Radial derivatives and integration

radial_derivatives.f90

Description

Radial derivatives functions

Quick access

Variables:

bulk_to_ghost, exch_ghosts, get_dcheb, get_dcheb_complex, get_dcheb_real_1d, get_ddcheb, get_dddcheb, get_ddddr_ghost, get_dddr, get_ddr, get_ddr_ghost, get_ddr_rloc, get_dr, get_dr_real_1d, get_dr_rloc, work_1d_real

Routines:

finalize_der_arrays(), initialize_der_arrays()

Needed modules

Variables

  • radial_der/bulk_to_ghost [public]
  • radial_der/exch_ghosts [public]
  • radial_der/get_dcheb [private]
  • radial_der/get_dcheb_complex [private]
  • radial_der/get_dcheb_real_1d [private]
  • radial_der/get_ddcheb [private]
  • radial_der/get_dddcheb [private]
  • radial_der/get_ddddr_ghost [public]
  • radial_der/get_dddr [public]
  • radial_der/get_ddr [public]
  • radial_der/get_ddr_ghost [public]
  • radial_der/get_ddr_rloc [public]
  • radial_der/get_dr [public]
  • radial_der/get_dr_real_1d [private]
  • radial_der/get_dr_rloc [public]
  • radial_der/work (*,*) [complex,private/allocatable]
  • radial_der/work_1d_real (*) [real,private/allocatable]

Subroutines and functions

subroutine  radial_der/initialize_der_arrays(n_r_max, llm, ulm)

Allocate work arrays to compute derivatives

Parameters:

  • n_r_max [integer ,in]

  • llm [integer ,in]

  • ulm [integer ,in]

Called from:

magic

subroutine  radial_der/finalize_der_arrays()

Deallocate work arrays

Called from:

magic

radial_derivatives_even.f90

Quick access

Variables:

get_dcheb_even, get_ddcheb_even

Routines:

get_ddr_even(), get_ddrns_even(), get_drns_even()

Needed modules

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

  • precision_mod: This module controls the precision used in MagIC

  • 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

Variables

  • radial_der_even/get_dcheb_even [private]
  • radial_der_even/get_ddcheb_even [private]

Subroutines and functions

subroutine  radial_der_even/get_ddr_even(f, df, ddf, n_f_max, n_f_start, n_f_stop, n_r_max, n_cheb_max, dr_fac, work1, work2, chebt_odd, chebt_even)

Returns first radial derivative df and second radial derivative ddf of the input function f. Array f(n_f_max,*) may contain several functions numbered by the first index. The subroutine calculates the derivatives of the functions f(n_f_start,*) to f(n_f_stop) by transforming to a Chebychev representation using n_r_max radial grid points. The cheb transforms have to be initialized by calling init_costf1 and init_costf2.

Parameters:

  • f (n_f_max,n_r_max) [complex ,in]

  • df (n_f_max,n_r_max) [complex ,out] :: first derivative of f

  • ddf (n_f_max,n_r_max) [complex ,out] :: second derivative of f

  • n_f_max [integer ,in,] :: first dim of f

  • n_f_start [integer ,in] :: first function to be treated

  • n_f_stop [integer ,in] :: last function to be treated

  • n_r_max [integer ,in,] :: number of radial grid points

  • n_cheb_max [integer ,in] :: number of cheb modes

  • dr_fac [real ,in] :: mapping factor

  • work1 (n_f_max,n_r_max) [complex ,out] :: work array needed for costf

  • work2 (n_f_max,n_r_max) [complex ,out] :: work array needed for costf

  • chebt_odd [costf_odd_t ,in]

  • chebt_even [costf_even_t ,in]

Called from:

get_mag_ic_rhs_imp()

subroutine  radial_der_even/get_drns_even(f, df, n_f_max, n_f_start, n_f_stop, n_r_max, n_cheb_max, dr_fac, work1, chebt_odd, chebt_even)

Returns first rarial derivative df. Array f(n_f_max,*) may contain several functions numbered by the first index. The subroutine calculates the derivative of the functions f(n_f_start,*) to f(n_f_stop) by transforming to a Chebychev representation using n_r_max radial grid points. The cheb transforms have to be initialized by calling init_costf1 and init_costf2.

Parameters:

  • f (n_f_max,n_r_max) [complex ,inout]

  • df (n_f_max,n_r_max) [complex ,out] :: first derivative of f

  • n_f_max [integer ,in,] :: first dim of f

  • n_f_start [integer ,in] :: first function to be treated

  • n_f_stop [integer ,in] :: last function to be treated

  • n_r_max [integer ,in,] :: number of radial grid points

  • n_cheb_max [integer ,in] :: number of cheb modes

  • dr_fac [real ,in] :: mapping factor

  • work1 (n_f_max,n_r_max) [complex ,out] :: work array needed for costf

  • chebt_odd [costf_odd_t ,in]

  • chebt_even [costf_even_t ,in]

Called from:

fields_average(), calc_dtb_frame_ic()

subroutine  radial_der_even/get_ddrns_even(f, df, ddf, n_f_max, n_f_start, n_f_stop, n_r_max, n_cheb_max, dr_fac, work1, chebt_odd, chebt_even)

Returns first radial derivative df and second radial derivative ddf of the input function f. Array f(n_f_max,*) may contain several functions numbered by the first index. The subroutine calculates the derivatives of the functions f(n_f_start,*) to f(n_f_stop) by transforming to a Chebychev representation using n_r_max radial grid points. The cheb transforms have to be initialized by calling init_costf1 and init_costf2.

Parameters:

  • f (n_f_max,n_r_max) [complex ,inout]

  • df (n_f_max,n_r_max) [complex ,out] :: first derivative of f

  • ddf (n_f_max,n_r_max) [complex ,out] :: second derivative of f

  • n_f_max [integer ,in,] :: first dim of f

  • n_f_start [integer ,in] :: first function to be treated

  • n_f_stop [integer ,in] :: last function to be treated

  • n_r_max [integer ,in,] :: number of radial grid points

  • n_cheb_max [integer ,in] :: number of cheb modes

  • dr_fac [real ,in] :: mapping factor

  • work1 (n_f_max,n_r_max) [complex ,out] :: work array needed for costf

  • chebt_odd [costf_odd_t ,in]

  • chebt_even [costf_even_t ,in]

Called from:

fields_average()

integration.f90

Description

Radial and geostrophic integration functions

Quick access

Variables:

cylmean_itc, cylmean_otc, simps

Routines:

rint_r(), rintic()

Needed modules

Variables

  • integration/cylmean_itc [public]
  • integration/cylmean_otc [public]
  • integration/simps [public]

Subroutines and functions

function  integration/rintic(f, nrmax, drfac, chebt)

This function performs the radial integral over a function f that is given on the appropriate nRmax radial Chebyshev grid points.

Parameters:

  • f (nrmax) [real ,inout] :: This is zero order contribution

  • nrmax [integer ,in,] :: Only even chebs for IC

  • drfac [real ,in]

  • chebt [costf_odd_t ,in]

Return:

rintic [real ]

Called from:

get_e_mag(), get_power()

function  integration/rint_r(f, r, r_scheme)

Same as function rInt but for a radial dependent mapping function dr_fac2.

Parameters:

  • f (*) [real ,in] :: Input function

  • r (*) [real ,in] :: Radius

  • r_scheme [real ] :: Radial scheme (FD or Cheb)

Return:

rint [real ]

Called from:

get_poltorrms(), getdlm(), get_e_kin(), get_u_square(), get_e_mag(), outhemi(), outhelicity(), outheat(), outphase(), get_onset(), outperppar(), get_angular_moment(), get_angular_moment_rloc(), output(), get_power(), precalc(), get_amplitude(), updatewp()