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, lphasecalc, 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]

• lphasecalc [logical ,in]

• l_probe_out [logical ,in]

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

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

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

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

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

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

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

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

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

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

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

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

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

Called from:

step_time()

rIteration.f90

Description

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

Quick access

Types:

riter_t

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/riter_t

Variables

• riteration/unknown_interface [private]

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

Types:

riter_single_t

Variables:

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(), l_dtrmagspec()): 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 \((\theta,\phi)\).

• 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()): This module handles the storage of the relevant diagnostics in the public array frames(*) and then the writing of the corresponding movie files

• 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(), v_center_sphere())

• 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(), 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

• special (ellip_fac_icb(), l_radial_flow_bc()): This module contains all variables for the case of an imposed IC dipole, an imposed external magnetic field and a special boundary forcing to excite inertial modes

Types

• type  riter_mod/riter_single_t

  Type fields:

  • % gsa [grid_space_arrays_t ]

  • % nl_lm [nonlinear_lm_t ]

Variables

• riter_mod/finalize [private]

• riter_mod/initialize [private]

• riter_mod/radialloop [private]

• riter_mod/transform_to_grid_space [private]

• riter_mod/transform_to_lm_space [private]

get_nl.f90

Quick access

Types:

general_arrays_t

Types

• type  general_arrays_mod/general_arrays_t

Variables

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

Types:

nonlinear_lm_t

Variables:

get_dbdt, get_dpdt, get_dsdt, get_dwdt, get_dwdt_double_curl, get_dxidt, get_dzdt, lm_min, 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(), 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/nonlinear_lm_t

  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/finalize [private]

• nonlinear_lm_mod/get_dbdt [private]

• nonlinear_lm_mod/get_dpdt [private]

• nonlinear_lm_mod/get_dsdt [private]

• nonlinear_lm_mod/get_dwdt [private]

• nonlinear_lm_mod/get_dwdt_double_curl [private]

• nonlinear_lm_mod/get_dxidt [private]

• nonlinear_lm_mod/get_dzdt [private]

• nonlinear_lm_mod/initialize [private]

• nonlinear_lm_mod/lm_min [integer,private]

• nonlinear_lm_mod/set_zero [private]

nonlinear_bcs.f90

Quick access

Routines:

get_b_nl_bcs(), get_br_v_bcs(), v_center_sphere(), v_rigid_boundary()

Needed modules

• iso_fortran_env (output_unit())

• precision_mod: This module controls the precision used in MagIC

• blocking (lm2()): Module containing blocking information

• truncation (n_phi_max(), l_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(), phi(), sintheta()): Module containing functions depending on longitude and latitude plus help arrays depending on degree and order

• constants (two(), y10_norm(), y11_norm(), zero()): 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 (*) [complex ,inout] :: br*vt/(sin(theta)**2*r**2)

• br_vp_lm (*) [complex ,inout] :: br*(vp/(sin(theta)**2*r**2)-omega_ma)

Call to:

spat_to_sphertor()

subroutine  nonlinear_bcs/get_b_nl_bcs(bc, br_vt_lm, br_vp_lm, 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.

Parameters:

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

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

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

• b_nl_bc (*) [complex ,out] :: nonlinear bc for b

• aj_nl_bc (*) [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]

subroutine  nonlinear_bcs/v_center_sphere(ddw, vrr, vtr, vpr)

This routine is only called for full sphere computations to construct a vector field at the center of the the sphere. At the center, we have wlm propto r^{l+1} and so vr = d2wlm/dr2 for l=1, 0 otherwise vtheta, vphi = sht(1/l*ddwlm, 0) for l=1, 0 otherwise

Parameters:

• ddw (*) [complex ,in]

• vrr (*,*) [real ,out]

• vtr (*,*) [real ,out]

• vpr (*,*) [real ,out]