Non-linear part of the time stepping (radial loop)

radialLoop.f90

Quick access

Routines

finalize_radialloop(), initialize_radialloop(), radialloopg()

Needed modules

• precision_mod: This module controls the precision used in MagIC

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

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

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

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

• riteration (riter_t()): This module is used to define an abstract class for the radial loop

• riter_mod (riter_single_t()): This module actually handles the loop over the radial levels. It contains the spherical harmonic transforms and the operations on the arrays in physical space….

Variables

Subroutines and functions

subroutine radialloop/initialize_radialloop()

Called from

magic

Call to

memwrite()

subroutine radialloop/finalize_radialloop()

Called from

magic

subroutine radialloop/radialloopg(l_graph, l_frame, time, timestage, tscheme, dtlast, ltocalc, ltonext, ltonext2, lhelcalc, lpowercalc, lrmscalc, lpresscalc, lpressnext, lviscbccalc, lfluxprofcalc, lperpparcalc, lgeoscalc, lhemicalc, l_probe_out, dsdt, dwdt, dzdt, dpdt, dxidt, dphidt, dbdt, djdt, dvxvhlm, dvxbhlm, dvsrlm, dvxirlm, lorentz_torque_ic, lorentz_torque_ma, br_vt_lm_cmb, br_vp_lm_cmb, br_vt_lm_icb, br_vp_lm_icb, dtrkc, dthkc)

This subroutine performs the actual time-stepping.

Parameters

• l_graph [logical ,in]

• l_frame [logical ,in]

• time [real ,in]

• timestage [real ,in]

• tscheme [real ]

• dtlast [real ,in]

• ltocalc [logical ,in]

• ltonext [logical ,in]

• ltonext2 [logical ,in]

• lhelcalc [logical ,in]

• lpowercalc [logical ,in]

• lrmscalc [logical ,in]

• lpresscalc [logical ,in]

• lpressnext [logical ,in]

• lviscbccalc [logical ,in]

• lfluxprofcalc [logical ,in]

• lperpparcalc [logical ,in]

• lgeoscalc [logical ,in]

• lhemicalc [logical ,in]

• l_probe_out [logical ,in]

• dsdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dwdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dzdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dpdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dxidt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dphidt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dbdt (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• djdt (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• dvxvhlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dvxbhlm (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• dvsrlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dvxirlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• lorentz_torque_ic [real ,out]

• lorentz_torque_ma [real ,out]

• br_vt_lm_cmb (lm_max) [complex ,out] :: product br*vt at CMB

• br_vp_lm_cmb (lm_max) [complex ,out] :: product br*vp at CMB

• br_vt_lm_icb (lm_max) [complex ,out] :: product br*vt at ICB

• br_vp_lm_icb (lm_max) [complex ,out] :: product br*vp at ICB

• dtrkc (nrstop-(nrstart)+1) [real ,out]

• dthkc (nrstop-(nrstart)+1) [real ,out]

Called from

step_time()

rIteration.f90

Description

This module is used to define an abstract class for the radial loop

Needed modules

• precision_mod: This module controls the precision used in MagIC

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

• truncation (lm_max(), lm_maxmag()): This module defines the grid points and the truncation

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

Types

• type riteration/unknown_type

rIter.f90

Description

This module actually handles the loop over the radial levels. It contains the spherical harmonic transforms and the operations on the arrays in physical space.

Quick access

Routines

radialloop(), transform_to_grid_space(), transform_to_lm_space()

Needed modules

• precision_mod: This module controls the precision used in MagIC

• num_param (phy2lm_counter(), lm2phy_counter(), nl_counter(), td_counter()): Module containing numerical and control parameters

• parallel_mod: This module contains the blocking information

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

• logic (l_mag(), l_conv(), l_mag_kin(), l_heat(), l_ht(), l_anel(), l_mag_lf(), l_conv_nl(), l_mag_nl(), l_b_nl_cmb(), l_b_nl_icb(), l_rot_ic(), l_cond_ic(), l_rot_ma(), l_cond_ma(), l_dtb(), l_store_frame(), l_movie_oc(), l_to(), l_chemical_conv(), l_probe(), l_full_sphere(), l_precession(), l_centrifuge(), l_adv_curl(), l_double_curl(), l_parallel_solve(), l_single_matrix(), l_temperature_diff(), l_rms(), l_phase_field(), l_onset()): Module containing the logicals that control the run

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

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

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

• nonlinear_lm_mod (nonlinear_lm_t()): This module is used to finish the assembly of the nonlinear terms in \((\ell,m)\) space. Derivatives along \(\theta\) and \(\phi\) are handled using recurrence relations….

• grid_space_arrays_mod (grid_space_arrays_t()): This module is used to compute the nonlinear products in physical space \((\theta,\phi)\).

• to_arrays_mod (to_arrays_t())

• dtb_arrays_mod (dtb_arrays_t())

• torsional_oscillations (prep_to_axi(), getto(), gettonext(), gettofinish()): This module contains information for TO calculation and output

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

• dtb_mod (get_dtblm(), get_dh_dtblm()): This module contains magnetic field stretching and advection terms plus a separate omega-effect. It is used for movie output….

• out_movie (store_movie_frame())

• outrot (get_lorentz_torque()): This module handles the writing of several diagnostic files related to the rotation: angular momentum (AM.TAG), drift (drift.TAG), inner core and mantle rotations….

• courant_mod (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_br_v_bcs(), v_rigid_boundary())

• power (get_visc_heat()): This module handles the writing of the power budget

• outmisc_mod (get_ekin_solid_liquid(), get_hemi(), get_helicity()): This module contains several subroutines that can compute and store various informations: helicity (helicity.TAG), heat transfer (heat.TAG), phase field (phase.TAG) and North/South hemisphericity of energies (hemi.TAG)

• outpar_mod (get_fluxes(), get_nlblayers(), get_perppar()): This module is used to compute several time-averaged radial profiles: fluxes, boundary layers, etc.

• geos (calcgeos()): This module is used to compute z-integrated diagnostics such as the degree of geostrophy or the separation of energies between inside and outside the tangent cylinder. This makes use of a local Simpson’s method. This also

• sht

• fields (s_rloc(), ds_rloc(), z_rloc(), dz_rloc(), p_rloc(), b_rloc(), db_rloc(), ddb_rloc(), aj_rloc(), dj_rloc(), w_rloc(), dw_rloc(), ddw_rloc(), xi_rloc(), omega_ic(), omega_ma(), dp_rloc(), phi_rloc()): 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….

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

• physical_parameters (ktops(), kbots(), n_r_lcr(), ktopv(), kbotv()): Module containing the physical parameters

• riteration (riter_t()): This module is used to define an abstract class for the radial loop

• rms (get_nl_rms(), transform_to_lm_rms(), compute_lm_forces(), transform_to_grid_rms()): This module contains the calculation of the RMS force balance and induction terms.

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

Types

• type riter_mod/unknown_type

  Type fields

  • % dtb_arrays [dtb_arrays_t ]

  • % gsa [grid_space_arrays_t ]

  • % nl_lm [nonlinear_lm_t ]

  • % to_arrays [to_arrays_t ]

Subroutines and functions

subroutine riter_mod/initialize(this)

Parameters

this [real ]

subroutine riter_mod/finalize(this)

Parameters

this [real ]

subroutine riter_mod/radialloop(this, l_graph, l_frame, time, timestage, tscheme, dtlast, ltocalc, ltonext, ltonext2, lhelcalc, lpowercalc, lrmscalc, lpresscalc, lpressnext, lviscbccalc, lfluxprofcalc, lperpparcalc, lgeoscalc, lhemicalc, l_probe_out, dsdt, dwdt, dzdt, dpdt, dxidt, dphidt, dbdt, djdt, dvxvhlm, dvxbhlm, dvsrlm, dvxirlm, lorentz_torque_ic, lorentz_torque_ma, br_vt_lm_cmb, br_vp_lm_cmb, br_vt_lm_icb, br_vp_lm_icb, dtrkc, dthkc)

This subroutine handles the main loop over the radial levels. It calls the SH transforms, computes the nonlinear terms on the grid and bring back the quantities in spectral space. This is the most time consuming part of MagIC.

Parameters

• this [real ]

• l_graph [logical ,in]

• l_frame [logical ,in]

• time [real ,in]

• timestage [real ,in]

• tscheme [real ]

• dtlast [real ,in]

• ltocalc [logical ,in]

• ltonext [logical ,in]

• ltonext2 [logical ,in]

• lhelcalc [logical ,in]

• lpowercalc [logical ,in]

• lrmscalc [logical ,in]

• lpresscalc [logical ,in]

• lpressnext [logical ,in]

• lviscbccalc [logical ,in]

• lfluxprofcalc [logical ,in]

• lperpparcalc [logical ,in]

• lgeoscalc [logical ,in]

• lhemicalc [logical ,in]

• l_probe_out [logical ,in]

• dsdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dwdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dzdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dpdt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dxidt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dphidt (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dbdt (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• djdt (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• dvxvhlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dvxbhlm (lm_maxmag,nrstopmag-(nrstartmag)+1) [complex ,out]

• dvsrlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• dvxirlm (lm_max,nrstop-(nrstart)+1) [complex ,out]

• lorentz_torque_ic [real ,out]

• lorentz_torque_ma [real ,out]

• br_vt_lm_cmb (*) [complex ,out] :: product br*vt at CMB

• br_vp_lm_cmb (*) [complex ,out] :: product br*vp at CMB

• br_vt_lm_icb (*) [complex ,out] :: product br*vt at ICB

• br_vp_lm_icb (*) [complex ,out] :: product br*vp at ICB

• dtrkc (nrstop-(nrstart)+1) [real ,out]

• dthkc (nrstop-(nrstart)+1) [real ,out]

Call to

graphout_mpi_header(), prep_to_axi(), get_nl_rms(), get_br_v_bcs(), get_lorentz_torque(), courant(), graphout_mpi(), probe_out(), get_helicity(), get_hemi(), get_visc_heat(), get_nlblayers(), get_fluxes(), get_ekin_solid_liquid(), get_perppar(), calcgeos(), store_movie_frame(), get_dtblm(), gettonext(), getto(), compute_lm_forces(), gettofinish(), get_dh_dtblm()

subroutine riter_mod/transform_to_grid_space(this, nr, nbc, lviscbccalc, lrmscalc, lpresscalc, ltocalc, lpowercalc, lfluxprofcalc, lperpparcalc, lhelcalc, lgeoscalc, lhemicalc, l_frame, lderiv)

This subroutine actually handles the spherical harmonic transforms from (ell,m) space to (theta,phi) space.

Parameters

• this [real ]

• nr [integer ,in]

• nbc [integer ,in]

• lviscbccalc [logical ,in]

• lrmscalc [logical ,in]

• lpresscalc [logical ,in]

• ltocalc [logical ,in]

• lpowercalc [logical ,in]

• lfluxprofcalc [logical ,in]

• lperpparcalc [logical ,in]

• lhelcalc [logical ,in]

• lgeoscalc [logical ,in]

• lhemicalc [logical ,in]

• l_frame [logical ,in]

• lderiv [logical ,in]

Call to

scal_to_spat(), scal_to_grad_spat(), transform_to_grid_rms(), torpol_to_spat(), torpol_to_curl_spat(), pol_to_grad_spat(), torpol_to_dphspat(), pol_to_curlr_spat(), v_rigid_boundary()

subroutine riter_mod/transform_to_lm_space(this, nr, lrmscalc, dvsrlm, dvxirlm, dphidt)

This subroutine actually handles the spherical harmonic transforms from (theta,phi) space to (ell,m) space.

Parameters

• this [real ]

• nr [integer ,in]

• lrmscalc [logical ,in]

• dvsrlm (lm_max) [complex ,out]

• dvxirlm (lm_max) [complex ,out]

• dphidt (lm_max) [complex ,out]

Call to

get_openmp_blocks(), spat_to_qst(), scal_to_sh(), spat_to_sphertor(), transform_to_lm_rms()

get_nl.f90

Types

• type general_arrays_mod/unknown_type

get_td.f90

Description

This module is used to finish the assembly of the nonlinear terms in \((\ell,m)\) space. Derivatives along \(\theta\) and \(\phi\) are handled using recurrence relations.

Quick access

Variables

lm_min

Routines

get_td(), set_zero()

Needed modules

• precision_mod: This module controls the precision used in MagIC

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

• truncation (lm_max(), lm_maxmag(), m_min()): This module defines the grid points and the truncation

• logic (l_anel(), l_conv_nl(), l_corr(), l_heat(), l_anelastic_liquid(), l_mag_nl(), l_mag_kin(), l_mag_lf(), l_conv(), l_mag(), l_chemical_conv(), l_single_matrix(), l_double_curl()): Module containing the logicals that control the run

• radial_functions (r(), or2(), or1(), beta(), epscprof(), or4(), temp0(), orho1(), l_r()): This module initiates all the radial functions (transport properties, density, temperature, cheb transforms, etc.)

• physical_parameters (corfac(), epsc(), n_r_lcr(), epscxi()): Module containing the physical parameters

• blocking (lm2l(), lm2m(), lm2lma(), lm2lms()): Module containing blocking information

• horizontal_data (dlh(), dphi(), dtheta2a(), dtheta3a(), dtheta4a(), dtheta2s(), dtheta3s(), dtheta4s()): Module containing functions depending on longitude and latitude plus help arrays depending on degree and order

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

• fields (w_rloc(), dw_rloc(), ddw_rloc(), z_rloc(), dz_rloc()): 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….

Types

• type nonlinear_lm_mod/unknown_type

  Type fields

  • % advplm (*) [complex ,allocatable]

  • % advrlm (*) [complex ,allocatable]

  • % advtlm (*) [complex ,allocatable]

  • % heattermslm (*) [complex ,allocatable]

  • % vsplm (*) [complex ,allocatable]

  • % vstlm (*) [complex ,allocatable]

  • % vxbplm (*) [complex ,allocatable]

  • % vxbrlm (*) [complex ,allocatable]

  • % vxbtlm (*) [complex ,allocatable]

  • % vxiplm (*) [complex ,allocatable]

  • % vxitlm (*) [complex ,allocatable]

Variables

• nonlinear_lm_mod/lm_min [integer,private]

Subroutines and functions

subroutine nonlinear_lm_mod/initialize(this, lmp_max)

Memory allocation of get_td arrays

Parameters

• this [real ]

• lmp_max [integer ,in]

subroutine nonlinear_lm_mod/finalize(this)

Memory deallocation

Parameters

this [real ]

subroutine nonlinear_lm_mod/set_zero(this)

Set all the arrays to zero

Parameters

this [real ]

subroutine nonlinear_lm_mod/get_td(this, nr, nbc, lpressnext, dvxvhlm, dvxbhlm, dwdt, dzdt, dpdt, dsdt, dxidt, dbdt, djdt)

Purpose of this to calculate time derivatives dwdt,``dzdt``,``dpdt``,``dsdt``,``dxidt``,``dbdt``,``djdt`` and auxiliary arrays dVxBhLM, dVxVhLM from non-linear terms in spectral form

Parameters

• this [real ]

• nr [integer ,in] :: Radial level

• nbc [integer ,in] :: signifies boundary conditions

• lpressnext [logical ,in]

• dvxvhlm (*) [complex ,out]

• dvxbhlm (*) [complex ,out]

• dwdt (*) [complex ,out] :: +CorPol_loc

• dzdt (*) [complex ,out]

• dpdt (*) [complex ,out]

• dsdt (*) [complex ,out]

• dxidt (*) [complex ,out]

• dbdt (*) [complex ,out]

• djdt (*) [complex ,out]

nonlinear_bcs.f90

Quick access

Routines

get_b_nl_bcs(), get_br_v_bcs(), v_rigid_boundary()

Needed modules

• iso_fortran_env (output_unit())

• precision_mod: This module controls the precision used in MagIC

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

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

• radial_functions (r_cmb(), r_icb(), rho0()): This module initiates all the radial functions (transport properties, density, temperature, cheb transforms, etc.)

• physical_parameters (sigma_ratio(), conductance_ma(), prmag(), oek()): Module containing the physical parameters

• horizontal_data (costheta(), sintheta_e2()): Module containing functions depending on longitude and latitude plus help arrays depending on degree and order

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

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

• sht (spat_to_sphertor())

Variables

Subroutines and functions

subroutine nonlinear_bcs/get_br_v_bcs(br, vt, vp, omega, o_r_e_2, o_rho, br_vt_lm, br_vp_lm)

Purpose of this subroutine is to calculate the nonlinear term of the magnetic boundary condition for a conducting mantle or inner core in space (r,lm). Calculation is performed for the theta block:

n_theta_min<=n_theta<=n_theta_min+n_theta_block-1

On input br, vt and vp are given on all phi points and thetas in the specific block. On output the contribution of these grid points to all degree and orders is stored in br_vt_lm and br_vp_lm. Output is [r/sin(theta)*Br*U]=[(0,br_vt_lm,br_vp_lm)]

Parameters

• br (*,*) [real ,in] :: \(r^2 B_r\)

• vt (*,*) [real ,in] :: \(r \sin\theta u_\theta\)

• vp (*,*) [real ,in] :: \(r \sin\theta u_\phi\)

• omega [real ,in] :: rotation rate of mantle or IC

• o_r_e_2 [real ,in] :: \(1/r^2\)

• o_rho [real ,in] :: \(1/\tilde{\rho}\) (anelastic)

• br_vt_lm (lm_max) [complex ,inout]

• br_vp_lm (lm_max) [complex ,inout]

Called from

radialloop()

Call to

spat_to_sphertor()

subroutine nonlinear_bcs/get_b_nl_bcs(bc, br_vt_lm, br_vp_lm, lm_min_b, lm_max_b, b_nl_bc, aj_nl_bc)

Purpose of this subroutine is to calculate the nonlinear term of the magnetic boundary condition for a conducting mantle in physical space (theta,phi), assuming that the conductance of the mantle is much smaller than that of the core. Calculation is performed for the theta block:

n_theta_min<=n_theta<=n_theta_min+n_theta_block-1

Parameters

• bc [character(len=3),in] :: Distinguishes ‘CMB’ and ‘ICB’

• br_vt_lm (lm_max) [complex ,in] :: \(B_r u_\theta/(r^2\sin^2\theta)\)

• br_vp_lm (lm_max) [complex ,in] :: \(B_r u_\phi/(r^2\sin^2\theta)\)

• lm_min_b [integer ,in]

• lm_max_b [integer ,in] :: limits of lm-block

• b_nl_bc (lm_max_b-lm_min_b+1) [complex ,out] :: nonlinear bc for b

• aj_nl_bc (lm_max_b-lm_min_b+1) [complex ,out] :: nonlinear bc for aj

Called from

step_time()

Call to

abortrun()

subroutine nonlinear_bcs/v_rigid_boundary(nr, omega, lderiv, vrr, vtr, vpr, cvrr, dvrdtr, dvrdpr, dvtdpr, dvpdpr)

Purpose of this subroutine is to set the velocities and their derivatives at a fixed boundary. While vt is zero, since we only allow for rotation about the \(z\)-axis, vp= r \sin(theta) v_phi = r**2 sin(theta)**2 omega and cvr= r**2 * radial component of (\curl v) = r**2  2 cos(theta) omega

Parameters

• nr [integer ,in] :: no of radial grid point

• omega [real ,in] :: boundary rotation rate

• lderiv [logical ,in] :: derivatives required ?

• vrr (*,*) [real ,out]

• vtr (*,*) [real ,out]

• vpr (*,*) [real ,out]

• cvrr (*,*) [real ,out]

• dvrdtr (*,*) [real ,out]

• dvrdpr (*,*) [real ,out]

• dvtdpr (*,*) [real ,out]

• dvpdpr (*,*) [real ,out]

Called from

transform_to_grid_space()