def test_mechanism_simple_api_methods(self):
try:
xml = abspath(join('tests', 'test_mechanisms', 'h2-burke.xml'))
sol = Solution(xml)
m = ChemicalMechanismSpec.from_solution(sol)
self.assertEqual(m.n_species, sol.n_species, 'ChemicalMechanismSpec.n_species vs ct.Solution.n_species')
self.assertEqual(m.n_reactions, sol.n_reactions,
'ChemicalMechanismSpec.n_reactions vs ct.Solution.n_reactions')
for i in range(m.n_species):
self.assertEqual(m.species_names[i], sol.species_names[i],
'ChemicalMechanismSpec.species_name[i] vs ct.Solution.species_name[i]')
for n in m.species_names:
self.assertEqual(m.species_index(n), sol.species_index(n),
'ChemicalMechanismSpec.species_index(name) vs ct.Solution.species_index(name)')
for i, n in enumerate(m.species_names):
self.assertEqual(m.species_index(n), i, 'species names and indices are consistent, index vs i')
self.assertEqual(n, m.species_names[i], 'species names and indices are consistent, name vs n')
self.assertEqual(m.molecular_weight(i), m.molecular_weight(n),
'ChemicalMechanismSpec molecular_weight(name) vs molecular_weight(idx)')
except:
self.assertTrue(False)
try:
xml = abspath(join('tests', 'test_mechanisms', 'h2-burke.xml'))
m = ChemicalMechanismSpec.from_solution(Solution(xml))
m.molecular_weight(list())
self.assertTrue(False)
except:
self.assertTrue(True)
def test_equilibrium():
mechanism = 'gri30.cti'
# define states
initial_gas = Solution(mechanism)
initial_gas.TPX = 300, 101325, {'H2': 1}
working_gas = Solution(mechanism)
working_gas.TPX = 300, 101325 * 2, {'H2': 1}
velocity_guess = 7
# errors from hand calculations
good_errors = [
-18.375000000, # enthalpy
101322.993718076, # pressure
]
test_errors = calculate_error.equilibrium(
working_gas=working_gas,
initial_state_gas=initial_gas,
initial_velocity_guess=velocity_guess)
for test, good in zip(test_errors, good_errors):
assert abs(test - good) / good < 1e-7
def test_reflected_shock_frozen():
mechanism = 'gri30.cti'
# define states
initial_gas = Solution(mechanism)
initial_gas.TPX = 300, 101325, {'H2': 1}
working_gas = Solution(mechanism)
working_gas.TPX = 300, 101325 * 2, {'H2': 1}
velocity_guess = 7
# errors from hand calculations
good_errors = [
-73.5, # enthalpy
101316.97487230592 # pressure
]
test_errors = calculate_error.reflected_shock_frozen(
working_gas=working_gas,
post_shock_gas=initial_gas,
shock_speed=velocity_guess)
for test, good in zip(test_errors, good_errors):
assert abs(test - good) / good < 1e-7
def test_no_convergence():
# ensure the proper warning is generated when solution doesn't converge
mechanism = 'gri30.cti'
initial_gas = Solution(mechanism)
initial_gas.TPX = 300, 101325, {'H2': 1}
working_gas = Solution(mechanism)
working_gas.TPX = 300, 101325 * 2, {'H2': 1}
with pytest.warns(Warning, match='No convergence within 1 iterations'):
sd.Detonation.cj_state(working_gas, initial_gas, 1e-50, 1e-50, 1.5,
1)
def pymars(model_file,
conditions,
error,
method,
target_species,
retained_species=None,
run_sensitivity_analysis=False,
epsilon_star=0.1):
"""Driver function for pyMARS to reduce a model.
Parameters
----------
model_file : str
Cantera-format model to be reduced (e.g., 'mech.cti').
conditions : str
File with list of autoignition initial conditions.
error : float
Maximum error % for the reduced model.
method : {'DRG', 'DRGEP', 'PFA'}
Skeletal reduction method to use.
target_species: list of str
List of target species for reduction.
retained_species : list of str, optional
List of non-target species to always retain.
run_sensitivity_analysis : bool, optional
Flag to run sensitivity analysis after completing another method.
epsilon_star : float, optional
Epsilon^* value used to determine species for sensitivity analysis.
Returns
-------
Converted mechanism file
Trimmed Solution Object
Trimmed Mechanism file
Examples
--------
>>> pymars('gri30.cti', conditions_file, 10.0, 'DRGEP', ['CH4', 'O2'], retained_species=['N2'])
"""
solution_object = Solution(model_file)
if method == 'DRG':
results = run_drg(solution_object, conditions, error, target_species,
retained_species)
elif method == 'PFA':
results = run_pfa(solution_object, conditions, error, target_species,
retained_species)
elif method == 'DRGEP':
results = run_drgep(solution_object, conditions, error, target_species,
retained_species)
reduced_model, reduced_error = results
if run_sensitivity_analysis:
results = run_sa(solution_object, reduced_model, epsilon_star,
conditions, error, retained_species)
reduced_model, reduced_error = results
sa_file = soln2cti.write(reduced_model)
def validate_on_mechanism(mech, temperature, pressure, tau, do_rhs, do_jac):
xml = join(test_mech_directory, mech + '.xml')
T = temperature
Tin = T + 1000.
p = pressure
r = ChemicalMechanismSpec(xml, 'gas').griffon
gas = Solution(xml)
ns = gas.n_species
y = np.ones(ns) # equal masses in the reactor
gas.TPY = T, p, y
y = np.copy(gas.Y)
xin = np.ones(ns) # equal moles in the feed
gas.TPX = Tin, p, xin
yin = np.copy(gas.Y)
state = hstack((T, y[:-1]))
rhsCN = rhs_cantera(p, T, y, Tin, yin, tau, gas)
rhsGR = np.empty(ns)
r.reactor_rhs_isobaric(state, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, rhsGR)
if do_rhs:
return max(abs(rhsGR - rhsCN) / (abs(rhsCN) + 1.)) < 1.e-4
if do_jac:
jacGR = np.empty(ns * ns)
r.reactor_jac_isobaric(state, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, 0, 0, rhsGR, jacGR)
jacGR = jacGR.reshape((ns, ns), order='F')
dT = 1.e-6
dY = 1.e-6
jacFD = np.empty((ns, ns))
rhsGR1, rhsGR2 = np.empty(ns), np.empty(ns)
state_m = hstack((T - dT, y[:-1]))
state_p = hstack((T + dT, y[:-1]))
r.reactor_rhs_isobaric(state_m, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, rhsGR1)
r.reactor_rhs_isobaric(state_p, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, rhsGR2)
jacFD[:, 0] = (- rhsGR1 + rhsGR2) / (2. * dT)
for i in range(ns - 1):
y_m1, y_p1 = np.copy(y), np.copy(y)
y_m1[i] += - dY
y_m1[-1] -= - dY
y_p1[i] += dY
y_p1[-1] -= dY
state_m = hstack((T, y_m1[:-1]))
state_p = hstack((T, y_p1[:-1]))
r.reactor_rhs_isobaric(state_m, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, rhsGR1)
r.reactor_rhs_isobaric(state_p, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, True, rhsGR2)
jacFD[:, 1 + i] = (- rhsGR1 + rhsGR2) / (2. * dY)
pass_jac = max(abs(jacGR - jacFD) / (abs(jacGR) + 1.)) < 1.e-2
return pass_jac
def test_good_input():
# compare against SDToolbox results
mechanism = 'gri30.cti'
initial_gas = Solution(mechanism)
initial_gas.TPX = 300, 101325, {'H2': 1}
working_gas = Solution(mechanism)
working_gas.TPX = 300, 101325 * 2, {'H2': 1}
cj_calcs = sd.Detonation.cj_state(
working_gas,
initial_gas,
1e-5,
1e-5,
1.5
)
good_temp = 355.77590742266216
good_press = 180244.9690980063
good_species = {'H': 2.8407416566652653e-30, 'H2': 1.0}
test_temp = cj_calcs[0].T
check_temp = abs(test_temp - good_temp) / good_temp < 1e-7
test_press = cj_calcs[0].P
check_press = abs(test_press - good_press) / good_press < 1e-7
good_velocity = 1700.3611387277992
test_velocity = cj_calcs[1]
check_velocity = abs(test_velocity - good_velocity) / good_velocity \
< 1e-7
checks = [check_temp, check_press, check_velocity]
# make sure the species in each solution are the same
test_species = cj_calcs[0].mole_fraction_dict()
for species in good_species:
checks.append(
good_species[species] - test_species[species] < 1e-7
)
assert all(checks)
def test_mechanism_serialization(self):
xml = abspath(join('tests', 'test_mechanisms', 'h2-burke.xml'))
sol = Solution(xml)
m1 = ChemicalMechanismSpec.from_solution(sol)
m1_pickle = pickle.dumps(m1)
m2 = pickle.loads(m1_pickle)
self.assertTrue(m1.mech_data['species'] == m2.mech_data['species'])
self.assertTrue(m1.mech_data['reactions'] == m2.mech_data['reactions'])
def test_create_valid_mechanism_spec_from_solution(self):
try:
xml = abspath(join('tests', 'test_mechanisms', 'h2-burke.xml'))
sol = Solution(xml)
m = ChemicalMechanismSpec.from_solution(sol)
g = m.griffon
x = m.mech_xml_path
n = m.group_name
s = m.gas
self.assertTrue(True)
except:
self.assertTrue(False)
def validate_on_mechanism(mech, temperature, pressure, test_rhs=True, test_jac=True):
xml = join(test_mech_directory, mech + '.xml')
T = temperature
p = pressure
r = ChemicalMechanismSpec(xml, 'gas').griffon
gas = Solution(xml)
ns = gas.n_species
gas.TPX = T, p, ones(ns)
y = gas.Y
state = hstack((T, y[:-1]))
rhsGR = np.empty(ns)
r.reactor_rhs_isobaric(state, p, 0., np.ndarray(1), 0, 0, 0, 0, 0, 0, 0, False, rhsGR)
if test_jac:
Tin, yin, tau = 0, np.ndarray(1), 0
rhsTmp = np.empty(ns)
jacGR = np.empty(ns * ns)
r.reactor_jac_isobaric(state, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, False, 0, 0, rhsTmp, jacGR)
jacGR = jacGR.reshape((ns, ns), order='F')
dT = 1.e-6
dY = 1.e-6
jacFD = np.empty((ns, ns))
rhsGR1, rhsGR2 = np.empty(ns), np.empty(ns)
state_m = hstack((T - dT, y[:-1]))
state_p = hstack((T + dT, y[:-1]))
r.reactor_rhs_isobaric(state_m, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, False, rhsGR1)
r.reactor_rhs_isobaric(state_p, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, False, rhsGR2)
jacFD[:, 0] = (- rhsGR1 + rhsGR2) / (2. * dT)
for i in range(ns - 1):
y_m1, y_p1 = np.copy(y), np.copy(y)
y_m1[i] += - dY
y_m1[-1] -= - dY
y_p1[i] += dY
y_p1[-1] -= dY
state_m = hstack((T, y_m1[:-1]))
state_p = hstack((T, y_p1[:-1]))
r.reactor_rhs_isobaric(state_m, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, False, rhsGR1)
r.reactor_rhs_isobaric(state_p, p, Tin, yin, tau, 0, 0, 0, 0, 0, 0, False, rhsGR2)
jacFD[:, 1 + i] = (- rhsGR1 + rhsGR2) / (2. * dY)
pass_jac = max(abs(jacGR - jacFD) / (abs(jacGR) + 1.)) < 1.e-2
w = gas.net_production_rates * gas.molecular_weights
h = gas.standard_enthalpies_RT * gas.T * gas_constant / gas.molecular_weights
rhsCN = zeros(ns)
rhsCN[1:] = w[:-1] / gas.density
rhsCN[0] = - sum(w * h) / gas.density / gas.cp_mass
pass_rhs = max(abs(rhsGR - rhsCN) / (abs(rhsCN) + 1.)) < 100. * sqrt(np.finfo(float).eps)
if test_rhs and test_jac:
return pass_rhs and pass_jac
if test_rhs:
return pass_rhs
if test_jac:
return pass_jac
def validate_on_mechanism(mech, temperature, pressure, tau, do_rhs, do_jac):
xml = join(test_mech_directory, mech + '.xml')
T = temperature
Tin = T + 1000.
p = pressure
r = ChemicalMechanismSpec(xml, 'gas').griffon
gas = Solution(xml)
ns = gas.n_species
y = np.ones(ns) # equal masses in the reactor
gas.TPY = T, p, y
y = np.copy(gas.Y)
rho = gas.density_mass
xin = np.ones(ns) # equal moles in the feed
gas.TPX = Tin, p, xin
yin = np.copy(gas.Y)
rhoin = gas.density_mass
state = hstack((rho, T, y[:-1]))
rhsGRChemOnly = np.zeros(ns + 1)
r.reactor_rhs_isochoric(state, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0, 0,
False, rhsGRChemOnly)
rhsCN = rhs_cantera(p, T, y, rhoin, Tin, yin, tau, gas, rhsGRChemOnly)
rhsGR = np.empty(ns + 1)
r.reactor_rhs_isochoric(state, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0, 0,
True, rhsGR)
if do_rhs:
return max(abs(rhsGR - rhsCN) /
(abs(rhsCN) + 1.)) < 100. * sqrt(np.finfo(float).eps)
if do_jac:
jacGR = np.empty((ns + 1) * (ns + 1))
r.reactor_jac_isochoric(state, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0, 0,
True, 0, rhsGR, jacGR)
jacGR = jacGR.reshape((ns + 1, ns + 1), order='F')
drho = 1.e-6
dT = 1.e-6
dY = 1.e-6
jacFD = np.empty((ns + 1, ns + 1))
rhsGR1, rhsGR2 = np.empty(ns + 1), np.empty(ns + 1)
state_m = hstack((rho - drho, T, y[:-1]))
state_p = hstack((rho + drho, T, y[:-1]))
r.reactor_rhs_isochoric(state_m, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0,
0, True, rhsGR1)
r.reactor_rhs_isochoric(state_p, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0,
0, True, rhsGR2)
jacFD[:, 0] = (-rhsGR1 + rhsGR2) / (2. * drho)
state_m = hstack((rho, T - dT, y[:-1]))
state_p = hstack((rho, T + dT, y[:-1]))
r.reactor_rhs_isochoric(state_m, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0,
0, True, rhsGR1)
r.reactor_rhs_isochoric(state_p, rhoin, Tin, yin, tau, 0, 0, 0, 0, 0,
0, True, rhsGR2)
jacFD[:, 1] = (-rhsGR1 + rhsGR2) / (2. * dT)
for i in range(ns - 1):
y_m1, y_p1 = np.copy(y), np.copy(y)
y_m1[i] += -dY
y_m1[-1] -= -dY
y_p1[i] += dY
y_p1[-1] -= dY
state_m = hstack((rho, T, y_m1[:-1]))
state_p = hstack((rho, T, y_p1[:-1]))
r.reactor_rhs_isochoric(state_m, rhoin, Tin, yin, tau, 0, 0, 0, 0,
0, 0, True, rhsGR1)
r.reactor_rhs_isochoric(state_p, rhoin, Tin, yin, tau, 0, 0, 0, 0,
0, 0, True, rhsGR2)
jacFD[:, 2 + i] = (-rhsGR1 + rhsGR2) / (2. * dY)
return max(abs(jacGR - jacFD) / (abs(jacGR) + 1.)) < 1.e-4
def validate_on_mechanism(mech, temperature, pressure, full_Jacobian,
isochoric):
xml = join(test_mech_directory, mech + '.xml')
r = ChemicalMechanismSpec(xml, 'gas').griffon
gas = Solution(xml)
ns = gas.n_species
T = temperature
p = pressure
gas.TPX = T, p, ones(ns)
y = gas.Y
rho = gas.density_mass
if full_Jacobian and isochoric:
state = hstack((rho, T, y[:-1]))
rhsGRTemporary = np.empty(ns + 1)
jac_dense = np.empty((ns + 1) * (ns + 1))
jac_sparse = np.empty((ns + 1) * (ns + 1))
r.reactor_jac_isochoric(state, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, 0, rhsGRTemporary, jac_dense)
r.reactor_jac_isochoric(state, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, 2, rhsGRTemporary, jac_sparse)
jac_dense = jac_dense.reshape((ns + 1, ns + 1), order='F')
jac_sparse = jac_sparse.reshape((ns + 1, ns + 1), order='F')
elif full_Jacobian and not isochoric:
state = hstack((T, y[:-1]))
k = np.empty(ns)
jac_dense = np.empty(ns * ns)
jac_sparse = np.empty(ns * ns)
r.reactor_jac_isobaric(state, p, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0, 0,
False, 0, 0, k, jac_dense)
r.reactor_jac_isobaric(state, p, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0, 0,
False, 2, 0, k, jac_sparse)
jac_dense = jac_dense.reshape((ns, ns), order='F')
jac_sparse = jac_sparse.reshape((ns, ns), order='F')
else:
jac_dense = np.zeros((ns + 1) * (ns + 1))
jac_sparse = np.zeros((ns + 1) * (ns + 1))
r.prod_rates_primitive_sensitivities(rho, T, y, 0, jac_dense)
r.prod_rates_primitive_sensitivities(rho, T, y, 2, jac_sparse)
jac_dense = jac_dense.reshape((ns + 1, ns + 1), order='F')[:-1, :]
jac_sparse = jac_sparse.reshape((ns + 1, ns + 1), order='F')[:-1, :]
jac_fd = np.zeros_like(jac_dense)
rhsGR1 = np.zeros(ns)
rhsGR2 = np.zeros(ns)
dT = 1.e-4
dr = 1.e-4
dY = 1.e-4
r.production_rates(T, rho + dr, y, rhsGR1)
r.production_rates(T, rho - dr, y, rhsGR2)
jac_fd[:, 0] = (rhsGR1 - rhsGR2) / dr * 0.5
r.production_rates(T + dT, rho, y, rhsGR1)
r.production_rates(T - dT, rho, y, rhsGR2)
jac_fd[:, 1] = (rhsGR1 - rhsGR2) / dT * 0.5
for spec_idx in range(ns - 1):
Yp = np.copy(y)
Yp[spec_idx] += dY
Yp[-1] -= dY
Ym = np.copy(y)
Ym[spec_idx] -= dY
Ym[-1] += dY
r.production_rates(T, rho, Yp, rhsGR1)
r.production_rates(T, rho, Ym, rhsGR2)
jac_fd[:, 2 + spec_idx] = (rhsGR1 - rhsGR2) / dY * 0.5
pass_sparse_vs_dense_jac = np.linalg.norm(
jac_dense.ravel() - jac_sparse.ravel(), ord=np.Inf) < 1.e-10
# if not pass_sparse_vs_dense_jac:
# print(mech)
# diff = abs(jac_dense - jac_sparse) / (abs(jac_dense) + 1.)
# nr, nc = jac_dense.shape
# print('dense')
# for ir in range(nr):
# for ic in range(nc):
# print(f'{jac_dense[ir, ic]:8.0e}', end=', ')
# print('')
# print('sparse')
# for ir in range(nr):
# for ic in range(nc):
# print(f'{jac_sparse[ir, ic]:8.0e}', end=', ')
# print('')
# print('finite difference')
# for ir in range(nr):
# for ic in range(nc):
# print(f'{jac_fd[ir, ic]:8.0e}', end=', ')
# print('')
# print('diff')
# for ir in range(nr):
# for ic in range(nc):
# print(f'{diff[ir, ic]:8.0e}' if diff[ir, ic] > 1.e-12 else f'{"":8}', end=', ')
# print('')
return pass_sparse_vs_dense_jac
def validate_on_mechanism(mech,
temperature,
pressure,
test_rhs=True,
test_jac=True):
xml = join(test_mech_directory, mech + '.xml')
r = ChemicalMechanismSpec(xml, 'gas').griffon
gas = Solution(xml)
ns = gas.n_species
T = temperature
p = pressure
gas.TPX = T, p, ones(ns)
y = gas.Y
rho = gas.density_mass
state = hstack((rho, T, y[:-1]))
rhsGR = np.empty(ns + 1)
rhsGRTemporary = np.empty(ns + 1)
jacGR = np.empty((ns + 1) * (ns + 1))
r.reactor_rhs_isochoric(state, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0, 0,
False, rhsGR)
r.reactor_jac_isochoric(state, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0, 0,
False, 0, rhsGRTemporary, jacGR)
jacGR = jacGR.reshape((ns + 1, ns + 1), order='F')
def cantera_rhs(rho_arg, T_arg, Y_arg):
gas.TDY = T_arg, rho_arg, Y_arg
w = gas.net_production_rates * gas.molecular_weights
e = gas.standard_int_energies_RT * gas.T * gas_constant / gas.molecular_weights
cv = gas.cv_mass
rhs = zeros(ns + 1)
rhs[0] = 0.
rhs[1] = -sum(w * e) / (rho_arg * cv)
rhs[2:] = w[:-1] / rho
return rhs
rhsCN = cantera_rhs(rho, T, y)
if test_rhs:
pass_rhs = max(abs(rhsGR - rhsCN) /
(abs(rhsCN) + 1.)) < 100. * sqrt(np.finfo(float).eps)
if test_jac:
jacFD = zeros((ns + 1, ns + 1))
wm1 = zeros(ns + 1)
wp1 = zeros(ns + 1)
drho = 1.e-4
dT = 1.e-2
dY = 1.e-6
state_m = hstack((rho - drho, T, y[:-1]))
state_p = hstack((rho + drho, T, y[:-1]))
r.reactor_rhs_isochoric(state_m, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, wm1)
r.reactor_rhs_isochoric(state_p, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, wp1)
jacFD[:, 0] = (-wm1 + wp1) / (2. * drho)
state_m = hstack((rho, T - dT, y[:-1]))
state_p = hstack((rho, T + dT, y[:-1]))
r.reactor_rhs_isochoric(state_m, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, wm1)
r.reactor_rhs_isochoric(state_p, 0, 0, np.ndarray(1), 0, 0, 0, 0, 0, 0,
0, False, wp1)
jacFD[:, 1] = (-wm1 + wp1) / (2. * dT)
for i in range(ns - 1):
y_m1, y_p1 = copy(y), copy(y)
y_m1[i] += -dY
y_m1[-1] -= -dY
y_p1[i] += dY
y_p1[-1] -= dY
state_m = hstack((rho, T, y_m1[:-1]))
state_p = hstack((rho, T, y_p1[:-1]))
r.reactor_rhs_isochoric(state_m, 0, 0, np.ndarray(1), 0, 0, 0, 0,
0, 0, 0, False, wm1)
r.reactor_rhs_isochoric(state_p, 0, 0, np.ndarray(1), 0, 0, 0, 0,
0, 0, 0, False, wp1)
jacFD[:, 2 + i] = (-wm1 + wp1) / (2. * dY)
gas.TDY = T, rho, y
cv = gas.cv_mass
cvi = gas.standard_cp_R * gas_constant / gas.molecular_weights
w = gas.net_production_rates * gas.molecular_weights
e = gas.standard_int_energies_RT * gas.T * gas_constant / gas.molecular_weights
gas.TDY = T + dT, rho, y
wp = gas.net_production_rates * gas.molecular_weights
cvp = gas.cv_mass
gas.TDY = T - dT, rho, y
wm = gas.net_production_rates * gas.molecular_weights
cvm = gas.cv_mass
wsensT = (wp - wm) / (2. * dT)
cvsensT = (cvp - cvm) / (2. * dT)
jacFD11 = np.copy(jacFD[1, 1])
jacSemiFD11 = -1. / cv * (1. / rho * (sum(wsensT * e) + sum(cvi * w)) +
cvsensT * rhsGR[1])
pass_jac = max(abs(jacGR - jacFD) / (abs(jacGR) + 1.)) < 1.e-4
if test_rhs:
return pass_rhs
if test_jac:
if not pass_jac:
print(jacGR[1, 1])
print(jacSemiFD11)
print(jacFD11)
print(abs(jacGR - jacFD) / (abs(jacGR) + 1.))
return pass_jac