def solve(config, t, R, mdot_ox, mdot_fuel, Pc, OF, Cstar, Pe, thrust, ISP):
    rho_fuel    = config.getfloat('Params', 'rho_fuel')
    L           = config.getfloat('Params', 'fuel_length') / M_TO_IN
    a           = config.getfloat('Params', 'a')
    n           = config.getfloat('Params', 'n')
    Rt          = config.getfloat('Params', 'throat_radius')
    AR          = config.getfloat('Params', 'area_ratio')
    P0          = config.getfloat('Params', 'p0')
    throat_area = np.pi * Rt**2

    N = t.shape[0]

    for i in range(N-1):
        dt = t[i+1] - t[i]
        R[i+1] = advance_R(a, n, R[i], mdot_ox[i], dt)

        mdot_fuel[i+1] = utils.get_mdot_fuel(R[i+1], L, rho_fuel,
            mdot_ox[i+1], a, n)

        mdot = mdot_fuel[i+1] + mdot_ox[i+1]
        Pc[i+1] = Cstar[i] / throat_area * mdot
        OF[i+1] = mdot_ox[i+1] / mdot_fuel[i+1]

        gamma, _, Cstar[i+1] = utils.get_CEA_results(CEA_object, Pc[i+1],
            P0, OF[i+1], AR)
        Pe[i+1] = utils.get_exit_pressure(Pc[i+1], gamma, AR, guess=Pe[i])
        CF = utils.get_thrust_coeff(Pc[i+1], Pe[i+1], P0, gamma, AR)
        thrust[i+1] = Pc[i+1]*throat_area*CF
        ISP[i+1] = thrust[i+1] / G0 / (mdot_ox[i+1] + mdot_fuel[i+1])
def initialize(config, R_0, mdot_ox_0, Cstar_0):
    n_timesteps = config.getint('Params', 'n_timesteps')
    burn_time   = config.getfloat('Params', 'burn_time')
    P0          = config.getfloat('Params', 'p0')
    rho_fuel    = config.getfloat('Params', 'rho_fuel')
    L           = config.getfloat('Params', 'fuel_length') / M_TO_IN
    a           = config.getfloat('Params', 'a')
    n           = config.getfloat('Params', 'n')
    Rt          = config.getfloat('Params', 'throat_radius')
    AR          = config.getfloat('Params', 'area_ratio')
    throat_area = np.pi * Rt**2

    t = np.linspace(0, burn_time, num=n_timesteps+1)

    R    = np.zeros(t.shape)
    R[0] = R_0

    mdot_ox    = np.zeros(t.shape)
    mdot_ox[0] = mdot_ox_0

    mdot_fuel    = np.zeros(t.shape)
    mdot_fuel[0] = utils.get_mdot_fuel(R[0], L, rho_fuel, mdot_ox[0],
        a, n)

    Pc    = np.zeros(t.shape)
    Pc[0] = Cstar_0 / throat_area * (mdot_ox[0]+mdot_fuel[0])

    OF    = np.zeros(t.shape)
    OF[0] = mdot_ox[0] / mdot_fuel[0]

    Cstar  = np.zeros(t.shape)
    thrust = np.zeros(t.shape)
    Pe     = np.zeros(t.shape)
    ISP    = np.zeros(t.shape)

    gamma, _, Cstar[0] = utils.get_CEA_results(CEA_object, Pc[0], P0,
        OF[0], AR)
    Pe[0] = utils.get_exit_pressure(Pc[0], gamma, AR)
    CF = utils.get_thrust_coeff(Pc[0], Pe[0], P0, gamma, AR)
    thrust[0] = Pc[0] * throat_area * CF
    ISP[0] = thrust[0] / G0 / (mdot_ox[0] + mdot_fuel[0])

    return t, R, mdot_ox, mdot_fuel, Pc, OF, Cstar, Pe, thrust, ISP