Pre-calculations

preCalc.f90

Description

This module is used to handle some pre-calculations of constants (moment of inertia, mass, volumes), determine the timesteps for I/O and fix boundary values for temperature/entropy and chemical composition

Quick access

Variables:

get_hit_times

Routines:

precalc(), precalctimes(), writeinfo()

Needed modules

• iso_fortran_env (output_unit())

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

• num_param: Module containing numerical and control parameters

• output_data: This module contains the parameters for output control

• precision_mod: This module controls the precision used in MagIC

• truncation (n_r_max(), l_max(), minc(), n_r_ic_max(), nalias(), n_cheb_ic_max(), m_max(), n_cheb_max(), m_min(), lm_max(), n_phi_max(), n_theta_max()): This module defines the grid points and the truncation

• init_fields (bots(), tops(), s_bot(), s_top(), n_s_bounds(), l_reset_t(), topxi(), botxi(), xi_bot(), xi_top(), n_xi_bounds(), omega_ma1(), omegaosz_ma1(), omega_ic1(), omegaosz_ic1()): This module is used to construct the initial solution.

• parallel_mod (rank(), n_procs(), rank_with_r_lcr()): This module contains the blocking information

• logic (l_mag(), l_cond_ic(), l_non_rot(), l_mag_lf(), l_newmap(), l_anel(), l_heat(), l_anelastic_liquid(), l_cmb_field(), l_save_out(), l_to(), l_tomovie(), l_r_field(), l_movie(), l_lcr(), l_dt_cmb_field(), l_non_adia(), l_temperature_diff(), l_chemical_conv(), l_probe(), l_precession(), l_finite_diff(), l_full_sphere()): Module containing the logicals that control the run

• radial_data (radial_balance()): This module defines the MPI decomposition in the radial direction.

• radial_functions (rscheme_oc(), temp0(), r_cmb(), ogrun(), r_surface(), visc(), or2(), r(), r_icb(), dltemp0(), beta(), rho0(), rgrav(), dbeta(), alpha0(), dentropy0(), sigma(), lambda(), dlkappa(), kappa(), dlvisc(), dllambda(), divktemp0(), radial(), transportproperties(), l_r()): This module initiates all the radial functions (transport properties, density, temperature, cheb transforms, etc.)

• physical_parameters (nvareps(), pr(), prmag(), ra(), rascaled(), ek(), ekscaled(), opr(), opm(), o_sr(), radratio(), sigma_ratio(), corfac(), lffac(), buofac(), polind(), nvarcond(), nvardiff(), nvarvisc(), rho_ratio_ic(), rho_ratio_ma(), epsc(), epsc0(), ktops(), kbots(), interior_model(), r_lcr(), n_r_lcr(), mode(), tmagcon(), oek(), bn(), imagcon(), ktopxi(), kbotxi(), epscxi(), epscxi0(), sc(), osc(), chemfac(), raxi(), po(), prec_angle()): Module containing the physical parameters

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

• integration (rint_r()): Radial and geostrophic integration functions

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

• special (l_curr(), fac_loop(), loopradratio(), amp_curr(), le(), n_imp(), l_imp(), l_radial_flow_bc(), ellipticity_cmb(), ellip_fac_cmb(), ellipticity_icb(), ellip_fac_icb(), tide_fac20(), tide_fac22p(), tide_fac22n(), amp_tide()): 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

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

Variables

• precalculations/get_hit_times [private]

Subroutines and functions

subroutine  precalculations/precalc(tscheme)

Purpose of this subroutine is to initialize the calc values, arrays, constants that are used all over the code.

Parameters:

tscheme [real ]

Called from:

magic

Call to:

radial(), transportproperties(), horizontal(), rint_r(), abortrun(), logwrite()

subroutine  precalculations/precalctimes(time, n_time_step)

Precalc. after time, time and dt has been read from startfile.

Parameters:

• time [real ,inout] :: Current time

• n_time_step [integer ,inout] :: Index of time loop

Called from:

magic

subroutine  precalculations/writeinfo(n_out)

Purpose of this subroutine is to write the namelist to file unit n_out. This file has to be open before calling this routine.

Parameters:

n_out [integer ,in] :: Normalized OC surface :’’,ES14.6)’) surf_cmb

Called from:

magic

Call to:

abortrun()

radial.f90

Description

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

Quick access

Variables:

alpha0, alpha1, alpha2, beta, cheb_ic, cheb_int, cheb_int_ic, cheb_norm_ic, chebt_ic, chebt_ic_even, d2cheb_ic, d2temp0, dbeta, dcheb_ic, ddbeta, ddlalpha0, ddltemp0, ddlvisc, dentropy0, divktemp0, dlalpha0, dlkappa, dllambda, dltemp0, dlvisc, dr_fac_ic, dr_top_ic, dxicond, epscprof, getbackground, getentropygradient, jvarcon, kappa, l_r, lambda, ndd_costf1, ndd_costf1_ic, ndd_costf2_ic, ndi_costf2_ic, o_r_ic, o_r_ic2, ogrun, or1, or2, or3, or4, orho1, orho2, otemp1, polynomialbackground, r, r_cmb, r_ic, r_icb, r_surface, rgrav, rho0, sigma, temp0, visc

Routines:

finalize_radial_functions(), initialize_radial_functions(), radial(), transportproperties()

Needed modules

• iso_fortran_env (output_unit())

• truncation (n_r_max(), n_cheb_max(), n_r_ic_max(), fd_ratio(), rcut_l(), fd_stretch(), fd_order(), fd_order_bound(), l_max(), n_cheb_ic_max()): This module defines the grid points and the truncation

• algebra (prepare_mat(), solve_mat())

• constants (sq4pi(), one(), two(), three(), four(), half(), pi()): module containing constants and parameters used in the code.

• physical_parameters: Module containing the physical parameters

• logic (l_mag(), l_cond_ic(), l_heat(), l_anelastic_liquid(), l_isothermal(), l_anel(), l_non_adia(), l_centrifuge(), l_temperature_diff(), l_single_matrix(), l_var_l(), l_finite_diff(), l_newmap(), l_full_sphere(), l_chemical_conv()): Module containing the logicals that control the run

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

• chebyshev_polynoms_mod

• cosine_transform_odd: This module contains the built-in type I discrete Cosine Transforms. This implementation is based on Numerical Recipes and FFTPACK. This only works for n_r_max-1 = 2**a 3**b 5**c, with a,b,c integers….

• cosine_transform_even

• radial_scheme (type_rscheme()): This is an abstract type that defines the radial scheme used in MagIC

• chebyshev (type_cheb_odd())

• finite_differences (type_fd()): This module is used to calculate the radial grid when finite differences are requested

• radial_der (get_dr()): Radial derivatives functions

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

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

• parallel_mod (rank()): This module contains the blocking information

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

• num_param (alph1(), alph2()): Module containing numerical and control parameters

Variables

• radial_functions/alpha0 (*) [real,allocatable/public]

  d log (alpha) / dr

• radial_functions/alpha1 [real,public]

  Input parameter for non-linear map to define degree of spacing (0.0:2.0)

• radial_functions/alpha2 [real,public]

  Input parameter for non-linear map to define central point of different spacing (-1.0:1.0)

• radial_functions/beta (*) [real,allocatable/public]

  Inverse of density scale height drho0/rho0

• radial_functions/cheb_ic (*,*) [real,allocatable/public]

  Chebyshev polynomials for IC

• radial_functions/cheb_int (*) [real,allocatable/public]

  Array for cheb integrals

• radial_functions/cheb_int_ic (*) [real,allocatable/public]

  Array for integrals of cheb for IC

• radial_functions/cheb_norm_ic [real,public]

  Chebyshev normalisation for IC

• radial_functions/chebt_ic [costf_odd_t,public]

• radial_functions/chebt_ic_even [costf_even_t,public]

• radial_functions/d2cheb_ic (*,*) [real,allocatable/public]

  Second radial derivative cheb_ic

• radial_functions/d2temp0 (*) [real,allocatable/private]

  Second rad. derivative of background temperature

• radial_functions/dbeta (*) [real,allocatable/public]

  Radial gradient of beta

• radial_functions/dcheb_ic (*,*) [real,allocatable/public]

  First radial derivative of cheb_ic

• radial_functions/ddbeta (*) [real,allocatable/public]

  2nd derivative of beta

• radial_functions/ddlalpha0 (*) [real,allocatable/public]

  \(d/dr(1/alpha d\alpha/dr)\)

• radial_functions/ddltemp0 (*) [real,allocatable/public]

  \(d/dr(1/T dT/dr)\)

• radial_functions/ddlvisc (*) [real,allocatable/public]

  2nd derivative of kinematic viscosity

• radial_functions/dentropy0 (*) [real,allocatable/public]

  Radial gradient of background entropy

• radial_functions/divktemp0 (*) [real,allocatable/public]

  Term for liquid anelastic approximation

• radial_functions/dlalpha0 (*) [real,allocatable/public]

  \(1/\alpha d\alpha/dr\)

• radial_functions/dlkappa (*) [real,allocatable/public]

  Derivative of thermal diffusivity

• radial_functions/dllambda (*) [real,allocatable/public]

  Derivative of magnetic diffusivity

• radial_functions/dltemp0 (*) [real,allocatable/public]

  Inverse of temperature scale height

• radial_functions/dlvisc (*) [real,allocatable/public]

  Derivative of kinematic viscosity

• radial_functions/dr_fac_ic [real,public]

  For IC: \(2/(2 r_i)\)

• radial_functions/dr_top_ic (*) [real,allocatable/public]

  Derivative in real space for r=r_i

• radial_functions/dxicond (*) [real,allocatable/public]

  Radial gradient of chemical composition

• radial_functions/epscprof (*) [real,allocatable/public]

  Sources in heat equations

• radial_functions/getbackground [private]

  ‘)

• radial_functions/getentropygradient [private]

• radial_functions/jvarcon (*) [real,allocatable/public]

  Analytical solution for toroidal field potential aj (see init_fields.f90)

• radial_functions/kappa (*) [real,allocatable/public]

  Thermal diffusivity

• radial_functions/l_r (*) [integer,allocatable/public]

  Variable degree with radius

• radial_functions/lambda (*) [real,allocatable/public]

  Array of magnetic diffusivity

• radial_functions/ndd_costf1 [integer,public]

  Radii for transform

• radial_functions/ndd_costf1_ic [integer,private]

  Radii for transform

• radial_functions/ndd_costf2_ic [integer,private]

  Radii for transform

• radial_functions/ndi_costf2_ic [integer,private]

  Radii for transform

• radial_functions/o_r_ic (*) [real,allocatable/public]

  Inverse of IC radii

• radial_functions/o_r_ic2 (*) [real,allocatable/public]

  Inverse of square of IC radii

• radial_functions/ogrun (*) [real,allocatable/public]

  \(1/\Gamma\)

• radial_functions/or1 (*) [real,allocatable/public]

  \(1/r\)

• radial_functions/or2 (*) [real,allocatable/public]

  \(1/r^2\)

• radial_functions/or3 (*) [real,allocatable/public]

  \(1/r^3\)

• radial_functions/or4 (*) [real,allocatable/public]

  \(1/r^4\)

• radial_functions/orho1 (*) [real,allocatable/public]

  \(1/\tilde{\rho}\)

• radial_functions/orho2 (*) [real,allocatable/public]

  \(1/\tilde{\rho}^2\)

• radial_functions/otemp1 (*) [real,allocatable/public]

  Inverse of background temperature

• radial_functions/polynomialbackground [private]

• radial_functions/r (*) [real,allocatable/public]

  radii

• radial_functions/r_cmb [real,public]

  OC radius

• radial_functions/r_ic (*) [real,allocatable/public]

  IC radii

• radial_functions/r_icb [real,public]

  IC radius

• radial_functions/r_surface [real,public]

  Surface radius for extrapolation in units of (r_cmb-r_icb)

• radial_functions/rgrav (*) [real,allocatable/public]

  Buoyancy term dtemp0/Di

• radial_functions/rho0 (*) [real,allocatable/public]

  Inverse of background density

• radial_functions/sigma (*) [real,allocatable/public]

  Electrical conductivity

• radial_functions/temp0 (*) [real,allocatable/public]

  Background temperature

• radial_functions/visc (*) [real,allocatable/public]

  Kinematic viscosity

Subroutines and functions

subroutine  radial_functions/initialize_radial_functions()

Initial memory allocation

Called from:

magic

subroutine  radial_functions/finalize_radial_functions()

Memory deallocation of radial functions

Called from:

magic

subroutine  radial_functions/radial()

Calculates everything needed for radial functions, transforms etc.

Called from:

precalc()

Call to:

logwrite(), cheb_grid(), get_chebs_even()

subroutine  radial_functions/transportproperties()

Calculates the transport properties: electrical conductivity, kinematic viscosity and thermal conductivity.

Called from:

precalc()

Call to:

abortrun()

horizontal.f90

Description

Module containing functions depending on longitude and latitude plus help arrays depending on degree and order

Quick access

Variables:

cosn_theta_e2, costheta, dlh, dphi, dpl0eq, dtheta1a, dtheta1s, dtheta2a, dtheta2s, dtheta3a, dtheta3s, dtheta4a, dtheta4s, gauss, hdif_b, hdif_s, hdif_v, hdif_xi, n_theta_cal2ord, n_theta_ord2cal, o_sin_theta, o_sin_theta_e2, phi, sintheta, sintheta_e2, theta_ord

Routines:

finalize_horizontal_data(), gauleg(), horizontal(), initialize_horizontal_data()

Needed modules

• truncation (l_max(), n_theta_max(), n_phi_max(), nlat_padded(), lm_max(), n_m_max(), minc(), m_min(), m_max(), l_axi()): This module defines the grid points and the truncation

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

• physical_parameters (ek()): Module containing the physical parameters

• num_param (difeta(), difnu(), difkap(), ldif(), ldifexp(), difchem()): Module containing numerical and control parameters

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

• logic (l_non_rot(), l_scramble_theta()): Module containing the logicals that control the run

• plms_theta (plm_theta())

• fft: This module contains the native subroutines used to compute FFT’s. They are based on the FFT99 package from Temperton: http://www.cesm.ucar.edu/models/cesm1.2/cesm/cesmBbrowser/html_code/cam/fft99.F90.html

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

• 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

Variables

• horizontal_data/cosn_theta_e2 (*) [real,allocatable/public]

  \(\cos\theta/\sin^2\theta\)

• horizontal_data/costheta (*) [real,allocatable/public]

  \(\cos\theta\)

• horizontal_data/dlh (*) [real,allocatable/public]

  \(\ell(\ell+1)\)

• horizontal_data/dphi (*) [complex,allocatable/public]

  \(\mathrm{i} m\)

• horizontal_data/dpl0eq (*) [real,allocatable/public]

• horizontal_data/dtheta1a (*) [real,allocatable/public]

• horizontal_data/dtheta1s (*) [real,allocatable/public]

• horizontal_data/dtheta2a (*) [real,allocatable/public]

• horizontal_data/dtheta2s (*) [real,allocatable/public]

• horizontal_data/dtheta3a (*) [real,allocatable/public]

• horizontal_data/dtheta3s (*) [real,allocatable/public]

• horizontal_data/dtheta4a (*) [real,allocatable/public]

• horizontal_data/dtheta4s (*) [real,allocatable/public]

• horizontal_data/gauss (*) [real,allocatable/public]

• horizontal_data/hdif_b (*) [real,allocatable/public]

• horizontal_data/hdif_s (*) [real,allocatable/public]

• horizontal_data/hdif_v (*) [real,allocatable/public]

• horizontal_data/hdif_xi (*) [real,allocatable/public]

• horizontal_data/n_theta_cal2ord (*) [integer,allocatable/public]

• horizontal_data/n_theta_ord2cal (*) [integer,allocatable/public]

• horizontal_data/o_sin_theta (*) [real,allocatable/public]

  \(1/\sin\theta\)

• horizontal_data/o_sin_theta_e2 (*) [real,allocatable/public]

  \(1/\sin^2\theta\)

• horizontal_data/phi (*) [real,allocatable/public]

• horizontal_data/sintheta (*) [real,allocatable/public]

  \(\sin\theta\)

• horizontal_data/sintheta_e2 (*) [real,allocatable/public]

  \(\sin^2\theta\)

• horizontal_data/theta_ord (*) [real,allocatable/public]

  Gauss points (unscrambled)

Subroutines and functions

subroutine  horizontal_data/initialize_horizontal_data()

Memory allocation of horizontal functions

Called from:

magic

subroutine  horizontal_data/finalize_horizontal_data()

Memory deallocation of horizontal functions

Called from:

magic

Call to:

finalize_fft()

subroutine  horizontal_data/horizontal()

Calculates functions of \(\theta\) and \(\phi\), for example the Legendre functions, and functions of degree \(\ell\) and order \(m\) of the legendres.

Called from:

precalc()

Call to:

gauleg(), plm_theta(), init_fft()

subroutine  horizontal_data/gauleg(sinthmin, sinthmax, theta_ord, gauss)

Subroutine is based on a NR code. Calculates N zeros of legendre polynomial P(l=N) in the interval [sinThMin,sinThMax]. Zeros are returned in radiants theta_ord(i) The respective weights for Gauss-integration are given in gauss(i).

Parameters:

• sinthmin [real ,in] :: lower bound in radiants

• sinthmax [real ,in] :: upper bound in radiants

• theta_ord (*) [real ,out] :: zeros cos(theta)

• gauss (*) [real ,out] :: associated Gauss-Legendre weights

Called from:

horizontal(), initialize_transforms()