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