[Cython/Examples] Add reactor example with ODEs implemented in Python

interfaces/cython/cantera/examples/reactors/custom.py

@@ -0,0 +1,78 @@
+"""
+Solve a constant pressure ignition problem where the governing equations are
+implemented in Python.
+
+This demonstrates an approach for solving problems where Cantera's reactor
+network model cannot be configured to describe the system in question. Here,
+Cantera is used for evaluating thermodynamic properties and kinetic rates while
+an external ODE solver is used to integrate the resulting equations. In this
+case, the SciPy wrapper for VODE is used, which uses the same variable-order BDF
+methods as the Sundials CVODES solver used by Cantera.
+"""
+
+import cantera as ct
+import numpy as np
+import scipy.integrate
+
+class ReactorOde(object):
+    def __init__(self, gas):
+        # Parameters of the ODE system and auxiliary data are stored in the
+        # ReactorOde object.
+        self.gas = gas
+        self.P = gas.P
+
+    def __call__(self, t, y):
+        """the ODE function, y' = f(t,y) """
+
+        # State vector is [T, Y_1, Y_2, ... Y_K]
+        self.gas.set_unnormalized_mass_fractions(y[1:])
+        self.gas.TP = y[0], self.P
+        rho = self.gas.density
+
+        wdot = self.gas.net_production_rates
+        dTdt = - (np.dot(self.gas.partial_molar_enthalpies, wdot) /
+                  (rho * self.gas.cp))
+        dYdt = wdot * self.gas.molecular_weights / rho
+
+        return np.hstack((dTdt, dYdt))
+
+
+gas = ct.Solution('gri30.xml')
+
+# Initial condition
+gas.TPX = 1001, ct.one_atm, 'H2:2,O2:1,N2:4'
+y0 = np.hstack((gas.T, gas.Y))
+
+# Set up objects representing the ODE and the solver
+ode = ReactorOde(gas)
+solver = scipy.integrate.ode(ode)
+solver.set_integrator('vode', method='bdf', with_jacobian=True)
+solver.set_initial_value(y0, 0.0)
+
+# Integrate the equations, keeping T(t) and Y(k,t)
+t_end = 1e-3
+t_out = [0.0]
+T_out = [gas.T]
+Y_out = [gas.Y]
+dt = 1e-5
+while solver.successful() and solver.t < t_end:
+    solver.integrate(solver.t + dt)
+    t_out.append(solver.t)
+    T_out.append(gas.T)
+    Y_out.append(gas.Y)
+
+Y_out = np.array(Y_out).T
+
+# Plot the results
+try:
+    import matplotlib.pyplot as plt
+    L1 = plt.plot(t_out, T_out, color='r', label='T', lw=2)
+    plt.xlabel('time (s)')
+    plt.ylabel('Temperature (K)')
+    plt.twinx()
+    L2 = plt.plot(t_out, Y_out[gas.species_index('OH')], label='OH', lw=2)
+    plt.ylabel('Mass Fraction')
+    plt.legend(L1+L2, [line.get_label() for line in L1+L2], loc='lower right')
+    plt.show()
+except ImportError:
+    print('Matplotlib not found. Unable to plot results.')