Time stepping

step_time.f90

Quick access

Variables:

start_from_another_scheme, transp_lmloc_to_rloc, transp_rloc_to_lmloc, transp_rloc_to_lmloc_io

Routines:

initialize_step_time(), step_time()

Needed modules

• iso_fortran_env (output_unit())

• fields: This module contains all the fields used in MagIC in the hybrid (LM,r) space as well as their radial derivatives. It defines both the LM-distributed arrays and the R-distributed arrays….

• fieldslast: This module contains all the work arrays of the previous time-steps needed to time advance the code. They are needed in the time-stepping scheme….

• parallel_mod: This module contains the blocking information

• precision_mod: This module controls the precision used in MagIC

• constants (zero(), one(), half()): module containing constants and parameters used in the code.

• truncation (n_r_max(), l_max(), l_maxmag(), lm_max(), fd_order(), fd_order_bound()): This module defines the grid points and the truncation

• num_param (n_time_steps(), run_time_limit(), tend(), dtmax(), dtmin(), tscale(), dct_counter(), nl_counter(), solve_counter(), lm2phy_counter(), td_counter(), phy2lm_counter(), f_exp_counter()): Module containing numerical and control parameters

• radial_data (nrstart(), nrstop(), nrstartmag(), nrstopmag(), n_r_icb(), n_r_cmb()): This module defines the MPI decomposition in the radial direction.

• radial_der (get_dr_rloc(), get_ddr_rloc(), exch_ghosts(), bulk_to_ghost()): Radial derivatives functions

• radial_functions (rscheme_oc()): This module initiates all the radial functions (transport properties, density, temperature, cheb transforms, etc.)

• logic (l_mag(), l_mag_lf(), l_dtb(), l_rms(), l_hel(), l_to(), l_tomovie(), l_r_field(), l_cmb_field(), l_htmovie(), l_dtrmagspec(), lverbose(), l_b_nl_icb(), l_par(), l_b_nl_cmb(), l_fluxprofs(), l_viscbccalc(), l_perppar(), l_ht(), l_dtbmovie(), l_heat(), l_conv(), l_movie(), l_runtimelimit(), l_save_out(), l_bridge_step(), l_dt_cmb_field(), l_chemical_conv(), l_mag_kin(), l_hemi(), l_power(), l_double_curl(), l_pressgraph(), l_probe(), l_ab1(), l_finite_diff(), l_cond_ic(), l_single_matrix(), l_packed_transp(), l_rot_ic(), l_rot_ma(), l_cond_ma(), l_parallel_solve(), l_mag_par_solve(), l_phase_field(), l_onset(), l_geosmovie(), l_phasemovie(), l_dtphasemovie()): Module containing the logicals that control the run

• init_fields (omega_ic1(), omega_ma1()): This module is used to construct the initial solution.

• radialloop (radialloopg())

• lmloop_mod (lmloop(), finish_explicit_assembly(), assemble_stage(), finish_explicit_assembly_rdist(), lmloop_rdist(), assemble_stage_rdist())

• signals_mod (initialize_signals(), check_signals()): This module handles the reading/writing of the signal.TAG file which allows to communicate with MagIC during its execution

• graphout_mod (open_graph_file(), close_graph_file()): This module contains the subroutines that store the 3-D graphic files.

• output_data (tag(), n_graph_step(), n_graphs(), dt_graph(), t_graph(), n_spec_step(), n_specs(), dt_spec(), t_spec(), n_movie_step(), n_movie_frames(), dt_movie(), t_movie(), n_tomovie_step(), n_tomovie_frames(), dt_tomovie(), t_tomovie(), n_pot_step(), n_pots(), dt_pot(), t_pot(), n_rst_step(), n_rsts(), dt_rst(), t_rst(), n_stores(), n_log_step(), n_logs(), dt_log(), t_log(), n_cmb_step(), n_cmbs(), dt_cmb(), t_cmb(), n_r_field_step(), n_r_fields(), dt_r_field(), t_r_field(), n_to_step(), n_tos(), dt_to(), t_to(), n_probe_step(), n_probe_out(), dt_probe(), t_probe(), log_file(), n_log_file(), n_time_hits()): This module contains the parameters for output control

• updateb_mod (get_mag_rhs_imp(), get_mag_ic_rhs_imp(), b_ghost(), aj_ghost(), get_mag_rhs_imp_ghost(), fill_ghosts_b()): This module handles the time advance of the magnetic field potentials b and aj as well as the inner core counterparts b_ic and aj_ic. It contains the computation of the implicit terms and the linear

• updatewp_mod (get_pol_rhs_imp(), get_pol_rhs_imp_ghost(), w_ghost(), fill_ghosts_w(), p0_ghost()): This module handles the time advance of the poloidal potential w and the pressure p. It contains the computation of the implicit terms and the linear solves.

• updatewps_mod (get_single_rhs_imp()): This module handles the time advance of the poloidal potential w, the pressure p and the entropy s in one single matrix per degree. It contains the computation of the implicit terms and the linear

• updates_mod (get_entropy_rhs_imp(), get_entropy_rhs_imp_ghost(), s_ghost(), fill_ghosts_s()): This module handles the time advance of the entropy s. It contains the computation of the implicit terms and the linear solves….

• updatexi_mod (get_comp_rhs_imp(), get_comp_rhs_imp_ghost(), xi_ghost(), fill_ghosts_xi()): This module handles the time advance of the chemical composition xi. It contains the computation of the implicit terms and the linear solves….

• updatephi_mod (get_phase_rhs_imp(), get_phase_rhs_imp_ghost(), phi_ghost(), fill_ghosts_phi()): This module handles the time advance of the phase field phi. It contains the computation of the implicit terms and the linear solves….

• updatez_mod (get_tor_rhs_imp(), get_tor_rhs_imp_ghost(), z_ghost(), fill_ghosts_z()): This module handles the time advance of the toroidal potential z It contains the computation of the implicit terms and the linear solves….

• output_mod (output()): This module handles the calls to the different output routines.

• time_schemes (type_tscheme()): This module defines an abstract class type_tscheme which is employed for the time advance of the code.

• useful (l_correct_step(), logwrite()): This module contains several useful routines.

• communications (lo2r_field(), lo2r_flow(), scatter_from_rank0_to_lo(), lo2r_xi(), r2lo_flow(), r2lo_s(), r2lo_xi(), r2lo_field(), lo2r_s(), lo2r_press(), lo2r_one(), r2lo_one()): This module contains the different MPI communicators used in MagIC.

• courant_mod (dt_courant()): This module handles the computation of Courant factors on grid space. It then checks whether the timestep size needs to be modified.

• nonlinear_bcs (get_b_nl_bcs())

• timing: This module contains functions that are used to measure the time spent.

• probe_mod: Module for artificial sensors to compare time series of physical data with experiments. Probes are located in a radially symmetrical way

Variables

• step_time_mod/start_from_another_scheme [private]

• step_time_mod/transp_lmloc_to_rloc [private]

• step_time_mod/transp_rloc_to_lmloc [private]

• step_time_mod/transp_rloc_to_lmloc_io [private]

Subroutines and functions

subroutine  step_time_mod/initialize_step_time()

Called from:

magic

Call to:

initialize_signals()

subroutine  step_time_mod/step_time(time, tscheme, n_time_step, run_time_start)

This subroutine performs the actual time-stepping.

Parameters:

• time [real ,inout]

• tscheme [real ]

• n_time_step [integer ,inout]

• run_time_start [timer_type ,in]

Called from:

magic

Call to:

check_signals(), logwrite(), l_correct_step(), open_graph_file(), radialloopg(), finish_explicit_assembly_rdist(), get_b_nl_bcs(), finish_explicit_assembly(), scatter_from_rank0_to_lo(), output(), close_graph_file(), dt_courant(), lmloop_rdist(), lmloop(), assemble_stage_rdist(), assemble_stage(), formattime()

courant.f90

Description

This module handles the computation of Courant factors on grid space. It then checks whether the timestep size needs to be modified.

Quick access

Variables:

file_handle

Routines:

courant(), dt_courant(), finalize_courant(), initialize_courant()

Needed modules

• parallel_mod: This module contains the blocking information

• precision_mod: This module controls the precision used in MagIC

• truncation (n_phi_max(), n_theta_max()): This module defines the grid points and the truncation

• radial_data (nrstart(), nrstop()): This module defines the MPI decomposition in the radial direction.

• radial_functions (orho1(), orho2(), or4(), or2()): This module initiates all the radial functions (transport properties, density, temperature, cheb transforms, etc.)

• physical_parameters (lffac(), opm()): Module containing the physical parameters

• num_param (delxr2(), delxh2()): Module containing numerical and control parameters

• horizontal_data (o_sin_theta_e2()): Module containing functions depending on longitude and latitude plus help arrays depending on degree and order

• logic (l_mag(), l_mag_lf(), l_mag_kin(), l_cour_alf_damp()): Module containing the logicals that control the run

• useful (logwrite()): This module contains several useful routines.

• constants (half(), one(), two()): module containing constants and parameters used in the code.

Variables

• courant_mod/file_handle [integer,private]

Subroutines and functions

subroutine  courant_mod/initialize_courant(time, dt, tag)

This subroutine opens the timestep.TAG file which stores the time step changes of MagIC.

Parameters:

• time [real ,in] :: time

• dt [real ,in] :: time step

• tag [character(len=*),in] :: trailing of the fime

Called from:

magic

subroutine  courant_mod/finalize_courant()

Called from:

magic

subroutine  courant_mod/courant(n_r, dtrkc, dthkc, vr, vt, vp, br, bt, bp, courfac, alffac)

courant condition check: calculates Courant advection lengths in radial direction dtrkc and in horizontal direction dthkc on the local radial level n_r

for the effective velocity, the abs. sum of fluid velocity and Alfven velocity is taken

instead of the full Alfven velocity a modified Alfven velocity is employed that takes viscous and Joule damping into account. Different Courant factors are used for the fluid velocity and the such modified Alfven velocity

Parameters:

• n_r [integer ,in] :: radial level

• dtrkc [real ,inout] :: Courant step (based on radial advection)

• dthkc [real ,inout] :: Courant step based on horizontal advection

• vr (*,*) [real ,in] :: radial velocity

• vt (*,*) [real ,in] :: longitudinal velocity

• vp (*,*) [real ,in] :: azimuthal velocity

• br (*,*) [real ,in] :: radial magnetic field

• bt (*,*) [real ,in] :: longitudinal magnetic field

• bp (*,*) [real ,in] :: azimuthal magnetic field

• courfac [real ,in]

• alffac [real ,in]

subroutine  courant_mod/dt_courant(l_new_dt, dt, dt_new, dtmax, dtrkc, dthkc, time)

This subroutine checks if the Courant criterion based on combined fluid and Alfven velocity is satisfied. It returns a new value for the time step size.

Parameters:

• l_new_dt [logical ,out] :: flag indicating that time step is changed (=1) or not (=0)

• dt [real ,in] :: old time step size

• dt_new [real ,out] :: new time step size

• dtmax [real ,in] ::

  ”

• dtrkc (1 - nrstart + nrstop) [real ,in] :: radial Courant time step as function of radial level

• dthkc (1 - nrstart + nrstop) [real ,in] :: horizontal Courant time step as function of radial level

• time [real ,in] :: Current time

Called from:

step_time()

Call to:

logwrite()

timing.f90

Description

This module contains functions that are used to measure the time spent.

Quick access

Types:

timer_type

Variables:

finalize, initialize, start_count, stop_count

Routines:

formattime()

Needed modules

• iso_fortran_env (output_unit())

• mpimod

• precision_mod: This module controls the precision used in MagIC

• parallel_mod: This module contains the blocking information

Types

• type  timing/timer_type

  Type fields:

  • % n_counts [integer ]

  • % tstart [real ]

  • % ttot [real ]

Variables

• timing/finalize [private]

• timing/initialize [private]

• timing/start_count [private]

• timing/stop_count [private]

Subroutines and functions

subroutine  timing/formattime(n_out, message, time_in_sec)

Parameters:

• n_out [integer ,in]

• message [character(len=*),in]

• time_in_sec [real ,in]

Called from:

step_time()

Time schemes

time_schemes.f90

Description

This module defines an abstract class type_tscheme which is employed for the time advance of the code.

Quick access

Types:

type_tscheme

Variables:

print_info, unknown_interface

Needed modules

• iso_fortran_env (output_unit())

• time_array: This module defines two types that are defined to store the implicit/explicit terms at the different sub-stage/step.

• logic (l_save_out()): Module containing the logicals that control the run

• output_data (log_file()): This module contains the parameters for output control

• precision_mod: This module controls the precision used in MagIC

Types

• type  time_schemes/type_tscheme

  Type fields:

  • % alffac [real ]

  • % courfac [real ]

  • % dt (*) [real ,allocatable]

  • % family [character(len=10)]

  • % intfac [real ]

  • % istage [integer ]

  • % l_assembly [logical ]

  • % l_exp_calc (*) [logical ,allocatable]

  • % l_imp_calc_rhs (*) [logical ,allocatable]

  • % nexp [integer ]

  • % nimp [integer ]

  • % nold [integer ]

  • % nstages [integer ]

  • % time_scheme [character(len=8)]

  • % wimp_lin (*) [real ,allocatable]

Variables

• time_schemes/print_info [private]

• time_schemes/unknown_interface [private]

multistep_schemes.f90

Description

This module defines the type_multistep which inherits from the abstract type_tscheme. It actually implements all the routine required to time-advance an IMEX multistep scheme such as CN/AB2, SBDF(2,3,4), CNLF, …

Quick access

Types:

type_multistep

Variables:

assemble_imex, assemble_imex_scalar, bridge_with_cnab2, get_time_stage, rotate_imex, rotate_imex_scalar, set_dt_array, set_imex_rhs, set_imex_rhs_ghost, set_imex_rhs_scalar, set_weights, start_with_ab1

Needed modules

• precision_mod: This module controls the precision used in MagIC

• iso_fortran_env (output_unit())

• parallel_mod: This module contains the blocking information

• num_param (alpha()): Module containing numerical and control parameters

• constants (one(), half(), two(), zero()): module containing constants and parameters used in the code.

• mem_alloc (bytes_allocated()): This little module is used to estimate the global memory allocation used in MagIC

• useful (abortrun()): This module contains several useful routines.

• output_data (log_file()): This module contains the parameters for output control

• logic (l_save_out()): Module containing the logicals that control the run

• time_schemes (type_tscheme()): This module defines an abstract class type_tscheme which is employed for the time advance of the code.

• time_array: This module defines two types that are defined to store the implicit/explicit terms at the different sub-stage/step.

Types

• type  multistep_schemes/type_multistep

  Type fields:

  • % wexp (*) [real ,allocatable]

  • % wimp (*) [real ,allocatable]

Variables

• multistep_schemes/assemble_imex [private]

• multistep_schemes/assemble_imex_scalar [private]

• multistep_schemes/bridge_with_cnab2 [private]

• multistep_schemes/finalize [private]

• multistep_schemes/get_time_stage [private]

• multistep_schemes/initialize [private]

• multistep_schemes/rotate_imex [private]

• multistep_schemes/rotate_imex_scalar [private]

• multistep_schemes/set_dt_array [private]

• multistep_schemes/set_imex_rhs [private]

• multistep_schemes/set_imex_rhs_ghost [private]

• multistep_schemes/set_imex_rhs_scalar [private]

• multistep_schemes/set_weights [private]

• multistep_schemes/start_with_ab1 [private]

dirk_schemes.f90

Description

This module defines the type_dirk which inherits from the abstract type_tscheme. It actually implements all the routine required to time-advance an diagonally implicit Runge-Kutta scheme. It makes use of Butcher tables to construct the right-hand-sides.

Quick access

Types:

type_dirk

Needed modules

• iso_fortran_env (output_unit())

• precision_mod: This module controls the precision used in MagIC

• parallel_mod: This module contains the blocking information

• num_param (alpha()): Module containing numerical and control parameters

• constants (one(), half(), two(), zero()): module containing constants and parameters used in the code.

• mem_alloc (bytes_allocated()): This little module is used to estimate the global memory allocation used in MagIC

• useful (abortrun()): This module contains several useful routines.

• logic (l_save_out()): Module containing the logicals that control the run

• output_data (log_file()): This module contains the parameters for output control

• time_schemes (type_tscheme()): This module defines an abstract class type_tscheme which is employed for the time advance of the code.

• time_array: This module defines two types that are defined to store the implicit/explicit terms at the different sub-stage/step.

Types

• type  dirk_schemes/type_dirk

  Type fields:

  • % butcher_ass_exp (*) [real ,allocatable]

  • % butcher_ass_imp (*) [real ,allocatable]

  • % butcher_c (*) [real ,allocatable]

  • % butcher_exp (*,*) [real ,allocatable]

  • % butcher_imp (*,*) [real ,allocatable]

Variables

• dirk_schemes/assemble_imex [private]

• dirk_schemes/assemble_imex_scalar [private]

• dirk_schemes/bridge_with_cnab2 [private]

• dirk_schemes/finalize [private]

• dirk_schemes/get_time_stage [private]

• dirk_schemes/initialize [private]

• dirk_schemes/rotate_imex [private]

• dirk_schemes/rotate_imex_scalar [private]

• dirk_schemes/set_dt_array [private]

• dirk_schemes/set_imex_rhs [private]

• dirk_schemes/set_imex_rhs_ghost [private]

• dirk_schemes/set_imex_rhs_scalar [private]

• dirk_schemes/set_weights [private]

• dirk_schemes/start_with_ab1 [private]

time_array.f90

Description

This module defines two types that are defined to store the implicit/explicit terms at the different sub-stage/step.

Quick access

Types:

type_tarray, type_tscalar

Variables:

finalize_scalar, initialize_scalar

Needed modules

• precision_mod: This module controls the precision used in MagIC

• constants (zero()): module containing constants and parameters used in the code.

• mem_alloc (bytes_allocated()): This little module is used to estimate the global memory allocation used in MagIC

Types

• type  time_array/type_tarray

  Type fields:

  • % expl (*,*,*) [complex ,pointer]

  • % impl (*,*,*) [complex ,allocatable]

  • % l_exp [logical ]

  • % llm [integer ]

  • % nrstart [integer ]

  • % nrstop [integer ]

  • % old (*,*,*) [complex ,allocatable]

  • % ulm [integer ]

• type  time_array/type_tscalar

  Type fields:

  • % expl (*) [real ,allocatable]

  • % impl (*) [real ,allocatable]

  • % old (*) [real ,allocatable]

Variables

• time_array/finalize [private]

• time_array/finalize_scalar [private]

• time_array/initialize [private]

• time_array/initialize_scalar [private]