Acceleration of reactor integration using a sparse preconditioned solver

Ideal gas, constant-pressure, adiabatic kinetics simulation that compares preconditioned and non-preconditioned integration of n-hexane.

Requires: cantera >= 3.0.0, matplotlib >= 2.0

Tags: Python combustion reactor network preconditioner

import cantera as ct
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.constrained_layout.use'] = True
from timeit import default_timer

Simulation setup

Create a reactor network for simulating the constant pressure ignition of a stoichiometric n-hexane/air mixture, with or without the use of the preconditioned solver.

def integrate_reactor(preconditioner=True):
    # Use a detailed n-hexane mechanism with 1268 species
    gas = ct.Solution('example_data/n-hexane-NUIG-2015.yaml')
    gas.TP = 1000, ct.one_atm
    gas.set_equivalence_ratio(1, 'NC6H14', 'N2:3.76, O2:1.0')
    reactor = ct.IdealGasConstPressureMoleReactor(gas)
    # set volume for reactors
    reactor.volume = 0.1
    # Create reactor network
    sim = ct.ReactorNet([reactor])
    # Add preconditioner
    if preconditioner:
        sim.derivative_settings = {"skip-third-bodies":True, "skip-falloff":True}
        sim.preconditioner = ct.AdaptivePreconditioner()
    sim.initialize()
    # Advance to steady state
    integ_time = default_timer()
    # solution array for state data
    states = ct.SolutionArray(reactor.thermo, extra=['time'])
    # advance to steady state manually
    while (sim.time < 0.1):
        states.append(reactor.thermo.state, time=sim.time)
        sim.step()
    integ_time = default_timer() - integ_time
    # Return time to integrate
    if preconditioner:
        print(f"Preconditioned Integration Time: {integ_time:f}")
    else:
        print(f"Non-preconditioned Integration Time: {integ_time:f}")
    # Get and output solver stats
    for key, value in sim.solver_stats.items():
        print(f"{key:>24s}: {value}")
    print("\n")
    # return some variables for plotting
    return states.time, states.T, states('CO2').Y, states('NC6H14').Y

Integrate with sparse, preconditioned solver

timep, Tp, CO2p, NC6H14p = integrate_reactor(preconditioner=True)

/home/runner/work/cantera/cantera/build/doc/samples/python/reactors/preconditioned_integration.py:27: UserWarning: NasaPoly2::validate:
For species OHV, discontinuity in h/RT detected at Tmid = 1000
        Value computed using low-temperature polynomial:  53.62056162666667
        Value computed using high-temperature polynomial: 53.5841554314

  gas = ct.Solution('example_data/n-hexane-NUIG-2015.yaml')
/home/runner/work/cantera/cantera/build/doc/samples/python/reactors/preconditioned_integration.py:27: UserWarning: NasaPoly2::validate:
For species CHV, discontinuity in h/RT detected at Tmid = 1000
        Value computed using low-temperature polynomial:  107.5046684
        Value computed using high-temperature polynomial: 107.34847808033332

  gas = ct.Solution('example_data/n-hexane-NUIG-2015.yaml')
Preconditioned Integration Time: 1.607902
        step_solve_fails: 4
                   steps: 966
               rhs_evals: 1170
         nonlinear_iters: 1167
    nonlinear_conv_fails: 20
          err_test_fails: 31
              last_order: 3
   stab_order_reductions: 0
               jac_evals: 0
        lin_solve_setups: 118
           lin_rhs_evals: 3985
               lin_iters: 3985
          lin_conv_fails: 298
              prec_evals: 30
             prec_solves: 5056
      jt_vec_setup_evals: 0
       jt_vec_prod_evals: 3985

Integrate with direct linear solver

timenp, Tnp, CO2np, NC6H14np  = integrate_reactor(preconditioner=False)

Non-preconditioned Integration Time: 21.241066
        step_solve_fails: 0
                   steps: 2704
               rhs_evals: 4294
         nonlinear_iters: 4291
    nonlinear_conv_fails: 36
          err_test_fails: 160
              last_order: 5
   stab_order_reductions: 0
               jac_evals: 61
        lin_solve_setups: 378
           lin_rhs_evals: 77409
               lin_iters: 0
          lin_conv_fails: 0
              prec_evals: 0
             prec_solves: 0
      jt_vec_setup_evals: 0
       jt_vec_prod_evals: 0

Plot selected state variables

fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(5, 8))
# temperature plot
ax1.set_xlabel("Time")
ax1.set_ylabel("Temperature")
ax1.plot(timenp, Tnp, linewidth=2)
ax1.plot(timep, Tp, linewidth=2, linestyle=":")
ax1.legend(["Normal", "Preconditioned"])
# CO2 plot
ax2.set_xlabel("Time")
ax2.set_ylabel("CO2")
ax2.plot(timenp, CO2np, linewidth=2)
ax2.plot(timep, CO2p, linewidth=2, linestyle=":")
ax2.legend(["Normal", "Preconditioned"])
# C12H26 plot
ax3.set_xlabel("Time")
ax3.set_ylabel("NC6H14")
ax3.plot(timenp, NC6H14np, linewidth=2)
ax3.plot(timep, NC6H14p, linewidth=2, linestyle=":")
ax3.legend(["Normal", "Preconditioned"])
plt.show()