def cj_cond(fuel, ash):
"""Calculate Cj velocity from Helmholtz Eos calculation
fits density for a set temperature
Args:
fuel (trojan): [[pressure, eint], [rho], [temp], [abar], [zbar]]
ash (trojan): [[pressure, eint], [rho], [temp], [abar], [zbar]]
"""
tol = 1e-8
itmax = 30
comprho = 1e10
for it in range(itmax):
# res = adiabat(fuel, ash, q)
res = helmholtz.helmeos(*ash[1:])
res.den = fuel[1][0] * (1.0 + (res.ptot - fuel[0][0]) /
(res.gam1 * res.ptot))
# print res.den, type(res.den[0])
dden = res.den[0] - comprho
if abs(dden) < tol * res.den:
return res
elif res == -1:
return -1
else:
ash[1][0] = res.den
comprho = res.den
return -1
def getPres(rhos, temps, xmasses, species, returnObj=False):
trojan = wrapVector(rhos, temps, xmasses, species)
sol = helmholtz.helmeos(*trojan)
if returnObj:
return sol
else:
return sol.ptot
def setBC(dens, temp=1e7, abar=4.0, zbar=2.0, start=1e4):
"""starting point for solver."""
helmobj = hh.helmeos(dens, temp, abar, zbar)
# intial conditions: first cell's mass, and central pressure
con1 = 4.0e0 * np.pi
ms0 = con1 * start**3 * dens
ps0 = helmobj.ptot[0] - 0.5e0 * con1 * G * start**2 * dens**2
return [ms0, ps0]
def test_code(nrand=100, vars_to_test=None, silent=False, tol=1e-12):
if vars_to_test is None:
vars_to_test = ['etot', 'ptot', 'cs', 'sele']
ht = HelmTable()
# density
dlo, dhi = tab.dens_log_min, tab.dens_log_max
dens = np.arange(dlo, dhi + 1)
dens = 10**np.concatenate((dens, (dhi - dlo) * np.random.random(nrand) + dlo))
# temperature
tlo, thi = tab.temp_log_min, tab.temp_log_max
temp = np.arange(tlo, thi + 1)
temp = 10**np.concatenate((temp, (thi - tlo) * np.random.random(nrand) + tlo))
rho_in = np.zeros(dens.size * temp.size)
temp_in = np.zeros(dens.size * temp.size)
# make 1D array of all combinations of dens, temp
ind = 0
for i in dens:
for j in temp:
rho_in[ind] = i
temp_in[ind] = j
ind += 1
print("Loading tables.")
# our method
ours = ht.eos_DT(rho_in, temp_in, 1.0, 1.0)
# their method
theirs = helmholtz.helmeos(rho_in, temp_in, 1.0, 1.0)
if not silent:
print("Showing max relative error for a few variables.")
print("var, rel_err")
pass_test = True
for var in vars_to_test:
a, b = ours[var], getattr(theirs, var)
dif = np.abs((a - b) / b)
i = dif.argmax()
if dif[i] > tol:
pass_test = False
if not silent:
print(var, dif[i])
if not pass_test:
raise RuntimeError
return pass_test
def invert_helm(pres, deng=4e6, abar=4.0, zbar=2.0, temp=1e7):
"""find the density and dpdd from a guess and a pressure."""
# local variables
steptol = 1.0e-6
maxiter = 50
deni = deng
for i in range(maxiter):
helmobj = hh.helmeos(deni, temp, abar, zbar)
presi, dpd = helmobj.ptot[0], helmobj.dpd[0]
z = abs((pres - presi) / pres)
if z < steptol:
return deni, dpd
else:
f = presi / pres - 1.0
df = dpd / pres
ratio = f / df
deni = deni - ratio
print("Reached max iterations ({:d})".format(maxiter))
return deni, dpd
def adiabat(fuel, ash, q):
"""Hack-feeding data to helmholtz:
fuel/ash = [[pressure, eint], [rho], [temp], [abar], [zbar]]
fits a temperature to a hugoniot curve
"""
# q value -- we need the change in molar fractions
# call ener_gener_rate(eos_state_ash % xn(:)/aion(:) - eos_state_fuel % xn(:)/aion(:), q_burn)
tol = 1e-8
itmax = 30
for it in range(itmax):
res = helmholtz.helmeos(*ash[1:])
aux = (1.0/fuel[1][0] - 1.0/res.den)
f = fuel[0][1] + q - res.etot + 0.5*(fuel[0][0]+res.ptot)*aux
dfdT = -res.det + 0.5*res.dpt*aux
dT = -f/dfdT
if abs(dT)<tol*res.temp:
return res
else:
ash[2][0] = ash[2][0] + dT[0]
return -1
def helm(dens, abar=4.0, zbar=2.0, temp=1e7):
"""get pressure and total energy from a target density."""
helmobj = hh.helmeos(dens, temp, abar, zbar)
return helmobj.ptot[0], helmobj.dpd[0], helmobj.etot[0], helmobj.ded[0]
import numpy as np
import matplotlib.pyplot as plt
import helmholtz
d = np.logspace(-3, 11, 512)
t = np.logspace(3, 9, 512)
# fig, axs = plt.subplots(3)
# for t in zip(ts):
# f = helmholtz.eosfxt(dens=d, temp=t, abar=1.0, zbar=1.0)
h = helmholtz.helmeos(dens=d, temp=t, abar=1.0, zbar=1.0)
print(len(h.etot), len(t), 512**2)
# ax.plot(d, np.abs((h.ptot - f.ptot)/f.ptot))
# ax.set_xlabel(r'$\rho$ (g/cc)')
# ax.set_ylabel(r'fractional difference')
# ax.set_xscale('log')
# ax.set_yscale('log')
# ax.set_ylim(1e-12, 1e0)
# logT = int(np.log10(t))
# ax.text(1e-2, 3e-6, '$T = 10^{{{}}}$ K'.format(logT))
# fig.suptitle('Pressure difference (Timmes vs Helmholtz)')
# fig.set_size_inches(6,6)
# fig.savefig('fig1.png', dpi=150)
import pandas as pd
import helmholtz
n = 20
den = 5e13 #np.logspace(13, 14, n)
temps = np.logspace(10, 11, n) #p.logspace(10, 11, n)
a = 55 #np.linspace(55, 65, n)
z = 28 #*= 28
ye = z / a
data = pd.DataFrame(columns=list('DTYE'))
i = 0
j = 0
for temp in temps:
j += 1
print("{} out of {}".format(j, n))
en = int(helmholtz.helmeos(den, temp, a, z).etot)
data.loc[i] = [den, temp, ye, en]
i += 1
#for temp in temps:
#for a in a_s:
# en = int(helmholtz.helmeos(den, temp, a, 28).etot)
# data.loc[i] = [den, temp, z_s[0]/a, en]
# i += 1
data.to_csv(r'Temp_resolution{}_{}.csv'.format('10-11', n),
index=None,
header=True)