Note
Go to the end to download the full example code.
Timestep Controls for 1D Flame Solvers#
This example demonstrates four solver controls that affect pseudo-transient convergence in one-dimensional flame calculations:
time_step_growth_strategy, which controls when the timestep grows after a successful transient step.time_step_growth_factor, which controls how much the timestep grows when growth is triggered.time_step_regrid, which controls how many times the solver may refine the grid and retry after timestepping is exhausted.max_time_step_count, which controls the number of transient steps allowed before a timestep attempt gives up.
The first comparison uses a burner-stabilized premixed flame. The following two comparisons use a high-pressure counterflow diffusion flame, where solver convergence can depend on both regridding and the transient-step budget.
Requires: cantera >= 4.0; matplotlib >= 2.0
from __future__ import annotations
import time
import matplotlib.pyplot as plt
plt.rcParams['figure.constrained_layout.use'] = True
import numpy as np
import cantera as ct
Timestep Growth Strategies#
The one-dimensional solver falls back to pseudo-transient timestepping when the Newton solver cannot converge directly to steady state. After a successful transient step, Cantera can either grow the timestep by a fixed factor or apply one of several heuristics that wait for evidence that the larger step is helpful.
This first problem uses a premixed methane / air burner-stabilized flame. The physical solution is the same for each case, so the differences in the table are from the timestep-growth rule. We test several combinations of growth strategies and growth factors.
growth_strategies = (
("fixed-growth", 1.5), # default growth strategy and factor
("fixed-growth", 2.0),
("steady-norm", 2.0),
("transient-residual", 2.0),
("residual-ratio", 2.0),
("newton-iterations", 2.0),
("steady-norm", 6.0),
("newton-iterations", 6.0),
)
def make_growth_flame() -> ct.BurnerFlame:
gas = ct.Solution("gri30.yaml")
gas.set_equivalence_ratio(0.8, "CH4", {"O2": 1.0, "N2": 3.76})
gas.TP = 300.0, ct.one_atm
flame = ct.BurnerFlame(gas, width=0.02)
flame.burner.mdot = 0.09
flame.set_refine_criteria(ratio=3.0, slope=0.25, curve=0.35, prune=0.05)
return flame
def run_growth_strategy(strategy: str, growth_factor: float) -> dict[str, object]:
flame = make_growth_flame()
timesteps = []
flame.set_time_step_callback(
lambda dt: timesteps.append(float(dt)) or 0
)
flame.time_step_growth_factor = growth_factor
flame.time_step_growth_strategy = strategy
tic = time.perf_counter()
print("** Running growth strategy:", strategy)
flame.solve(loglevel=1, refine_grid=True)
elapsed = time.perf_counter() - tic
return {
"strategy": f"{strategy} (growth factor = {growth_factor:.1f})",
"n_steps": len(timesteps),
"dt_sum": float(np.sum(timesteps)),
"dt_min": float(np.min(timesteps)),
"dt_max": float(np.max(timesteps)),
"jacobians": int(sum(flame.jacobian_count_stats)),
"T_max": float(np.max(flame.T)),
"wall_time": elapsed,
"dts": np.asarray(timesteps, dtype=float),
}
growth_results = [run_growth_strategy(strategy, growth_factor)
for strategy, growth_factor in growth_strategies]
** Running growth strategy: fixed-growth
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4.271e-05 log(ss)= 5.239
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0007298 log(ss)= 4.703
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.008313 log(ss)= 3.507
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0001709 log(ss)= 4.337
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 3.421e-05 log(ss)= 6.192
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0001948 log(ss)= 5.057
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.002219 log(ss)= 4.208
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0002222 log(ss)= 5.224
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 1.483e-05 log(ss)= 6.29
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0002563 log(ss)= 4.605
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 5.132e-05 log(ss)= 6.052
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0001139 log(ss)= 5.434
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0004325 log(ss)= 5.026
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: fixed-growth
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.061
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.01024 log(ss)= 3.572
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 5.243 log(ss)= -4.145
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.017
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.941
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.439
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.428
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.979
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00064 log(ss)= 4.895
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.315
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.135
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.309
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: steady-norm
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.061
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.01024 log(ss)= 3.572
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 5.243 log(ss)= -4.145
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.017
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.888
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.234
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.272
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.811
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 4.703
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.524
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.135
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.309
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: transient-residual
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.061
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.01024 log(ss)= 3.572
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 5.243 log(ss)= -4.145
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.017
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.941
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.439
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.428
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.979
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00064 log(ss)= 4.895
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.315
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.135
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.309
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: residual-ratio
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.061
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.01024 log(ss)= 3.572
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 1.221 log(ss)= -4.526
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.017
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.941
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.439
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.428
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.979
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00064 log(ss)= 4.895
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.315
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00032 log(ss)= 5.135
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00256 log(ss)= 4.309
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: newton-iterations
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 1e-05 log(ss)= 5.332
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.02
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00128 log(ss)= 4.521
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00128 log(ss)= 3.673
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00512 log(ss)= 2.995
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 2e-05 log(ss)= 4.536
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.322
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.891
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 4.966
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00064 log(ss)= 4.325
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00128 log(ss)= 4.187
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 2e-05 log(ss)= 5.834
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.464
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 4.626
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.701
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.18
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 4e-05 log(ss)= 5.625
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00016 log(ss)= 5.085
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8e-05 log(ss)= 5.201
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: steady-norm
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00972 log(ss)= 4.12
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 2721 log(ss)= -3.628
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 3.375e-05 log(ss)= 5.707
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.003645 log(ss)= 4.633
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 8.543e-05 log(ss)= 5.706
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.002307 log(ss)= 4.779
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 6.75e-05 log(ss)= 5.275
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00729 log(ss)= 4.547
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00243 log(ss)= 5.071
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
** Running growth strategy: newton-iterations
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 1.5e-05 log(ss)= 5.26
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00324 log(ss)= 4.496
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00972 log(ss)= 3.622
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 453.5 log(ss)= -3.913
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [7] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCNO HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 6e-05 log(ss)= 4.361
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 1.125e-05 log(ss)= 6.325
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 6.75e-05 log(ss)= 5.521
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00243 log(ss)= 4.56
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0006075 log(ss)= 4.51
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 9.492e-06 log(ss)= 6.336
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.0003417 log(ss)= 5.026
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [11] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00036 log(ss)= 4.602
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 2.25e-05 log(ss)= 5.97
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [15] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 N2O NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00036 log(ss)= 5.399
Attempt Newton solution of steady-state problem.
Newton steady-state solve failed.
Attempt 10 timesteps.
Final timestep info: dt= 0.00018 log(ss)= 5.002
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [20] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H7 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO CO2 H H2 H2O H2O2 HCCO HCCOH HCN HCO HNCO HO2 N2 NO NO2 O O2 OH T velocity
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [27] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 0 1 2 3 4 5 6 7 8 9
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH CH2 CH2(S) CH2CHO CH2CO CH2O CH2OH CH3 CH3CHO CH3O CH3OH CH4 CO H H2 H2O H2O2 HCCO HCN HCO HNCO HO2 N2 NO2 O OH
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [37] point grid(s).
##############################################################################
Refining grid in flame.
New points inserted after grid points 3 4 5 9 10 11 12 13 14 15 16
to resolve C2H2 C2H3 C2H4 C2H5 C2H6 C3H8 CH2 CH2(S) CH2CHO CH2CO CH2OH CH3 CH3CHO CH3O HCCO HCO
##############################################################################
Attempt Newton solution of steady-state problem.
Newton steady-state solve succeeded.
Problem solved on [48] point grid(s).
no new points needed in flame
The timestep history is collected with set_time_step_callback.
The columns below report the number of timesteps, the total transient
time covered by those steps, the largest timestep, the number of
Jacobian evaluations, and the maximum temperature of the converged flame.
growth_header = (
f"{'Strategy':<42} {'Steps':>8} {'sum(dt) [s]':>12} "
f"{'max(dt) [s]':>12} {'Jac':>5} {'T_max [K]':>12} {'Runtime [s]':>9}"
)
print(growth_header)
print("-" * len(growth_header))
for row in growth_results:
print(
f"{row['strategy']:<42} {row['n_steps']:>8d} "
f"{row['dt_sum']:>12.4e} {row['dt_max']:>12.4e} "
f"{row['jacobians']:>5d} {row['T_max']:>12.4f} {row['wall_time']:>9.2f}"
)
Strategy Steps sum(dt) [s] max(dt) [s] Jac T_max [K] Runtime [s]
------------------------------------------------------------------------------------------------------------
fixed-growth (growth factor = 1.5) 130 7.4413e-02 8.3131e-03 190 1694.7603 13.67
fixed-growth (growth factor = 2.0) 120 1.0626e+01 5.2429e+00 215 1694.7603 15.69
steady-norm (growth factor = 2.0) 120 1.0622e+01 5.2429e+00 146 1694.7603 11.09
transient-residual (growth factor = 2.0) 120 1.0626e+01 5.2429e+00 215 1694.7603 15.69
residual-ratio (growth factor = 2.0) 120 3.1080e+00 1.2214e+00 215 1694.7603 15.68
newton-iterations (growth factor = 2.0) 190 8.5223e-02 5.1200e-03 140 1694.7603 10.95
steady-norm (growth factor = 6.0) 90 5.9863e+03 2.7210e+03 164 1694.7603 12.76
newton-iterations (growth factor = 6.0) 150 5.4444e+02 4.5350e+02 132 1694.7603 9.69
In short, fixed-growth always applies time_step_growth_factor after a
successful step. steady-norm and transient-residual require the
corresponding residual norm to decrease. residual-ratio scales the growth
using the transient residual improvement, capped by
time_step_growth_factor. newton-iterations grows the step only after a
low-iteration Newton solve. Setting time_step_growth_factor = 1.0 disables
growth.
Timestep Histories#
The timestep histories show how the strategy changes the sequence of transient steps even when all cases reach the same steady fixed-temperature solution.
cmap = plt.get_cmap('Dark2')
fig, ax = plt.subplots()
for i,row in enumerate(growth_results):
steps = np.arange(1, row["n_steps"] + 1)
ax.semilogy(
steps + 0.1*i, row["dts"], "o-", linewidth=1.6, markersize=4,
color=cmap(i), label=row["strategy"]
)
ax.set_xlabel("timestep number")
ax.set_ylabel("dt [s]")
ax.grid(True, which="both", alpha=0.3)
ax.legend(fontsize=8)
plt.show()
Regridding After Timestep Failure#
The next comparison uses a high-pressure hydrogen / oxygen counterflow
diffusion flame. The initial grid has only 20 points across a 30 mm domain, which is
too coarse for the steady-state solver to converge. The time_step_regrid option
lets the solver refine the grid and retry when a timestepping sequence has reached
max_time_step_count.
diffusion_width = 30e-3
diffusion_initial_points = 20
diffusion_fuel_mdot = 0.3
diffusion_oxidizer_mdot_factor = 3.0
def make_regrid_flame(
pressure: float,
regrid_max: int,
max_time_step_count: int = 200,
growth_strategy: str = "fixed-growth",
growth_factor: float = 1.5,
) -> ct.CounterflowDiffusionFlame:
gas = ct.Solution("h2o2.yaml")
flame = ct.CounterflowDiffusionFlame(
gas, grid=np.linspace(0.0, diffusion_width, diffusion_initial_points)
)
flame.max_time_step_count = max_time_step_count
flame.set_refine_criteria(ratio=2.0, slope=0.06, curve=0.08, prune=0.02)
flame.time_step_regrid = regrid_max
flame.time_step_growth_strategy = growth_strategy
flame.time_step_growth_factor = growth_factor
flame.P = pressure
flame.fuel_inlet.X = "H2:1.0"
flame.fuel_inlet.T = 800.0
flame.oxidizer_inlet.X = "O2:1.0"
flame.oxidizer_inlet.T = 711.0
rho_fuel = flame.fuel_inlet.phase.density
rho_oxidizer = flame.oxidizer_inlet.phase.density
flame.fuel_inlet.mdot = diffusion_fuel_mdot
flame.oxidizer_inlet.mdot = (
diffusion_fuel_mdot / rho_fuel * rho_oxidizer * diffusion_oxidizer_mdot_factor
)
return flame
def run_regrid_case(case: dict[str, object]) -> dict[str, object]:
flame = make_regrid_flame(
pressure=case["pressure"],
regrid_max=case["regrid_max"],
max_time_step_count=case["max_time_step_count"],
growth_strategy=case["growth_strategy"],
growth_factor=case["growth_factor"],
)
flame.clear_stats()
tic = time.perf_counter()
try:
flame.solve(loglevel=0, auto=False)
success = True
except ct.CanteraError as err:
success = False
elapsed = time.perf_counter() - tic
return {
"label": case["label"],
"plot_label": case["plot_label"],
"pressure": case["pressure"],
"success": success,
"grid_points": len(flame.grid),
"timesteps": int(sum(flame.time_step_stats)),
"jacobians": int(sum(flame.jacobian_count_stats)),
"peak_temperature": float(np.max(flame.T)) if success else None,
"grid": np.array(flame.grid, copy=True),
"temperature": np.array(flame.T, copy=True),
"wall_time": elapsed,
"max_time_step_count": case["max_time_step_count"],
"regrid_max": case["regrid_max"],
"growth_strategy": case["growth_strategy"],
"growth_factor": case["growth_factor"],
}
def print_regrid_rows(results: list[dict[str, object]], label_width: int = 28) -> None:
header = (
f"{'Mode':<{label_width}} {'Success':>7} {'Grid':>6} "
f"{'Steps':>7} {'Jac':>5} {'Tmax [K]':>10} {'Wall [s]':>9}"
)
print(header)
print("-" * len(header))
for row in results:
peak_temperature = (
f"{row['peak_temperature']:>10.1f}"
if row["peak_temperature"] is not None else f"{'--':>10}"
)
print(
f"{row['label']:<{label_width}} {str(row['success']):>7} "
f"{row['grid_points']:>6d} {row['timesteps']:>7d} "
f"{row['jacobians']:>5d} {peak_temperature} {row['wall_time']:>9.2f}"
)
regrid_pressure = 7e6
regrid_cases = (
{
"label": "time_step_regrid = 0",
"plot_label": "0",
"pressure": regrid_pressure,
"regrid_max": 0,
"max_time_step_count": 200,
"growth_strategy": "fixed-growth",
"growth_factor": 1.5,
},
{
"label": "time_step_regrid = 1",
"plot_label": "1",
"pressure": regrid_pressure,
"regrid_max": 1,
"max_time_step_count": 200,
"growth_strategy": "fixed-growth",
"growth_factor": 1.5,
},
{
"label": "time_step_regrid = 3",
"plot_label": "3",
"pressure": regrid_pressure,
"regrid_max": 3,
"max_time_step_count": 200,
"growth_strategy": "fixed-growth",
"growth_factor": 1.5,
},
)
regrid_results = [run_regrid_case(case) for case in regrid_cases]
/home/runner/work/cantera/cantera/build/python/cantera/onedim.py:1002: UserWarning: ChemEquil::equilibrate: Temperature (3781.5508300517395 K) outside valid range of 300 K to 3500 K
self.gas.equilibrate('HP')
Here the growth-factor and growth-strategy settings are held at their defaults. Only the number of regrid retries changes.
print("Regrid retries after timestep failure")
print(
f"Case: H2/O2 counterflow diffusion flame at {regrid_pressure / 1e6:.1f} MPa "
f"on an initial {diffusion_initial_points}-point grid"
)
print("Varied option: time_step_regrid")
print()
print_regrid_rows(regrid_results, label_width=43)
Regrid retries after timestep failure
Case: H2/O2 counterflow diffusion flame at 7.0 MPa on an initial 20-point grid
Varied option: time_step_regrid
Mode Success Grid Steps Jac Tmax [K] Wall [s]
---------------------------------------------------------------------------------------------
time_step_regrid = 0 False 20 200 290 -- 1.20
time_step_regrid = 1 False 38 400 549 -- 3.10
time_step_regrid = 3 True 186 800 1044 3787.1 11.12
time_step_regrid = 0 disables retry-after-regrid. Positive values allow up to that
many grid-refinement retries after timestep failure. If the refinement criteria do not
change the grid, the retry path aborts because there is no new discretization to try.
Regrid Retry Comparison#
The first two cases exit before reaching a steady solution. With three regrid retries, the solver has enough opportunities to add points and continue.
colors = ["#ae2012" if not row["success"] else "#0a9396" for row in regrid_results]
fig, ax = plt.subplots()
bars = ax.bar(
[row["plot_label"] for row in regrid_results],
[row["timesteps"] for row in regrid_results],
color=colors,
)
ax.set_xlabel("time_step_regrid")
ax.set_ylabel("timesteps before exit")
ax.grid(True, axis="y", alpha=0.3)
for bar, row in zip(bars, regrid_results):
status = "ok" if row["success"] else "fail"
ax.text(
bar.get_x() + bar.get_width() / 2,
bar.get_height() + 10,
f"grid={row['grid_points']}\n{status}",
ha="center",
va="bottom",
fontsize=8,
)
plt.show()
Flame Profile#
The successful 7 MPa case is not just a solver-status change: after regridding, the solver finds a steady-state solution for a resolved diffusion flame with a hot reaction zone in the counterflow domain.
regrid_result = next(
row for row in regrid_results if row["success"] and row["regrid_max"] == 3
)
fig, ax = plt.subplots()
ax.plot(
1e3 * regrid_result["grid"],
regrid_result["temperature"],
".-",
)
ax.set_xlabel("distance from fuel inlet [mm]")
ax.set_ylabel("temperature [K]")
ax.grid(True, alpha=0.3)
plt.show()
A More Difficult Pressure#
At 15 MPa, the same coarse counterflow problem is more demanding. Regridding is
enabled for all cases in this section, but a 200-step timestep budget is still
insufficient. The first comparison shows the effect of increasing
max_time_step_count while leaving the growth strategy fixed.
difficult_pressure = 15e6
difficult_budget_cases = (
{
"label": "max_time_step_count = 200",
"plot_label": "200",
"pressure": difficult_pressure,
"max_time_step_count": 200,
"regrid_max": 3,
"growth_strategy": "fixed-growth",
"growth_factor": 1.5,
},
{
"label": "max_time_step_count = 1250",
"plot_label": "1250",
"pressure": difficult_pressure,
"max_time_step_count": 1250,
"regrid_max": 3,
"growth_strategy": "fixed-growth",
"growth_factor": 1.5,
},
)
difficult_budget_results = [run_regrid_case(case) for case in difficult_budget_cases]
print("Solving with a larger timestep budget")
print(
f"Case: H2/O2 counterflow diffusion flame at "
f"{difficult_pressure / 1e6:.1f} MPa"
)
print("Fixed settings: time_step_regrid = 3, time_step_growth_strategy = fixed-growth")
print()
print_regrid_rows(difficult_budget_results, label_width=28)
/home/runner/work/cantera/cantera/build/python/cantera/onedim.py:1002: UserWarning: ChemEquil::equilibrate: Temperature (3908.657324085196 K) outside valid range of 300 K to 3500 K
self.gas.equilibrate('HP')
Solving with a larger timestep budget
Case: H2/O2 counterflow diffusion flame at 15.0 MPa
Fixed settings: time_step_regrid = 3, time_step_growth_strategy = fixed-growth
Mode Success Grid Steps Jac Tmax [K] Wall [s]
------------------------------------------------------------------------------
max_time_step_count = 200 False 95 800 1155 -- 11.90
max_time_step_count = 1250 True 175 3850 5060 3926.3 59.78
Once the timestep budget is large enough enable solution of the steady-state problem, the growth strategy can still affect the work required to reach the converged steady solution. The fixed-growth row below reuses the successful result from the previous table, and the remaining rows rerun the same problem with adaptive growth strategies.
timestep_budget_result = next(
row for row in difficult_budget_results if row["max_time_step_count"] == 1250
)
difficult_strategy_cases = (
{
"label": "residual-ratio",
"plot_label": "ratio",
"pressure": difficult_pressure,
"max_time_step_count": 1250,
"regrid_max": 3,
"growth_strategy": "residual-ratio",
"growth_factor": 1.5,
},
{
"label": "newton-iterations",
"plot_label": "newton",
"pressure": difficult_pressure,
"max_time_step_count": 1250,
"regrid_max": 3,
"growth_strategy": "newton-iterations",
"growth_factor": 1.5,
},
)
difficult_strategy_results = [
{
**timestep_budget_result,
"label": "fixed-growth",
"plot_label": "fixed",
},
*[run_regrid_case(case) for case in difficult_strategy_cases],
]
print("Growth-strategy sensitivity after recovery")
print(
"Fixed settings: max_time_step_count = 1250, time_step_regrid = 3, "
"time_step_growth_factor = 1.5"
)
print()
print_regrid_rows(difficult_strategy_results, label_width=18)
Growth-strategy sensitivity after recovery
Fixed settings: max_time_step_count = 1250, time_step_regrid = 3, time_step_growth_factor = 1.5
Mode Success Grid Steps Jac Tmax [K] Wall [s]
--------------------------------------------------------------------
fixed-growth True 175 3850 5060 3926.3 59.78
residual-ratio True 178 5570 3345 3926.1 43.72
newton-iterations True 178 4210 3224 3926.4 41.17
max_time_step_count limits the number of transient steps before a timestep attempt
gives up. Larger values can allow harder cases to converge, but solving these cases
will be slow. On this 15 MPa case, adaptive growth strategies can reduce wall time
once the timestep budget is large enough.
Total running time of the script: (4 minutes 38.699 seconds)