def mySolve(xf,boltz_eqs,rtol,atol,verbosity=50):
"""Sets the main options for the ODE solver and solve the equations. Returns the
array of x,y points for all components.
If numerical instabilities are found, re-do the problematic part of the evolution with smaller steps"""
boltz_solver = CVode(boltz_eqs) #Define solver method
boltz_solver.rtol = rtol
boltz_solver.atol = atol
boltz_solver.verbosity = verbosity
boltz_solver.linear_solver = 'SPGMR'
boltz_solver.maxh = xf/300.
xfinal = xf
xres = []
yres = []
sw = boltz_solver.sw[:]
while xfinal <= xf:
try:
boltz_solver.re_init(boltz_eqs.t0,boltz_eqs.y0)
boltz_solver.sw = sw[:]
x,y = boltz_solver.simulate(xfinal)
xres += x
for ypt in y: yres.append(ypt)
if xfinal == xf: break #Evolution has been performed until xf -> exit
except Exception,e:
print e
if not e.t or 'first call' in e.msg[e.value]:
logger.error("Error solving equations:\n "+str(e))
return False
xfinal = max(e.t*random.uniform(0.85,0.95),boltz_eqs.t0+boltz_solver.maxh) #Try again, but now only until the error
logger.warning("Numerical instability found. Restarting evolution from x = "
+str(boltz_eqs.t0)+" to x = "+str(xfinal))
continue
xfinal = xf #In the next step try to evolve from xfinal -> xf
sw = boltz_solver.sw[:]
x0 = float(x[-1])
y0 = [float(yval) for yval in y[-1]]
boltz_eqs.updateValues(x0,y0,sw)
def run_simulation(filename, save_output, start_time, temp, RH, RO2_indices,
H2O, PInit, y_cond, input_dict, simulation_time, batch_step,
plot_mass):
from assimulo.solvers import RodasODE, CVode, RungeKutta4, LSODAR #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# The variables passed to this function are defined as follows:
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
dy_dt = numpy.zeros((total_length_y, 1), )
#pdb.set_trace()
# Calculate time of day
time_of_day_seconds = start_time + t
#pdb.set_trace()
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
Model_temp = temp
#pdb.set_trace()
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
rates = evaluate_rates_fortran(RO2, H2O, Model_temp,
time_of_day_seconds)
#pdb.set_trace()
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactants_fortran(y_asnumpy[0:num_species - 1])
#pdb.set_trace()
#Multiply product of reactants with rate coefficient to get reaction rate
reactants = numpy.multiply(reactants, rates)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt_gas = loss_gain_fortran(reactants)
#pdb.set_trace()
dy_dt[0:num_species - 1, 0] = dydt_gas
# Change the saturation vapour pressure of water
# Need to re-think the change of organic vapour pressures with temperature.
# At the moment this is kept constant as re-calulation using UManSysProp very slow
sat_vap_water = numpy.exp((-0.58002206E4 / Model_temp) + 0.13914993E1 - \
(0.48640239E-1 * Model_temp) + (0.41764768E-4 * (Model_temp**2.0E0))- \
(0.14452093E-7 * (Model_temp**3.0E0)) + (0.65459673E1 * numpy.log(Model_temp)))
sat_vp[-1] = (numpy.log10(sat_vap_water * 9.86923E-6))
Psat = numpy.power(10.0, sat_vp)
# Convert the concentration of each component in the gas phase into a partial pressure using the ideal gas law
# Units are Pascals
Pressure_gas = (y_asnumpy[0:num_species, ] /
NA) * 8.314E+6 * Model_temp #[using R]
core_mass_array = numpy.multiply(ycore_asnumpy / NA, core_molw_asnumpy)
####### Calculate the thermal conductivity of gases according to the new temperature ########
K_water_vapour = (
5.69 + 0.017 *
(Model_temp - 273.15)) * 1e-3 * 4.187 #[W/mK []has to be in W/m.K]
# Use this value for all organics, for now. If you start using a non-zero enthalpy of
# vapourisation, this needs to change.
therm_cond_air = K_water_vapour
#----------------------------------------------------------------------------
#F2c) Extract the current gas phase concentrations to be used in pressure difference calculations
C_g_i_t = y_asnumpy[0:num_species, ]
#Set the values for oxidants etc to 0 as will force no mass transfer
#C_g_i_t[ignore_index]=0.0
C_g_i_t = C_g_i_t[include_index]
#pdb.set_trace()
total_SOA_mass,aw_array,size_array,dy_dt_calc = dydt_partition_fortran(y_asnumpy,ycore_asnumpy,core_dissociation, \
core_mass_array,y_density_array_asnumpy,core_density_array_asnumpy,ignore_index_fortran,y_mw,Psat, \
DStar_org_asnumpy,alpha_d_org_asnumpy,C_g_i_t,N_perbin,gamma_gas_asnumpy,Latent_heat_asnumpy,GRAV, \
Updraft,sigma,NA,kb,Rv,R_gas,Model_temp,cp,Ra,Lv_water_vapour)
#pdb.set_trace()
# Add the calculated gains/losses to the complete dy_dt array
dy_dt[0:num_species + (num_species_condensed * num_bins),
0] += dy_dt_calc[:]
#pdb.set_trace()
#----------------------------------------------------------------------------
#F4) Now calculate the change in water vapour mixing ratio.
#To do this we need to know what the index key for the very last element is
#pdb.set_trace()
#pdb.set_trace()
#print "elapsed time=", elapsedTime
dydt_func.total_SOA_mass = total_SOA_mass
dydt_func.size_array = size_array
dydt_func.temp = Model_temp
dydt_func.RH = Pressure_gas[-1] / (Psat[-1] * 101325.0)
dydt_func.water_activity = aw_array
#----------------------------------------------------------------------------
return dy_dt
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
#import static compilation of Fortran functions for use in ODE solver
print("Importing pre-compiled Fortran modules")
from rate_coeff_f2py import evaluate_rates as evaluate_rates_fortran
from reactants_conc_f2py import reactants as reactants_fortran
from loss_gain_f2py import loss_gain as loss_gain_fortran
from partition_f2py import dydt_partition as dydt_partition_fortran
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
num_species = input_dict['num_species']
num_species_condensed = input_dict['num_species_condensed']
y_density_array_asnumpy = input_dict['y_density_array_asnumpy']
y_mw = input_dict['y_mw']
sat_vp = input_dict['sat_vp']
Delta_H = input_dict['Delta_H']
Latent_heat_asnumpy = input_dict['Latent_heat_asnumpy']
DStar_org_asnumpy = input_dict['DStar_org_asnumpy']
alpha_d_org_asnumpy = input_dict['alpha_d_org_asnumpy']
gamma_gas_asnumpy = input_dict['gamma_gas_asnumpy']
Updraft = input_dict['Updraft']
GRAV = input_dict['GRAV']
Rv = input_dict['Rv']
Ra = input_dict['Ra']
R_gas = input_dict['R_gas']
R_gas_other = input_dict['R_gas_other']
cp = input_dict['cp']
sigma = input_dict['sigma']
NA = input_dict['NA']
kb = input_dict['kb']
Lv_water_vapour = input_dict['Lv_water_vapour']
ignore_index = input_dict['ignore_index']
ignore_index_fortran = input_dict['ignore_index_fortran']
ycore_asnumpy = input_dict['ycore_asnumpy']
core_density_array_asnumpy = input_dict['core_density_array_asnumpy']
y_cond = input_dict['y_cond_initial']
num_bins = input_dict['num_bins']
core_molw_asnumpy = input_dict['core_molw_asnumpy']
core_dissociation = input_dict['core_dissociation']
N_perbin = input_dict['N_perbin']
include_index = input_dict['include_index']
# pdb.set_trace()
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
y0 = [0] * (num_species + num_species_condensed * num_bins
) #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb fr the gas phase
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
if specie is not 'H2O':
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
elif specie is 'H2O':
y0[species_dict2array[specie]] = species_initial_conc[specie]
# Now add the initial condensed phase [including water]
#pdb.set_trace()
y0[num_species:num_species +
((num_bins) * num_species_condensed)] = y_cond[:]
#pdb.set_trace()
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Define a 'key' that represents the end of the composition variables to track
total_length_y = len(y0)
key = num_species + ((num_bins) * num_species) - 1
#pdb.set_trace()
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
# simulation_time= 3600.0
# batch_step=300.0
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
# Also define arrays and matrices that hold information such as total SOA mass
SOA_matrix = numpy.zeros((int(number_steps), 1))
size_matrix = numpy.zeros((int(number_steps), num_bins))
print("Starting simulation")
# In the following, we can
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-2] * len(y0)
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 1.0e-4 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = False # To be provided as an option in future update.
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
SOA_matrix[time_step, 0] = dydt_func.total_SOA_mass
size_matrix[time_step, :] = dydt_func.size_array
print("SOA [micrograms/m3] = ", dydt_func.total_SOA_mass)
#now save this information into a matrix for later plotting.
time_step += 1
if save_output is True:
print(
"Saving the model output as a pickled object for later retrieval")
# save the dictionary to a file for later retrieval - have to do each seperately.
with open(filename + '_y_output.pickle', 'wb') as handle:
pickle.dump(y_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_t_output.pickle', 'wb') as handle:
pickle.dump(t_array, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_SOA_output.pickle', 'wb') as handle:
pickle.dump(SOA_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + '_size_output.pickle', 'wb') as handle:
pickle.dump(size_matrix, handle, protocol=pickle.HIGHEST_PROTOCOL)
with open(filename + 'include_index.pickle', 'wb') as handle:
pickle.dump(include_index,
handle,
protocol=pickle.HIGHEST_PROTOCOL)
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if plot_mass is True:
try:
P.plot(t_array, SOA_matrix[:, 0], marker='o')
P.title(exp_mod.name)
P.ylabel("SOA mass [micrograms/m3]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def run_simulation(filename, start_time, save_output, temp, RH, RO2_indices,
H2O, input_dict, simulation_time, batch_step):
from assimulo.solvers import RodasODE, CVode #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# The variables passed to this function are defined as follows:
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
#pdb.set_trace()
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
rates = evaluate_rates_fortran(RO2, H2O, temp, time_of_day_seconds)
#pdb.set_trace()
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactants_fortran(y_asnumpy)
#pdb.set_trace()
#Multiply product of reactants with rate coefficient to get reaction rate
reactants = numpy.multiply(reactants, rates)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt = loss_gain_fortran(reactants)
#pdb.set_trace()
return dydt
#-------------------------------------------------------------------------------------
#-------------------------------------------------------------------------------------
# define jacobian function to be called
def jacobian(t, y):
"""
This function defines Jacobian of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt_dydt - the N_compounds x N_compounds matrix of Jacobian values
"""
# Different solvers might call jacobian at different stages, so we have to redo some calculations here
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode
rates = evaluate_rates_fortran(RO2, H2O, temp, time_of_day_seconds)
#pdb.set_trace()
# Now use reaction rates with the loss_gain matrix to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
dydt_dydt = jacobian_fortran(rates, y_asnumpy)
#pdb.set_trace()
return dydt_dydt
#-------------------------------------------------------------------------------------
#import static compilation of Fortran functions for use in ODE solver
print("Importing pre-compiled Fortran modules")
from rate_coeff_f2py import evaluate_rates as evaluate_rates_fortran
from reactants_conc_f2py import reactants as reactants_fortran
from loss_gain_f2py import loss_gain as loss_gain_fortran
from jacobian_f2py import jacobian as jacobian_fortran
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
num_species = len(species_dict.keys())
y0 = [0] * num_species #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
#simulation_time= 3600.0
#batch_step=100.0
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
print("Starting simulation")
# In the following, we can
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-3] * num_species
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 0.03 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = True # To be provided as an option in future update.
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
#now save this information into a matrix for later plotting.
time_step += 1
# Do you want to save the generated matrix of outputs?
if save_output:
numpy.save(filename + '_output', y_matrix)
df = pd.DataFrame(y_matrix)
df.to_csv(filename + "_output_matrix.csv")
w = csv.writer(open(filename + "_output_names.csv", "w"))
for specie, number in species_dict2array.items():
w.writerow([specie, number])
with_plots = True
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if with_plots:
try:
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['APINENE']]),
marker='o',
label="APINENE")
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['PINONIC']]),
marker='o',
label="PINONIC")
P.title(exp_mod.name)
P.legend(loc='upper left')
P.ylabel("Concetration log10[molecules/cc]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def func_set_system():
##############################################
#% initial conditions
P_0 = depth*9.8*2500. #; % initial chamber pressure (Pa)
T_0 = 1200 #; % initial chamber temperature (K)
eps_g0 = 0.04 #; % initial gas volume fraction
rho_m0 = 2600 #; % initial melt density (kg/m^3)
rho_x0 = 3065 #; % initial crystal density (kg/m^3)
a = 1000 #; % initial radius of the chamber (m)
V_0 = (4.*pi/3.)*a**3. #; % initial volume of the chamber (m^3)
##############################################
##############################################
IC = numpy.array([P_0,T_0,eps_g0,V_0,rho_m0,rho_x0]) # % store initial conditions
## Gas (eps_g = zero), eps_x is zero, too many crystals, 50 % crystallinity,eruption (yes/no)
sw0 = [False,False,False,False,False]
##############################################
#% error tolerances used in ode method
dt = 30e7
N = int(round((end_time-begin_time)/dt))
##############################################
#Define an Assimulo problem
exp_mod = Chamber_Problem(depth=depth,t0=begin_time,y0=IC,sw0=sw0)
exp_mod.param['T_in'] = 1200.
exp_mod.param['eps_g_in'] = 0.0 # Gas fraction of incoming melt - gas phase ..
exp_mod.param['m_eq_in'] = 0.05 # Volatile fraction of incoming melt
exp_mod.param['Mdot_in'] = mdot
exp_mod.param['eta_x_max'] = 0.64 # Locking fraction
exp_mod.param['delta_Pc'] = 20e6
exp_mod.tcurrent = begin_time
exp_mod.radius = a
exp_mod.permeability = perm_val
exp_mod.R_steps = 1500
exp_mod.dt_init = dt
#################
exp_mod.R_outside = numpy.linspace(a,3.*a,exp_mod.R_steps);
exp_mod.T_out_all =numpy.array([exp_mod.R_outside*0.])
exp_mod.P_out_all =numpy.array([exp_mod.R_outside*0.])
exp_mod.sigma_rr_all = numpy.array([exp_mod.R_outside*0.])
exp_mod.sigma_theta_all = numpy.array([exp_mod.R_outside*0.])
exp_mod.sigma_eff_rr_all = numpy.array([exp_mod.R_outside*0.])
exp_mod.sigma_eff_theta_all = numpy.array([exp_mod.R_outside*0.])
exp_mod.max_count = 1 # counting for the append me arrays ..
exp_mod.P_list = append_me()
exp_mod.P_list.update(P_0-exp_mod.plith)
exp_mod.T_list = append_me()
exp_mod.T_list.update(T_0-exp_mod.param['T_S'])
exp_mod.P_flux_list = append_me()
exp_mod.P_flux_list.update(0)
exp_mod.T_flux_list = append_me()
exp_mod.T_flux_list.update(0)
exp_mod.times_list = append_me()
exp_mod.times_list.update(1e-7)
exp_mod.T_out,exp_mod.P_out,exp_mod.sigma_rr,exp_mod.sigma_theta,exp_mod.T_der= Analytical_sol_cavity_T_Use(exp_mod.T_list.data[:exp_mod.max_count],exp_mod.P_list.data[:exp_mod.max_count],exp_mod.radius,exp_mod.times_list.data[:exp_mod.max_count],exp_mod.R_outside,exp_mod.permeability,exp_mod.param['material'])
exp_mod.param['heat_cond'] = 1 # Turn on/off heat conduction
exp_mod.param['visc_relax'] = 1 # Turn on/off viscous relaxation
exp_mod.param['press_relax'] = 1 ## Turn on/off pressure diffusion
exp_mod.param['frac_rad_Temp'] =0.75
exp_mod.param['vol_degass'] = 1.
#exp_mod.state_events = stopChamber #Sets the state events to the problem
#exp_mod.handle_event = handle_event #Sets the event handling to the problem
#Sets the options to the problem
#exp_mod.p0 = [beta_r, beta_m]#, beta_x, alpha_r, alpha_m, alpha_x, L_e, L_m, c_m, c_g, c_x, eruption, heat_cond, visc_relax] #Initial conditions for parameters
#exp_mod.pbar = [beta_r, beta_m]#, beta_x, alpha_r, alpha_m, alpha_x, L_e, L_m, c_m, c_g, c_x, eruption, heat_cond, visc_relax]
#Define an explicit solver
exp_sim = CVode(exp_mod) #Create a CVode solver
#Sets the parameters
#exp_sim.iter = 'Newton'
#exp_sim.discr = 'BDF'
#exp_sim.inith = 1e-7
exp_sim.rtol = 1.e-7
exp_sim.maxh = 3e7
exp_sim.atol = 1e-7
exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
#exp_sim.usesens = True
#exp_sim.report_continuously = True
return exp_mod,exp_sim,N
#Create Assimulo problem model
mod_pen = Explicit_Problem(rhs, y0, t0)
mod_pen.name = 'Elastic Pendulum with CVode'
"""
Run simulation
"""
#Create solver object
sim_pen = CVode(mod_pen)
#Simulation parameters
#atol = 1.e-6*ones(shape(y0))
atol = rtol * N.array([1, 1, 1, 1]) #default 1e-06
sim_pen.atol = atol
sim_pen.rtol = rtol
sim_pen.maxh = hmax
sim_pen.maxord = maxord
sim_pen.inith = h0
#Simulate
t, y = sim_pen.simulate(tf)
"""
Plot results
"""
#Plot
#P.plot(t,y)
#P.legend(['$x$','$y$','$\dot{x}$','$\dot{y}$'])
#P.title('Elastic pendulum with k = ' + str(k) + ', stretch = ' + str(stretch))
#P.xlabel('time')
#P.ylabel('state')
#show()
def run_simulation(filename, save_output, start_time, temp, RH, RO2_indices,
H2O, input_dict, simulation_time, batch_step):
from assimulo.solvers import RodasODE, CVode #Choose solver accoring to your need.
from assimulo.problem import Explicit_Problem
# In this function, we import functions that have been pre-compiled for use in the ODE solver
# The function that calculates the RHS of the ODE is also defined within this function, such
# that it can be used by the Assimulo solvers
# In the standard Python version [not using Numba] I use Sparse matrix operations in calculating loss/gain of each compound.
# This function loads the matrix created at the beginning of the module.
def load_sparse_csr(filename):
loader = numpy.load('loss_gain_' + filename + '.npz')
return csr_matrix(
(loader['data'], loader['indices'], loader['indptr']),
shape=loader['shape'])
def load_sparse_csr_reactants(filename):
loader = numpy.load('reactants_indices_sparse_' + filename + '.npz')
return csr_matrix(
(loader['data'], loader['indices'], loader['indptr']),
shape=loader['shape'])
#-------------------------------------------------------------------------------------
# define the ODE function to be called
def dydt_func(t, y):
"""
This function defines the right-hand side [RHS] of the ordinary differential equations [ODEs] to be solved
input:
• t - time variable [internal to solver]
• y - array holding concentrations of all compounds in both gas and particulate [molecules/cc]
output:
dydt - the dy_dt of each compound in both gas and particulate phase [molecules/cc.sec]
"""
#pdb.set_trace()
#Here we use the pre-created Numba based functions to arrive at our value for dydt
# Calculate time of day
time_of_day_seconds = start_time + t
# make sure the y array is not a list. Assimulo uses lists
y_asnumpy = numpy.array(y)
#pdb.set_trace()
# reactants=numpy.zeros((equations),)
#pdb.set_trace()
#Calculate the concentration of RO2 species, using an index file created during parsing
RO2 = numpy.sum(y[RO2_indices])
#Calculate reaction rate for each equation.
# Note that H2O will change in parcel mode [to be changed in the full aerosol mode]
# The time_of_day_seconds is used for photolysis rates - need to change this if want constant values
#pdb.set_trace()
rates = evaluate_rates(time_of_day_seconds, RO2, H2O, temp,
numpy.zeros((equations)), numpy.zeros((63)))
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
reactants = reactant_product(y_asnumpy, equations,
numpy.zeros((equations)))
#Multiply product of reactants with rate coefficient to get reaction rate
#pdb.set_trace()
reactants = numpy.multiply(reactants, rates)
# Now use reaction rates with the loss_gain information in a pre-created Numba file to calculate the final dydt for each compound
dydt = dydt_eval(numpy.zeros((len(y_asnumpy))), reactants)
#pdb.set_trace()
############ Development place-holder ##############
# ----------------------------------------------------------------------------------
# The following demonstrates the same procedure but using only Numpy and pure python
# For the full MCM this is too slow, but is useful for demonstrations and testing
#Calculate reaction rate for each equation.
## rates=test(time_of_day_seconds,RO2,H2O,temp)
# Calculate product of all reactants and stochiometry for each reaction [A^a*B^b etc]
# Take the approach of using sparse matrix operations from a python perspective
# This approach uses the rule of logarithms and sparse matrix multiplication
##temp_array=reactants_indices_sparse @ numpy.log(y_asnumpy)
##indices=numpy.where(temp_array > 0.0)
##reactants[indices]=numpy.exp(temp_array[indices])
#Multiply product of reactants with rate coefficient to get reaction rate
## reactants = numpy.multiply(reactants,rates)
# Now use reaction rates with the loss_gain matri to calculate the final dydt for each compound
# With the assimulo solvers we need to output numpy arrays
##dydt=numpy.array(loss_gain @ reactants)
# ----------------------------------------------------------------------------------
return dydt
#-------------------------------------------------------------------------------------
print(
"Importing Numba modules [compiling if first import or clean build...please be patient]"
)
#import Numba functions for use in ODE solver
from Rate_coefficients_numba import evaluate_rates
from Reactants_conc_numba import reactants as reactant_product
from Loss_Gain_numba import dydt as dydt_eval
# 'Unpack' variables from input_dict
species_dict = input_dict['species_dict']
species_dict2array = input_dict['species_dict2array']
species_initial_conc = input_dict['species_initial_conc']
equations = input_dict['equations']
# Set dive by zero to ignore for use of any sparse matrix multiplication
numpy.errstate(divide='ignore')
# --- For Numpy and pure Python runs ----
# Load the sparse matrix used in calculating the reactant products and dydt function
## reactants_indices_sparse = load_sparse_csr_reactants(filename)
## loss_gain = load_sparse_csr(filename)
#Specify some starting concentrations [ppt]
Cfactor = 2.55e+10 #ppb-to-molecules/cc
# Create variables required to initialise ODE
num_species = len(species_dict.keys())
y0 = [0] * num_species #Initial concentrations, set to 0
t0 = 0.0 #T0
# Define species concentrations in ppb
# You have already set this in the front end script, and now we populate the y array with those concentrations
for specie in species_initial_conc.keys():
y0[species_dict2array[specie]] = species_initial_conc[
specie] * Cfactor #convert from pbb to molcules/cc
#Set the total_time of the simulation to 0 [havent done anything yet]
total_time = 0.0
# Now run through the simulation in batches.
# I do this to enable testing of coupling processes. Some initial investigations with non-ideality in
# the condensed phase indicated that even defining a maximum step was not enough for ODE solvers to
# overshoot a stable region. It also helps with in-simulation debugging. Its up to you if you want to keep this.
# To not run in batches, just define one batch as your total simulation time. This will reduce any overhead with
# initialising the solvers
# Set total simulation time and batch steps in seconds
# Note also that the current module outputs solver information after each batch step. This can be turned off and the
# the batch step change for increased speed
# simulation_time= 3600.0 # seconds
# batch_step=100.0 # seconds
t_array = []
time_step = 0
number_steps = int(
simulation_time /
batch_step) # Just cycling through 3 steps to get to a solution
# Define a matrix that stores values as outputs from the end of each batch step. Again, you can remove
# the need to run in batches. You can tell the Assimulo solvers the frequency of outputs.
y_matrix = numpy.zeros((int(number_steps), len(y0)))
print("Starting simulation")
#pdb.set_trace()
while total_time < simulation_time:
if total_time == 0.0:
#Define an Assimulo problem
#Define an explicit solver
#pdb.set_trace()
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
else:
y0 = y_output[
-1, :] # Take the output from the last batch as the start of this
exp_mod = Explicit_Problem(dydt_func, y0, t0, name=filename)
# Define ODE parameters.
# Initial steps might be slower than mid-simulation. It varies.
#exp_mod.jac = dydt_jac
# Define which ODE solver you want to use
exp_sim = CVode(exp_mod)
tol_list = [1.0e-3] * num_species
exp_sim.atol = tol_list #Default 1e-6
exp_sim.rtol = 1e-6 #Default 1e-6
exp_sim.inith = 1.0e-6 #Initial step-size
#exp_sim.discr = 'Adams'
exp_sim.maxh = 100.0
# Use of a jacobian makes a big differece in simulation time. This is relatively
# easy to define for a gas phase - not sure for an aerosol phase with composition
# dependent processes.
exp_sim.usejac = False # To be provided as an option in future update. See Fortran variant for use of Jacobian
#exp_sim.fac1 = 0.05
#exp_sim.fac2 = 50.0
exp_sim.report_continuously = True
exp_sim.maxncf = 1000
#Sets the parameters
t_output, y_output = exp_sim.simulate(
batch_step) #Simulate 'batch' seconds
total_time += batch_step
t_array.append(
total_time
) # Save the output from the end step, of the current batch, to a matrix
y_matrix[time_step, :] = y_output[-1, :]
#pdb.set_trace()
#now save this information into a matrix for later plotting.
time_step += 1
# Do you want to save the generated matrix of outputs?
if save_output:
numpy.save(filename + '_output', y_matrix)
df = pd.DataFrame(y_matrix)
df.to_csv(filename + "_output_matrix.csv")
w = csv.writer(open(filename + "_output_names.csv", "w"))
for specie, number in species_dict2array.items():
w.writerow([specie, number])
with_plots = True
#pdb.set_trace()
#Plot the change in concentration over time for a given specie. For the user to change / remove
#In a future release I will add this as a seperate module
if with_plots:
try:
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['APINENE']]),
marker='o',
label="APINENE")
P.plot(t_array,
numpy.log10(y_matrix[:, species_dict2array['PINONIC']]),
marker='o',
label="PINONIC")
P.title(exp_mod.name)
P.legend(loc='upper left')
P.ylabel("Concetration log10[molecules/cc]")
P.xlabel("Time [seconds] since start of simulation")
P.show()
except:
print(
"There is a problem using Matplotlib in your environment. If using this within a docker container, you will need to transfer the data to the host or configure your container to enable graphical displays. More information can be found at http://wiki.ros.org/docker/Tutorials/GUI "
)
def stiff_ode_solver(matrix,
y_initial,
forward_rate,
rev_rate,
third_body=None,
iteration='Newton',
discr='BDF',
atol=1e-10,
rtol=1e-6,
sim_time=0.001,
num_data_points=500):
"""
Sets up the initial condition for solving the odes
Parameters
----------
matrix : ndarray
stoichiometric matrix
y_initial : list
A list of initial concentrations
forward_rate : list
A list of forward reaction rates
for all the reactions in the mechanism
rev_rate : list
A list of reverse reaction rates
for all the reactions in the mechanism
sim_time : float
total time to simulate in seconds
third_body : ndarray
third body matrix, default = None
iteration : str
determines the iteration method that is be
used by the solver, default='Newton'
discr : determines the discretization method,
default='BDF'
atol : float
absolute tolerance(s) that is to be used
by the solver, default=1e-10
rtol : float
relative tolerance that is to be
used by the solver, default= 1e-7
num_data_points : integer
number of even space data points in output
arrays, default = 500
Returns
----------
t1 : list
A list of time-points at which
the system of ODEs is solved
[t1, t2, t3,...]
y1 : list of lists
A list of concentrations of all the species
at t1 time-points
[[y1(t1), y2(t1),...], [y1(t2), y2(t2),...],...]
"""
# y0[0] = 0
# y0[0] = 0
# dydt = np.zeros((len(species_list)), dtype=float)
# Define the rhs
kf = forward_rate
kr = rev_rate
mat_reac = np.abs(np.asarray(np.where(matrix < 0, matrix, 0)))
mat_prod = np.asarray(np.where(matrix > 0, matrix, 0))
# d = kf * np.prod(y0**np.abs(mat_reac), axis = 1) - kr * np.prod(y0**mat_prod, axis = 1)
def rhs(t, concentration):
# print(t)
y = concentration
if third_body is not None:
third_body_eff = np.dot(third_body, y)
third_body_eff = np.where(third_body_eff > 0, third_body_eff, 1)
# print(third_body_eff)
else:
third_body_eff = np.ones(len(forward_rate))
# print(len(third_body_matrix))
rate_concentration = (kf * np.prod(np.power(y, mat_reac), axis=1) -
kr * np.prod(np.power(y, mat_prod), axis=1))
dydt = np.dot(
third_body_eff,
np.multiply(matrix, rate_concentration.reshape(matrix.shape[0],
1)))
# dydt = [np.sum(third_body_eff * (matrix[:, i] * rate_concentration)) for i in
# range(len(species_list))]
del t
del y
return dydt
t0 = 0
# Define an Assimulo problem
exp_mod = Explicit_Problem(rhs, y_initial, t0)
# Define an explicit solver
exp_sim = CVode(exp_mod) # Create a CVode solver
# Sets the parameters
exp_sim.iter = iteration # Default 'FixedPoint'
exp_sim.discr = discr # Default 'Adams'
exp_sim.atol = [atol] # Default 1e-6
exp_sim.rtol = rtol # Default 1e-6
exp_sim.maxh = 0.1
exp_sim.minh = 1e-18
exp_sim.num_threads = 1
while True:
try:
t1, y1 = exp_sim.simulate(sim_time, num_data_points)
break
except CVodeError:
# reduce absolute error by two orders of magnitude
# and try to solve again.
print("next process started")
atol = atol * 1e-2
exp_sim.atol = atol
# if atol < 1e-15:
# t1 = 0
# y1 = 0
# break
# print(exp_sim.atol)
return t1, y1
