def eos_derivatives(gas0, gmodel, tol=0.0001):
# Finite difference evaluation, assuming that gas0 is valid state already.
gas1 = GasState(gmodel)
gas1.copy_values(gas0)
p0 = gas0.p; rho0 = gas0.rho; u0 = gas0.u
#
drho = rho0 * tol; gas1.rho = rho0 + drho
gas1.update_thermo_from_rhou()
dpdrho = (gas1.p - p0)/drho
#
gas1.rho = rho0; du = u0 * tol; gas1.u = u0 + du
gas1.update_thermo_from_rhou()
dpdu = (gas1.p - p0)/du
#
return dpdrho, dpdu
gas1.update_thermo_from_rhou()
dpdrho = (gas1.p - p0) / drho
#
gas1.rho = rho0
du = u0 * tol
gas1.u = u0 + du
gas1.update_thermo_from_rhou()
dpdu = (gas1.p - p0) / du
#
return dpdrho, dpdu
#------------------------------------------------------------------
print("Step in time, allowing the gas to react and drift along in x.")
gas0 = GasState(gmodel)
gas0.copy_values(state2) # start with post-shock conditions
x = 0 # position of shock, m
x_final = 1.0 # the marching will stop at this point, metres
v = v2 # velocity of gas post-shock, m/s
dt_suggest = 1.0e-8 # suggested starting time-step for chemistry updater
#
f = open(output_filename, 'w')
f.write(header)
f.write(string_data(x, v, gas0, dt_suggest))
#
t = 0 # time of drift is in seconds
t_final = 3.0e-3 # User-selected drift time, s
t_inc = 0.1e-6 # User-selected time steps, s
nsteps = int(t_final / t_inc)
# Notes:
# Select t_final to be long enough to reach x_final.
print("# Start reactions...")
reactor = ThermochemicalReactor(gmodel, "h2-o2-n2-9sp-18r.lua")
t = 0 # time is in seconds
t_final = 22.0e-6
t_inc = 0.05e-6
nsteps = int(t_final / t_inc)
for j in range(1, nsteps + 1):
# At the start of the step...
rho = gas0.rho
T = gas0.T
p = gas0.p
u = gas0.u
#
# Do the chemical increment.
gas1 = GasState(gmodel) # make the new one as a clone
gas1.copy_values(gas0)
dt_suggest = reactor.update_state(gas1, t_inc, dt_suggest)
gas1.update_thermo_from_rhou()
#
du_chem = gas1.u - u
dp_chem = gas1.p - p
if debug: print("# du_chem=", du_chem, "dp_chem=", dp_chem)
#
# Do the gas-dynamic accommodation after the chemical change.
etot = u + 0.5 * v * v
dfdr, dfdu = eos_derivatives(gas1, gmodel)
if debug: print("# dfdr=", dfdr, "dfdu=", dfdu)
# Linear solve to get the accommodation increments.
# [v, rho, 0.0, 0.0 ] [drho ] [0.0 ]
# [0.0, rho*v, 1.0, 0.0 ] * [dv ] = [-dp_chem ]
# [v*etot, rho*etot+p, 0.0, rho*v] [dp_gda] [-rho*v*du_chem]