!!******************************************************************************
!!
!! This file is part of the AMUN source code, a program to perform
!! Newtonian or relativistic magnetohydrodynamical simulations on uniform or
!! adaptive mesh.
!!
!! Copyright (C) 2008-2020 Grzegorz Kowal <grzegorz@amuncode.org>
!!
!! This program is free software: you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation, either version 3 of the License, or
!! (at your option) any later version.
!!
!! This program is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with this program. If not, see <http://www.gnu.org/licenses/>.
!!
!!******************************************************************************
!!
!! module: REFINEMENT
!!
!! This module handles the error estimation and refinement criterion
!! determination.
!!
!!
!!******************************************************************************
!
module refinement
#ifdef PROFILE
! import external subroutines
!
use timers, only : set_timer, start_timer, stop_timer
#endif /* PROFILE */
! module variables are not implicit by default
!
implicit none
#ifdef PROFILE
! timer indices
!
integer , save :: iri, irc
#endif /* PROFILE */
! refinement criterion parameters
!
real(kind=8), save :: crefmin = 2.0d-01
real(kind=8), save :: crefmax = 8.0d-01
real(kind=8), save :: vortmin = 1.0d-03
real(kind=8), save :: vortmax = 1.0d-01
real(kind=8), save :: currmin = 1.0d-03
real(kind=8), save :: currmax = 1.0d-01
real(kind=8), save :: epsref = 1.0d-02
! flags for variable included in the refinement criterion calculation
!
logical, dimension(:), allocatable, save :: qvar_ref
logical , save :: vort_ref = .false.
logical , save :: curr_ref = .false.
! by default everything is private
!
private
! declare public subroutines
!
public :: initialize_refinement, finalize_refinement, print_refinement
public :: check_refinement_criterion
!- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
contains
!
!===============================================================================
!!
!!*** PUBLIC SUBROUTINES *****************************************************
!!
!===============================================================================
!
!===============================================================================
!
! subroutine INITIALIZE_REFINEMENT:
! --------------------------------
!
! Subroutine initializes module REFINEMENT.
!
! Arguments:
!
! verbose - flag determining if the subroutine should be verbose;
! status - return flag of the procedure execution status;
!
!===============================================================================
!
subroutine initialize_refinement(verbose, status)
! import external procedures and variables
!
use equations , only : magnetized, nv, pvars
use parameters, only : get_parameter
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
logical, intent(in) :: verbose
integer, intent(out) :: status
! local variables
!
logical :: test
integer :: p
character(len=255) :: variables = "dens pres"
!
!-------------------------------------------------------------------------------
!
#ifdef PROFILE
! set timer descriptions
!
call set_timer('refinement:: initialization', iri)
call set_timer('refinement:: criterion' , irc)
! start accounting time for module initialization/finalization
!
call start_timer(iri)
#endif /* PROFILE */
! reset the status flag
!
status = 0
! get the refinement parameters
!
call get_parameter("crefmin", crefmin)
call get_parameter("crefmax", crefmax)
call get_parameter("vortmin", vortmin)
call get_parameter("vortmax", vortmax)
call get_parameter("currmin", currmin)
call get_parameter("currmax", currmax)
call get_parameter("epsref" , epsref )
! get variables to include in the refinement criterion calculation
!
call get_parameter("refinement_variables", variables)
! allocate vector for indicators, which variables are taken into account in
! calculating the refinement criterion
!
allocate(qvar_ref(nv))
! check which primitive variable is used to determine the refinement criterion
!
do p = 1, nv
qvar_ref(p) = index(variables, trim(pvars(p))) > 0
end do ! p = 1, nv
! turn on refinement based on vorticity if specified
!
vort_ref = index(variables, 'vort') > 0
! check if any resonable variable controls the refinement
!
test = any(qvar_ref(:)) .or. vort_ref
! turn on refinement based on current density if specified
!
if (magnetized) then
curr_ref = index(variables, 'curr') > 0 .or. index(variables, 'jabs') > 0
test = test .or. curr_ref
end if
! check if there is any variable selected to control refinement
!
if (.not. test) then
if (verbose) then
write(*,*)
write(*,"(1x,a)") "ERROR!"
write(*,"(1x,a)") "No or wrong variable selected to control" // &
" the refinement."
write(*,"(1x,a)") "Available control variables: any primitive" // &
" variable, or 'vort' for the magnitude of" // &
" vorticity, or 'curr' for the magnitude of" // &
" current density."
end if
status = 1
end if
if (crefmin > crefmax .or. crefmin < 0.0d+00) then
if (verbose) then
write(*,*)
write(*,"(1x,a)") "ERROR!"
write(*,"(1x,a)") "Wrong 'crefmin' or 'crefmax' parameters."
write(*,"(1x,a)") "Both should be positive and 'crefmin' <= 'crefmax'."
end if
status = 1
end if
if (epsref < 0.0d+00) then
if (verbose) then
write(*,*)
write(*,"(1x,a)") "ERROR!"
write(*,"(1x,a)") "Wrong 'epsref' parameters."
write(*,"(1x,a)") "It should be positive."
end if
status = 1
end if
if (vortmin > vortmax .or. vortmin < 0.0d+00) then
if (verbose) then
write(*,*)
write(*,"(1x,a)") "ERROR!"
write(*,"(1x,a)") "Wrong 'vortmin' or 'vortmax' parameters."
write(*,"(1x,a)") "Both should be positive and 'vortmin' <= 'vortmax'."
end if
status = 1
end if
if ((currmin > currmax .or. currmin < 0.0d+00) .and. magnetized) then
if (verbose) then
write(*,*)
write(*,"(1x,a)") "ERROR!"
write(*,"(1x,a)") "Wrong 'currmin' or 'currmax' parameters."
write(*,"(1x,a)") "Both should be positive and 'currmin' <= 'currmax'."
end if
status = 1
end if
#ifdef PROFILE
! stop accounting time for module initialization/finalization
!
call stop_timer(iri)
#endif /* PROFILE */
!-------------------------------------------------------------------------------
!
end subroutine initialize_refinement
!
!===============================================================================
!
! subroutine FINALIZE_REFINEMENT:
! ------------------------------
!
! Subroutine releases memory used by the module variables.
!
! Arguments:
!
! status - return flag of the procedure execution status;
!
!===============================================================================
!
subroutine finalize_refinement(status)
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
integer, intent(out) :: status
!
!-------------------------------------------------------------------------------
!
#ifdef PROFILE
! start accounting time for module initialization/finalization
!
call start_timer(iri)
#endif /* PROFILE */
! reset the status flag
!
status = 0
! deallocate refined variable indicators
!
if (allocated(qvar_ref)) deallocate(qvar_ref)
#ifdef PROFILE
! stop accounting time for module initialization/finalization
!
call stop_timer(iri)
#endif /* PROFILE */
!-------------------------------------------------------------------------------
!
end subroutine finalize_refinement
!
!===============================================================================
!
! subroutine PRINT_REFINEMENT:
! ---------------------------
!
! Subroutine prints module parameters.
!
! Arguments:
!
! verbose - flag determining if the subroutine should be verbose;
!
!===============================================================================
!
subroutine print_refinement(verbose)
! import external procedures and variables
!
use helpers , only : print_section, print_parameter
use equations, only : magnetized, pvars, nv
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
logical, intent(in) :: verbose
! local variables
!
character(len=80) :: rvars = "", msg
character(len=64) :: sfmt
integer :: p
!
!-------------------------------------------------------------------------------
!
if (verbose) then
rvars = ""
do p = 1, nv
if (qvar_ref(p)) rvars = adjustl(trim(rvars) // ' ' // trim(pvars(p)))
end do
if (vort_ref) then
rvars = adjustl(trim(rvars) // ' vort')
end if
if (magnetized .and. curr_ref) then
rvars = adjustl(trim(rvars) // ' curr')
end if
call print_section(verbose, "Refinement")
call print_parameter(verbose, "refined variables", rvars)
sfmt = "(es9.2,1x,'...',1x,es9.2)"
write(msg,sfmt) crefmin, crefmax
call print_parameter(verbose, "2nd order error limits", msg)
if (vort_ref) then
write(msg,sfmt) vortmin, vortmax
call print_parameter(verbose, "vorticity limits" , msg)
end if
if (magnetized .and. curr_ref) then
write(msg,sfmt) currmin, currmax
call print_parameter(verbose, "current density limits", msg)
end if
end if
!-------------------------------------------------------------------------------
!
end subroutine print_refinement
!
!===============================================================================
!
! function CHECK_REFINEMENT_CRITERION:
! -----------------------------------
!
! Function scans the given data block and checks for the refinement
! criterion. It returns +1 if the criterion is met, which indicates that
! the block needs to be refined, 0 if there is no need for the refinement,
! and -1 if the block can be derefined.
!
! Arguments:
!
! pdata - pointer to the data block for which the refinement criterion
! has to be determined;
!
!===============================================================================
!
function check_refinement_criterion(pdata) result(criterion)
! import external procedures and variables
!
use blocks , only : block_data
use equations , only : nv
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
type(block_data), pointer, intent(in) :: pdata
! return variable
!
integer(kind=4) :: criterion
! local variables
!
integer :: p
real(kind=4) :: cref
!
!-------------------------------------------------------------------------------
!
#ifdef PROFILE
! start accounting time for the refinement criterion estimation
!
call start_timer(irc)
#endif /* PROFILE */
! reset the refinement criterion flag
!
criterion = -1
! check the second derivative error from selected primitive variables
!
do p = 1, nv
if (qvar_ref(p)) then
cref = second_derivative_error(p, pdata)
if (cref > crefmin) criterion = max(criterion, 0)
if (cref > crefmax) criterion = max(criterion, 1)
end if
end do ! p = 1, nv
! check vorticity criterion
!
if (vort_ref) then
cref = vorticity_magnitude(pdata)
if (cref > vortmin) criterion = max(criterion, 0)
if (cref > vortmax) criterion = max(criterion, 1)
end if
! check current density criterion
!
if (curr_ref) then
cref = current_density_magnitude(pdata)
if (cref > currmin) criterion = max(criterion, 0)
if (cref > currmax) criterion = max(criterion, 1)
end if
#ifdef PROFILE
! stop accounting time for the refinement criterion estimation
!
call stop_timer(irc)
#endif /* PROFILE */
! return the refinement flag
!
return
!-------------------------------------------------------------------------------
!
end function check_refinement_criterion
!
!===============================================================================
!!
!!*** PRIVATE SUBROUTINES ****************************************************
!!
!===============================================================================
!
!===============================================================================
!
! function SECOND_DERIVATIVE_ERROR:
! --------------------------------
!
! Function calculate the second derivative error for a given data block
! and selected primitive variables. The total error is returned then.
!
! Arguments:
!
! iqt - the index of primitive variable;
! pdata - pointer to the data block for which error is calculated;
!
!===============================================================================
!
function second_derivative_error(iqt, pdata) result(error)
! import external procedures and variables
!
use blocks , only : block_data
use coordinates, only : nbl, neu
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
integer , intent(in) :: iqt
type(block_data), pointer, intent(in) :: pdata
! return variable
!
real(kind=4) :: error
! local variables
!
integer :: i, im1, ip1
integer :: j, jm1, jp1
integer :: k = 1, km1, kp1
real(kind=4) :: fl, fr, fc, fx, fy, fz
! local parameters
!
real(kind=8), parameter :: eps = epsilon(1.0d+00)
!
!-------------------------------------------------------------------------------
!
! reset indicators
!
error = 0.0e+00
! calculate local refinement criterion for variable which exists
!
if (iqt > 0) then
! find the maximum smoothness indicator over all cells
!
#if NDIMS == 3
do k = nbl, neu
km1 = k - 1
kp1 = k + 1
#endif /* NDIMS == 3 */
do j = nbl, neu
jm1 = j - 1
jp1 = j + 1
do i = nbl, neu
im1 = i - 1
ip1 = i + 1
! calculate the second derivative error the X direction
!
fr = pdata%q(iqt,ip1,j,k) - pdata%q(iqt,i ,j,k)
fl = pdata%q(iqt,im1,j,k) - pdata%q(iqt,i ,j,k)
fc = abs(pdata%q(iqt,ip1,j,k)) + abs(pdata%q(iqt,im1,j,k)) &
+ 2.0d+00 * abs(pdata%q(iqt,i,j,k))
fx = abs(fr + fl) / (abs(fr) + abs(fl) + epsref * fc + eps)
! calculate the second derivative error along the Y direction
!
fr = pdata%q(iqt,i,jp1,k) - pdata%q(iqt,i,j ,k)
fl = pdata%q(iqt,i,jm1,k) - pdata%q(iqt,i,j ,k)
fc = abs(pdata%q(iqt,i,jp1,k)) + abs(pdata%q(iqt,i,jm1,k)) &
+ 2.0d+00 * abs(pdata%q(iqt,i,j,k))
fy = abs(fr + fl) / (abs(fr) + abs(fl) + epsref * fc + eps)
#if NDIMS == 3
! calculate the second derivative error along the Z direction
!
fr = pdata%q(iqt,i,j,kp1) - pdata%q(iqt,i,j,k )
fl = pdata%q(iqt,i,j,km1) - pdata%q(iqt,i,j,k )
fc = abs(pdata%q(iqt,i,j,kp1)) + abs(pdata%q(iqt,i,j,km1)) &
+ 2.0d+00 * abs(pdata%q(iqt,i,j,k))
fz = abs(fr + fl) / (abs(fr) + abs(fl) + epsref * fc + eps)
#endif /* NDIMS == 3 */
! take the maximum second derivative error
!
#if NDIMS == 2
error = max(error, fx, fy)
#endif /* NDIMS == 2 */
#if NDIMS == 3
error = max(error, fx, fy, fz)
#endif /* NDIMS == 3 */
end do ! i = nbl, neu
end do ! j = nbl, neu
#if NDIMS == 3
end do ! k = nbl, neu
#endif /* NDIMS == 3 */
end if ! iqt > 0
! return the refinement flag
!
return
!-------------------------------------------------------------------------------
!
end function second_derivative_error
!
!===============================================================================
!
! function VORTICITY_MAGNITUDE:
! ----------------------------
!
! Function finds the maximum magnitude of vorticity in the block associated
! with pdata.
!
! Arguments:
!
! pdata - pointer to the data block for which error is calculated;
!
!===============================================================================
!
function vorticity_magnitude(pdata) result(wmax)
! import external procedures and variables
!
use blocks , only : block_data
use coordinates, only : nn => bcells
use coordinates, only : nbl, neu
use coordinates, only : adx, ady, adz
use equations , only : inx, iny, inz
use equations , only : ivx, ivy, ivz
use operators , only : curl
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
type(block_data), pointer, intent(in) :: pdata
! return variable
!
real(kind=4) :: wmax
! local variables
!
integer :: i, j, k = 1
real(kind=8) :: vort
! local arrays
!
real(kind=8), dimension(3) :: dh = 1.0d+00
#if NDIMS == 3
real(kind=8), dimension(3,nn,nn,nn) :: wc
#else /* NDIMS == 3 */
real(kind=8), dimension(3,nn,nn, 1) :: wc
#endif /* NDIMS == 3 */
!
!-------------------------------------------------------------------------------
!
! reset indicators
!
wmax = 0.0e+00
! calculate current density W = ∇xV
!
call curl(dh(:), pdata%q(ivx:ivz,:,:,:), wc(inx:inz,:,:,:))
! find maximum current density
!
#if NDIMS == 3
do k = nbl, neu
#endif /* NDIMS == 3 */
do j = nbl, neu
do i = nbl, neu
! calculate the squared magnitude of vorticity
!
vort = sum(wc(inx:inz,i,j,k)**2)
! find the maximum of squared vorticity
!
wmax = max(wmax, real(vort, kind=4))
end do ! i = nbl, neu
end do ! j = nbl, neu
#if NDIMS == 3
end do ! k = nbl, neu
#endif /* NDIMS == 3 */
! return the maximum vorticity
!
wmax = sqrt(wmax)
!-------------------------------------------------------------------------------
!
end function vorticity_magnitude
!
!===============================================================================
!
! function CURRENT_DENSITY_MAGNITUDE:
! ----------------------------------
!
! Function finds the maximum magnitude of current density from magnetic field
! in the block associated with pdata.
!
! Arguments:
!
! pdata - pointer to the data block for which error is calculated;
!
!===============================================================================
!
function current_density_magnitude(pdata) result(jmax)
! import external procedures and variables
!
use blocks , only : block_data
use coordinates, only : nn => bcells
use coordinates, only : nbl, neu
use coordinates, only : adx, ady, adz
use equations , only : inx, iny, inz
use equations , only : ibx, iby, ibz
use operators , only : curl
! local variables are not implicit by default
!
implicit none
! subroutine arguments
!
type(block_data), pointer, intent(in) :: pdata
! return variable
!
real(kind=4) :: jmax
! local variables
!
integer :: i, j, k = 1
real(kind=8) :: jabs
! local arrays
!
real(kind=8), dimension(3) :: dh = 1.0d+00
#if NDIMS == 3
real(kind=8), dimension(3,nn,nn,nn) :: jc
#else /* NDIMS == 3 */
real(kind=8), dimension(3,nn,nn, 1) :: jc
#endif /* NDIMS == 3 */
!
!-------------------------------------------------------------------------------
!
! reset indicators
!
jmax = 0.0e+00
! return if there is no magnetic field
!
if (ibx <= 0) return
! calculate current density J = ∇xB
!
call curl(dh(:), pdata%q(ibx:ibz,:,:,:), jc(inx:inz,:,:,:))
! find maximum current density
!
#if NDIMS == 3
do k = nbl, neu
#endif /* NDIMS == 3 */
do j = nbl, neu
do i = nbl, neu
! calculate the squared magnitude of current density
!
jabs = sum(jc(inx:inz,i,j,k)**2)
! find the maximum of squared current density
!
jmax = max(jmax, real(jabs, kind=4))
end do ! i = nbl, neu
end do ! j = nbl, neu
#if NDIMS == 3
end do ! k = nbl, neu
#endif /* NDIMS == 3 */
! return the maximum current density
!
jmax = sqrt(jmax)
!-------------------------------------------------------------------------------
!
end function current_density_magnitude
!===============================================================================
!
end module refinement