at nmax: 5.9999965521597574 != 0.0 for range(nmax)
self.assertAlmostEqual(solutiontimmes.density[i],
solutionkamm.density[i],
delta=tolerance)
self.assertAlmostEqual(solutiontimmes.velocity[i],
solutionkamm.velocity[i],
delta=tolerance)
self.assertAlmostEqual(solutiontimmes.pressure[i],
solutionkamm.pressure[i],
delta=tolerance)
def test_shock_state(self):
"""Tests density, velocity, pressure, specific internal energy, and
sound speed.
"""
# construct spatial grid and choose time
rmax = 1.2
r = np.linspace(0.0, rmax, 101)
t = 1.
solver = SedovTimmes(eblast=0.851072, gamma=1.4)
solution = solver(r, t)
i = 84 # shock location
self.assertAlmostEqual(solution.density[i - 1], 5.52681913398)
self.assertAlmostEqual(solution.density[i], 1.0000000E+00)
self.assertAlmostEqual(solution.velocity[i - 1], 0.330465254524)
self.assertAlmostEqual(solution.velocity[i], 0.0)
self.assertAlmostEqual(solution.pressure[i - 1], 0.127634037837)
self.assertAlmostEqual(solution.pressure[i], 1.4E-22)
self.assertAlmostEqual(solution.sie[i - 1], 0.0577339491049)
self.assertAlmostEqual(solution.sie[i], 0.0)
self.assertAlmostEqual(solution.sound[i - 1], 0.179808263155)
self.assertAlmostEqual(solution.sound[i], 0.0)
class TestSedovTimmesShock(unittest.TestCase):
"""Tests Timmes Sedov for correct pre and post shock values.
"""
# construct spatial grid and choose time
rmax = 1.2
r = np.linspace(0.0, rmax, 121)
t = 1.
solver = SedovTimmes(eblast=0.851072, gamma=1.4)
solution = solver(r, t)
ishock = 100 # shock location
# analytic solution pre-shock (initial conditions)
analytic_preshock = {
'position': r[ishock + 1],
'density': 1.0,
'specific_internal_energy': 0.0,
'pressure': 0.0,
'velocity': 0.0,
'sound_speed': 0.0
}
# analytic solution at the shock, from Kamm & Timmes 2007,
# equations 13-18 (to 6 significant figures)
analytic_postshock = {
'position': 1.0,
'density': 6.0,
'specific_internal_energy': 5.5555e-2,
'pressure': 1.33333e-1,
'velocity': 3.33333e-1,
'sound_speed': 1.76383e-1
}
def test_preshock_state(self):
"""Tests density, velocity, pressure, specific internal energy, and
sound speed immediately before the shock.
"""
for ikey in self.analytic_preshock.keys():
self.assertAlmostEqual(self.solution[ikey][self.ishock + 1],
self.analytic_preshock[ikey],
places=5)
def test_postshock_state(self):
"""Tests density, velocity, pressure, specific internal energy, and
sound speed immediately after the shock.
"""
for ikey in self.analytic_postshock.keys():
self.assertAlmostEqual(self.solution[ikey][self.ishock],
self.analytic_postshock[ikey],
places=5)
def test_interpolate(self):
r"""Sedov test: interpolation to large number of points.
"""
# construct spatial grid and choose time
rmax = 1.2
t = 1.
solver = SedovTimmes(eblast=0.851072, gamma=1.4)
#
# Solve for small number of points
r_small = np.linspace(0.0, rmax, 501)
solution_small = solver(r_small, t)
#
# Solve for large number of points
r_big = np.linspace(0.0, rmax, 6001)
solution_big = solver(r_big, t)
# Interpolate small to big
from scipy.interpolate import interp1d
interpfcn = interp1d(r_small, solution_small.density)
solution_big_interp = interpfcn(r_big)
err = np.linalg.norm((solution_big_interp - solution_big.density), 1)
self.assertTrue(err < 16.0)
def test_geometry_assignment(self):
r"""Sedov test: geometry assignment.
"""
self.assertRaises(ValueError, SedovTimmes, geometry=-1)
plt.xlabel('Position (cm)')
plt.ylabel('Pressure (erg/cc)')
plt.grid(True)
plt.gca().legend().set_visible(False)
plt.tight_layout()
fig.subplots_adjust(top=0.85) # Makes room for suptitle
#plt.savefig('fig08doebling.pdf')
if timmes_import:
#
# Figure 8timmes: Standard test cases, Timmes Solver
#
solver_timmes_pla = SedovTimmes(geometry=1, eblast=0.0673185, gamma=1.4)
solution_timmes_pla = solver_timmes_pla(r=rvec, t=t)
solver_timmes_cyl = SedovTimmes(geometry=2, eblast=0.311357, gamma=1.4)
solution_timmes_cyl = solver_timmes_cyl(r=rvec, t=t)
solver_timmes_sph = SedovTimmes(geometry=3, eblast=0.851072, gamma=1.4)
solution_timmes_sph = solver_timmes_sph(r=rvec, t=t)
fig = plt.figure(figsize=(10, 10))
plt.suptitle(
'''Sedov solutions for $\gamma=1.4$, standard cases, Timmes solver.
Compare to Fig. 8 from Kamm & Timmes 2007''')
plt.subplot(221)
solution_timmes_pla.plot('density')