!!******************************************************************************
!!
!! 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) 2017-2022 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: USER_PROBLEM
!!
!! This module provides subroutines to setup custom problem.
!!
!!*****************************************************************************
!
module user_problem
implicit none
real(kind=8), save :: beta = 1.00d+00
real(kind=8), save :: zeta = 0.00d+00
real(kind=8), save :: eta = 0.00d+00
real(kind=8), save :: dens = 1.00d+00
real(kind=8), save :: bamp = 1.00d+00
real(kind=8), save :: bgui = 0.00d+00
real(kind=8), save :: pres = 5.00d-01
real(kind=8), save :: pmag = 5.00d-01
real(kind=8), save :: ptot = 1.00d+00
real(kind=8), save :: valf = 1.00d+00
real(kind=8), save :: lund = 1.00d+00
real(kind=8), save :: dlta = 1.00d-16
real(kind=8), save :: blim = 1.00d+00
integer , save :: pert = 0
integer , save :: nper = 10
real(kind=8), save :: bper = 0.00d+00
real(kind=8), save :: vper = 0.00d+00
real(kind=8), save :: kper = 1.00d+00
real(kind=8), save :: kvec = 1.00d+00
real(kind=8), save :: xcut = 1.00d+99
real(kind=8), save :: ycut = 1.00d+99
real(kind=8), save :: xdec = 1.00d-01
real(kind=8), save :: ydec = 1.00d-01
real(kind=8), save :: ylo = -9.00d+99
real(kind=8), save :: yup = 9.00d+99
real(kind=8), save :: tabs = 1.00d+00
real(kind=8), save :: adif = 5.00d-01
real(kind=8), save :: acut = 1.00d+00
real(kind=8), save :: adec = 1.00d+00
real(kind=8), save :: yabs = 9.00d+99
integer(kind=4), save :: runit = 33
logical, save :: absorption = .false.
logical, save :: resistive = .false.
real(kind=8), dimension(:), allocatable :: kx, ky, kz, ux, uy, uz, ph
private
public :: initialize_user_problem, finalize_user_problem
public :: user_statistics
!- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
contains
!
!===============================================================================
!
! subroutine INITIALIZE_USER_PROBLEM:
! ----------------------------------
!
! Subroutine initializes user problem. It could read problem parameters which
! are used in all subroutines defining this specific problem.
!
! Arguments:
!
! problem - the problem name
! rcount - the run count for restarted jobs
! verbose - a logical flag turning the information printing;
! status - an integer flag for error return value;
!
!===============================================================================
!
subroutine initialize_user_problem(problem, rcount, verbose, status)
use boundaries , only : custom_boundary_x, custom_boundary_y
#if NDIMS == 3
use constants , only : pi
#endif /* NDIMS == 3 */
use constants , only : pi2
use coordinates, only : ng => nghosts, ady, xlen, zlen, ymax
use equations , only : magnetized, csnd, csnd2
use helpers , only : print_section, print_parameter, print_message
use mesh , only : setup_problem
use parameters , only : get_parameter
use random , only : randuni, randsym
use shapes , only : update_shapes
implicit none
character(len=64), intent(in) :: problem
integer , intent(in) :: rcount
logical , intent(in) :: verbose
integer , intent(out) :: status
character(len=64) :: perturbation = "noise", append = "off", fname
character(len=64) :: enable_absorption = "off"
logical :: flag
integer :: n, kd
real(kind=8) :: thh, fc, ydis = 9.00d+99
#if NDIMS == 3
real(kind=8) :: thv, tx, ty, tz, tt
#else /* NDIMS == 3 */
real(kind=8) :: ka
#endif /* NDIMS == 3 */
character(len=*), parameter :: &
loc = 'USER_PROBLEM::initialize_user_problem()'
!-------------------------------------------------------------------------------
!
status = 0
if (.not. magnetized) then
if (verbose) &
call print_message(loc, &
"The reconnection problem does not work without magnetic field.")
status = 1
return
end if
! get the reconnection equilibrium parameters
!
call get_parameter("beta", beta)
if (beta <= 0.0d+00) then
if (verbose) &
call print_message(loc, "Plasma-beta must be positive (beta > 0.0)!")
status = 1
return
end if
call get_parameter("zeta", zeta)
if (zeta < 0.0d+00 .or. zeta > 1.0d+00) then
if (verbose) &
call print_message(loc, "Parameter 'zeta' must be between 0.0 and 1.0!")
status = 1
return
end if
call get_parameter("resistivity", eta)
if (eta < 0.0d+00) then
if (verbose) &
call print_message(loc, "Resistivity cannot be negative!")
status = 1
return
else
resistive = .true.
end if
call get_parameter("dens", dens)
if (dens <= 0.0d+00) then
if (verbose) &
call print_message(loc, "Density must be positive (dens > 0.0)!")
status = 1
return
end if
call get_parameter("bamp", bamp)
call get_parameter("bgui", bgui)
call get_parameter("blimit", blim)
! calculate the maximum magnetic pressure, thermal pressure from the plasma-β
! parameters, and the sound speed in the case of isothermal equations of state
!
pmag = 0.5d+00 * (bamp**2 + bgui**2)
pres = beta * pmag
ptot = pres + pmag
csnd2 = pres / dens
csnd = sqrt(csnd2)
valf = sqrt(2.0d+00 * pmag / dens)
lund = valf / max(tiny(eta), eta)
dlta = lund**(- 1.0d+00 / 3.0d+00)
blim = max(blim, ng * ady(1))
! get the geometry parameters
!
call get_parameter("delta", dlta)
if (dlta < 0.0d+00) then
if (verbose) &
call print_message(loc, "Density must be positive (dens > 0.0)!")
status = 1
return
end if
! get the perturbation parameters
!
call get_parameter("perturbation", perturbation)
call get_parameter("nper" , nper)
call get_parameter("bper" , bper)
call get_parameter("vper" , vper)
call get_parameter("kper" , kper)
call get_parameter("xcut" , xcut)
call get_parameter("ycut" , ycut)
call get_parameter("xdec" , xdec)
call get_parameter("ydec" , ydec)
! choose the perturbation type
!
select case(perturbation)
case('noise', 'random')
pert = 0
case('mode', 'one mode', 'one-mode', 'one_mode')
pert = 1
case('multi-wave', 'random waves', 'random-waves', 'random_waves')
pert = 2
case default
perturbation = 'mode'
pert = 1
end select
! prepare the wave vector of the perturbation
!
kvec = pi2 * kper
! prepare the wave vectors for multi-wave perturbation
!
if (pert == 2) then
! allocate phase and wave vector components
!
allocate(kx(nper), ky(nper), kz(nper), ux(nper), uy(nper), uz(nper), &
ph(nper), stat = status)
if (status == 0) then
! choose random wave vector directions
!
kd = int(xlen / zlen)
fc = 1.0d+00 / sqrt(1.0d+00 * nper)
do n = 1, nper
thh = pi2 * randuni()
#if NDIMS == 3
thv = pi * randsym()
tx = cos(thh) * cos(thv)
ty = sin(thh) * cos(thv)
tz = sin(thv)
kx(n) = pi2 * nint(kper * tx)
ky(n) = pi2 * nint(kper * ty)
kz(n) = pi2 * nint(kper * tz / kd) * kd
tt = 0.0d+00
do while(tt < 1.0d-08)
thh = pi2 * randuni()
thv = pi * randsym()
tx = cos(thh) * cos(thv)
ty = sin(thh) * cos(thv)
tz = sin(thv)
ux(n) = ty * kz(n) - tz * ky(n)
uy(n) = tz * kx(n) - tx * kz(n)
uz(n) = tx * ky(n) - ty * kx(n)
tt = sqrt(ux(n)**2 + uy(n)**2 + uz(n)**2)
end do
ux(n) = fc * ux(n) / tt
uy(n) = fc * uy(n) / tt
uz(n) = fc * uz(n) / tt
#else /* NDIMS == 3 */
kx(n) = pi2 * nint(kper * cos(thh))
ky(n) = pi2 * nint(kper * sin(thh))
kz(n) = 0.0d+00
ka = sqrt(kx(n)**2 + ky(n)**2)
ux(n) = fc * ky(n) / ka
uy(n) = - fc * kx(n) / ka
uz(n) = 0.0d+00
#endif /* NDIMS == 3 */
ph(n) = pi2 * randuni()
end do
else
if (verbose) &
call print_message(loc, &
"Could not allocate space for perturbation vectors!")
return
end if
end if ! pert = 2
! determine if to append or create another file
!
call get_parameter("reconnection_append", append)
select case(trim(append))
case ("on", "ON", "t", "T", "y", "Y", "true", "TRUE", "yes", "YES")
write(fname, "('reconnection.dat')")
inquire(file = fname, exist = flag)
case default
write(fname, "('reconnection_',i2.2,'.dat')") rcount
flag = .false.
end select
! check if the file exists; if not, create a new one, otherwise move to the end
!
if (flag .and. rcount > 1) then
#ifdef __INTEL_COMPILER
open(newunit = runit, file = fname, form = 'formatted', status = 'old' &
, position = 'append', buffered = 'yes')
#else /* __INTEL_COMPILER */
open(newunit = runit, file = fname, form = 'formatted', status = 'old' &
, position = 'append')
#endif /* __INTEL_COMPILER */
write(runit,"('#')")
else
#ifdef __INTEL_COMPILER
open(newunit = runit, file = fname, form = 'formatted' &
, status = 'replace', buffered = 'yes')
#else /* __INTEL_COMPILER */
open(newunit = runit, file = fname, form = 'formatted' &
, status = 'replace')
#endif /* __INTEL_COMPILER */
end if
! write the integral file header
!
write(runit,'("#",a24,26a25)') &
'time', '|Bx| int', '|Bx| inf' &
, '|Bx| y-adv', '|Bx| z-adv', '|Bx| y-shr', '|Bx| z-shr' &
, '|Bx| y-dif', '|Bx| z-dif', '|Bx| Psi' &
, 'Vin lower' , 'Vin upper' &
, 'Emag', 'Emag inf' &
, 'Emag x-adv', 'Emag y-adv', 'Emag z-adv' &
, 'Emag x-v.b', 'Emag y-v.b', 'Emag z-v.b' &
, 'Emag x-dif', 'Emag y-dif', 'Emag z-dif' &
, 'Emag-Ekin', 'Emag-Eint', 'Emag-Psi'
write(runit,"('#')")
call get_parameter("ydistance", ydis)
ydis = min(ydis, ymax)
ylo = - ydis
yup = ydis
! absorption parameters
!
call get_parameter("enable_shapes", enable_absorption)
select case(trim(enable_absorption))
case ("on", "ON", "t", "T", "y", "Y", "true", "TRUE", "yes", "YES")
absorption = .true.
case default
absorption = .false.
end select
call get_parameter("tabs", tabs)
call get_parameter("adif", adif)
call get_parameter("acut", acut)
call get_parameter("adec", adec)
yabs = ymax - abs(acut)
! print information about the user problem setup
!
call print_section(verbose, "Parameters (* - set, otherwise calculated)")
call print_parameter(verbose, '(*) beta (plasma-beta)' , beta)
call print_parameter(verbose, '(*) zeta' , zeta)
call print_parameter(verbose, '(*) dens' , dens)
call print_parameter(verbose, '(*) bamp' , bamp)
call print_parameter(verbose, '(*) bgui (guide field)' , bgui)
call print_parameter(verbose, '( ) pres (thermal pres.)' , pres)
call print_parameter(verbose, '( ) pmag (magnetic pres.)', pmag)
call print_parameter(verbose, '( ) ptot (total pressure)', ptot)
call print_parameter(verbose, '( ) csnd (sound speed)' , csnd)
call print_parameter(verbose, '( ) Valf (Alfven speed)' , valf)
if (resistive) then
call print_parameter(verbose, '( ) S (Lundquist number)', lund)
end if
call print_parameter(verbose, '(*) delta (thickness)', dlta)
call print_parameter(verbose, '(*) blim' , blim)
call print_parameter(verbose, '(*) perturbation', perturbation)
call print_parameter(verbose, '(*) bper' , bper)
call print_parameter(verbose, '(*) vper' , vper)
if (pert >= 1) then
call print_parameter(verbose, '(*) kper' , kper)
end if
if (pert == 2) then
call print_parameter(verbose, '(*) nper' , nper)
end if
call print_parameter(verbose, '(*) xcut' , xcut)
call print_parameter(verbose, '(*) ycut' , ycut)
call print_parameter(verbose, '(*) xdec' , xdec)
call print_parameter(verbose, '(*) ydec' , ydec)
call print_parameter(verbose, '(*) ydistance (Vrec)', ydis)
if (absorption) then
call print_parameter(verbose, '(*) tabs (absorption)', tabs)
call print_parameter(verbose, '(*) adif (diffusion)' , adif)
call print_parameter(verbose, '(*) acut' , acut)
call print_parameter(verbose, '(*) adec' , adec)
call print_parameter(verbose, '( ) yabs' , yabs)
end if
! set procedure pointers for the problem setup subroutine, the shapes update
! for the absorption layer, and boundary conditions;
!
setup_problem => setup_user_problem
update_shapes => update_user_shapes
custom_boundary_x => user_boundary_x
custom_boundary_y => user_boundary_y
!-------------------------------------------------------------------------------
!
end subroutine initialize_user_problem
!
!===============================================================================
!
! subroutine FINALIZE_USER_PROBLEM:
! --------------------------------
!
! Subroutine releases memory used by the module.
!
! Arguments:
!
! status - an integer flag for error return value;
!
!===============================================================================
!
subroutine finalize_user_problem(status)
use helpers, only : print_message
implicit none
integer, intent(out) :: status
character(len=*), parameter :: loc = 'USER_PROBLEM::finalize_user_problem()'
!-------------------------------------------------------------------------------
!
status = 0
close(runit)
if (pert == 2) then
deallocate(kx, ky, kz, ux, uy, uz, ph, stat = status)
if (status /= 0) &
call print_message(loc, &
"Could not deallocate space for perturbation vectors!")
end if
!-------------------------------------------------------------------------------
!
end subroutine finalize_user_problem
!
!===============================================================================
!
! subroutine SETUP_USER_PROBLEM:
! -----------------------------
!
! Subroutine sets the initial conditions for the user specific problem.
!
! Arguments:
!
! pdata - pointer to the datablock structure of the currently initialized
! block;
!
!===============================================================================
!
subroutine setup_user_problem(pdata)
use blocks , only : block_data
use constants , only : pi, pi2
use coordinates, only : nn => bcells
use coordinates, only : ax, ay, adx, ady, ylen
#if NDIMS == 3
use coordinates, only : az, adz
#endif /* NDIMS == 3 */
use equations , only : prim2cons
use equations , only : nv, ns
use equations , only : idn, ivx, ivy, ivz, ipr, ibx, iby, ibz, ibp, isl
use equations , only : csnd2
use helpers , only : print_message
use operators , only : curl
use random , only : randsym
use workspace , only : resize_workspace, work, work_in_use
implicit none
type(block_data), pointer, intent(inout) :: pdata
logical, save :: first = .true.
integer :: i, j, k, n, status
real(kind=8) :: xpl, xpu, ypl, ypu
real(kind=8) :: xp, yp
real(kind=8) :: yrat
real(kind=8) :: kv, fv
real(kind=8) :: vx = 0.0d+00, vy = 0.0d+00, vv, va
#if NDIMS == 3
real(kind=8) :: vz = 0.0d+00
#endif /* NDIMS == 3 */
real(kind=8) :: pz = 0.0d+00, pp, ba
#if NDIMS == 3
real(kind=8) :: px = 0.0d+00, py = 0.0d+00
#endif /* NDIMS == 3 */
integer, save :: nt
!$ integer :: omp_get_thread_num
real(kind=8), dimension(:,:,:,:), pointer, save :: qpert, pot
!$omp threadprivate(first, nt, qpert, pot)
real(kind=8), dimension(nv,nn) :: q, u, qprof
real(kind=8), dimension(nn) :: xl, xu, xc, fx
real(kind=8), dimension(nn) :: yl, yu, yc, fy
#if NDIMS == 3
real(kind=8), dimension(nn) :: zc
#endif /* NDIMS == 3 */
real(kind=8), dimension(3) :: dh
character(len=*), parameter :: loc = 'USER_PROBLEM:setup_user_problem()'
!-------------------------------------------------------------------------------
!
#if NDIMS == 2
k = 1
#endif /* NDIMS == 2 */
nt = 0
!$ nt = omp_get_thread_num()
if (first) then
n = (nv + 3) * nn**NDIMS
call resize_workspace(n, status)
if (status /= 0) then
call print_message(loc, "Could not resize the workspace!")
go to 100
end if
i = nv * nn**NDIMS
#if NDIMS == 3
qpert(1:nv,1:nn,1:nn,1:nn) => work( 1:i,nt)
pot (1:3,1:nn,1:nn,1:nn) => work(i+1:n,nt)
#else /* NDIMS == 3 */
qpert(1:nv,1:nn,1:nn,1: 1) => work( 1:i,nt)
pot (1:3,1:nn,1:nn,1: 1) => work(i+1:n,nt)
#endif /* NDIMS == 3 */
first = .false.
end if
dh(1) = adx(pdata%meta%level)
dh(2) = ady(pdata%meta%level)
#if NDIMS == 3
dh(3) = adz(pdata%meta%level)
#endif /* NDIMS == 3 */
xc(:) = pdata%meta%xmin + ax(pdata%meta%level,:)
yc(:) = pdata%meta%ymin + ay(pdata%meta%level,:)
#if NDIMS == 3
zc(:) = pdata%meta%zmin + az(pdata%meta%level,:)
#endif /* NDIMS == 3 */
xl(:) = pdata%meta%xmin + ax(pdata%meta%level,:) - 5.0d-01 * dh(1)
xu(:) = xl(:) + dh(1)
yl(:) = pdata%meta%ymin + ay(pdata%meta%level,:) - 5.0d-01 * dh(2)
yu(:) = yl(:) + dh(2)
! set the equilibrium profile
!
do j = 1, nn
qprof(ibx,j) = bamp * max(-1.0d+00, min(1.0d+00, &
dlta * (log_cosh(yu(j) / dlta) &
- log_cosh(yl(j) / dlta)) / dh(2)))
end do
qprof(iby,:) = 0.0d+00
qprof(ibz,:) = zeta * sqrt(bamp**2 - qprof(ibx,:)**2) + bgui
if (ipr > 0) then
qprof(idn,:) = dens
qprof(ipr,:) = ptot - 0.5d+00 * sum(qprof(ibx:ibz,:)**2, 1)
else
qprof(idn,:) = (ptot - 0.5d+00 * sum(qprof(ibx:ibz,:)**2, 1)) / csnd2
end if
qprof(ivx,:) = 0.0d+00
qprof(ivy,:) = 0.0d+00
qprof(ivz,:) = 0.0d+00
qprof(ibp,:) = 0.0d+00
if (ns > 0) then
qprof(isl,:) = sign(1.0d+00, yc(:))
end if
! ratio of the current sheet thickness to the cell size
!
yrat = dlta / dh(2)
! prepare decaying factors
!
fv = 0.5d+00 * pi
do i = 1, nn
xp = fv * min(1.0d+00, max(0.0d+00, abs(xc(i)) - xcut) / xdec)
fx(i) = cos(xp)**2
end do ! i = 1, nn
do j = 1, nn
yp = fv * min(1.0d+00, max(0.0d+00, abs(yc(j)) - ycut) / ydec)
fy(j) = cos(yp)**2
end do ! i = 1, nn
if (work_in_use(nt)) &
call print_message(loc, "Workspace is being used right now! " // &
"Corruptions can occur!")
work_in_use(nt) = .true.
qpert(:,:,:,:) = 0.0d+00
if (pert == 0) then
! of velocity
!
if (abs(vper) > 0.0d+00) then
! initiate the random velocity components
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do j = 1, nn
if (fy(j) > 0.0d+00) then
do i = 1, nn
if (fx(i) > 0.0d+00) then
! calculate the profile of perturbation amplitude
!
va = vper * fx(i) * fy(j)
! get the random direction
!
vv = 0.0d+00
do while(vv < 1.0d-08)
vx = randsym()
vy = randsym()
#if NDIMS == 3
vz = randsym()
#endif /* NDIMS == 3 */
#if NDIMS == 3
vv = sqrt(vx * vx + vy * vy + vz * vz)
#else /* NDIMS == 3 */
vv = sqrt(vx * vx + vy * vy)
#endif /* NDIMS == 3 */
end do
qpert(ivx,i,j,k) = va * (vx / vv)
qpert(ivy,i,j,k) = va * (vy / vv)
#if NDIMS == 3
qpert(ivz,i,j,k) = va * (vz / vv)
#endif /* NDIMS == 3 */
end if ! |x| < xcut
end do ! i = 1, nn
end if ! |y| < ycut
end do ! j = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
end if ! vper /= 0.0
! of magnetic field
!
if (abs(bper) > 0.0d+00) then
! reset the potential
!
pot(:,:,:,:) = 0.0d+00
! initiate the random magnetic field components
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do j = 1, nn
if (fy(j) > 0.0d+00) then
do i = 1, nn
if (fx(i) > 0.0d+00) then
! calculate the profile of perturbation amplitude
!
ba = dh(1) * bper * fx(i) * fy(j)
! get the random direction
!
pp = 0.0d+00
do while(pp < 1.0d-08)
#if NDIMS == 3
px = randsym()
py = randsym()
#endif /* NDIMS == 3 */
pz = randsym()
#if NDIMS == 3
pp = sqrt(px * px + py * py + pz * pz)
#else /* NDIMS == 3 */
pp = abs(pz)
#endif /* NDIMS == 3 */
end do
#if NDIMS == 3
pot(1,i,j,k) = ba * (px / pp)
pot(2,i,j,k) = ba * (py / pp)
#endif /* NDIMS == 3 */
pot(3,i,j,k) = ba * (pz / pp)
end if ! |x| < xcut
end do ! i = 1, nn
end if ! |y| < ycut
end do ! j = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
! calculate magnetic field perturbation components from vector potential
!
call curl(dh(1:3), pot(:,:,:,:), qpert(ibx:ibz,:,:,:))
end if ! bper /= 0.0
end if ! pert == 0
! one-mode perturbation
!
if (pert == 1) then
! of velocity
!
if (abs(vper) > 0.0d+00) then
! reset the potential
!
pot(:,:,:,:) = 0.0d+00
! calculate the perturbation factor
!
fv = vper * ylen / (pi2 * pi2 * pi * dh(1) * dh(2) * kper)
! calculate the perturbation profile
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do j = 1, nn
if (fy(j) > 0.0d+00) then
ypl = pi * yl(j) / ylen
ypu = pi * yu(j) / ylen
do i = 1, nn
if (fx(i) > 0.0d+00) then
xpl = pi2 * kper * xl(i)
xpu = pi2 * kper * xu(i)
pot(3,i,j,k) = fv * fx(i) * fy(j) * (cos(xpl) - cos(xpu)) &
* (cos(ypl) - cos(ypu))
end if ! |x| < xcut
end do ! i = 1, nn
end if ! |y| < ycut
end do ! j = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
! calculate magnetic field components from vector potential
!
call curl(dh(1:3), pot(:,:,:,:), qpert(ivx:ivz,:,:,:))
end if ! vper /= 0.0
! of magnetic field
!
if (abs(bper) > 0.0d+00) then
! reset the potential
!
pot(:,:,:,:) = 0.0d+00
! calculate the perturbation factor
!
fv = bper * ylen / (pi2 * pi2 * pi * dh(1) * dh(2) * kper)
! calculate the perturbation profile
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do j = 1, nn
if (fy(j) > 0.0d+00) then
ypl = pi * yl(j) / ylen
ypu = pi * yu(j) / ylen
do i = 1, nn
if (fx(i) > 0.0d+00) then
xpl = pi2 * kper * xl(i)
xpu = pi2 * kper * xu(i)
pot(3,i,j,k) = fv * fx(i) * fy(j) * (sin(xpl) - sin(xpu)) &
* (sin(ypl) - sin(ypu))
end if ! |x| < xcut
end do ! i = 1, nn
end if ! |y| < ycut
end do ! j = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
! calculate magnetic field components from vector potential
!
call curl(dh(1:3), pot(:,:,:,:), qpert(ibx:ibz,:,:,:))
end if ! bper /= 0.0
end if ! pert == 1
! prepare the random perturbation of velocity
!
if (pert == 2) then
if (abs(vper) > 0.0d+00) then
! iterate over the block position and initiate the velocity perturbation
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do j = 1, nn
if (fy(j) > 0.0d+00) then
do i = 1, nn
if (fx(i) > 0.0d+00) then
! calculate the velocity amplitude profile
!
fv = vper * fx(i) * fy(j)
! add perturbation components
!
do n = 1, nper
#if NDIMS == 3
kv = kx(n) * xc(i) + ky(n) * yc(j) + kz(n) * zc(k) + ph(n)
#else /* NDIMS == 3 */
kv = kx(n) * xc(i) + ky(n) * yc(j) + ph(n)
#endif /* NDIMS == 3 */
va = fv * sin(kv)
qpert(ivx,i,j,k) = qpert(ivx,i,j,k) + va * ux(n)
qpert(ivy,i,j,k) = qpert(ivy,i,j,k) + va * uy(n)
#if NDIMS == 3
qpert(ivz,i,j,k) = qpert(ivz,i,j,k) + va * uz(n)
#endif /* NDIMS == 3 */
end do
end if ! fx > 0.0
end do ! i = 1, nn
end if ! fy > 0.0
end do ! j = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
end if ! vper /= 0.0
end if ! pert == 2
! iterate over all positions in the XZ plane
!
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
do i = 1, nn
! set the variable profiles with perturbations
!
q(:,:) = qprof(:,:) + qpert(:,i,:,k)
! convert the primitive variables to the conservative ones
!
call prim2cons(q(:,:), u(:,:), .true.)
! copy the primitive variables to the current block
!
pdata%q(:,i,:,k) = q(:,:)
! copy the conserved variables to the current block
!
pdata%u(:,i,:,k) = u(:,:)
end do ! i = 1, nn
#if NDIMS == 3
end do ! k = 1, nn
#endif /* NDIMS == 3 */
work_in_use(nt) = .false.
100 continue
!-------------------------------------------------------------------------------
!
end subroutine setup_user_problem
!
!===============================================================================
!
! subroutine UPDATE_USER_SOURCES:
! ------------------------------
!
! Subroutine adds the user defined source terms.
!
! Arguments:
!
! pdata - the pointer to a data block;
! t, dt - the time and time increment;
! du - the array of variable increment;
!
!===============================================================================
!
subroutine update_user_sources(pdata, t, dt, du)
use blocks, only : block_data
implicit none
type(block_data), pointer , intent(inout) :: pdata
real(kind=8) , intent(in) :: t, dt
real(kind=8), dimension(:,:,:,:), intent(inout) :: du
!-------------------------------------------------------------------------------
!
!-------------------------------------------------------------------------------
!
end subroutine update_user_sources
!
!===============================================================================
!
! subroutine UPDATE_USER_SHAPES:
! -----------------------------
!
! Subroutine defines the regions updated by user.
!
! Arguments:
!
! pdata - pointer to the data block structure of the currently initialized
! block;
! time - time at the moment of update;
! dt - time step since the last update;
!
!===============================================================================
!
subroutine update_user_shapes(pdata, time, dt)
use blocks , only : block_data
use constants , only : pi
use coordinates, only : nn => bcells
use coordinates, only : ay, adx, ady
#if NDIMS == 3
use coordinates, only : adz
#endif /* NDIMS == 3 */
use equations , only : nv
use equations , only : idn, ivx, ivy, ivz, ipr, ibx, iby, ibz, ibp
use equations , only : prim2cons
use helpers , only : print_message
use operators , only : laplace
use workspace , only : resize_workspace, work, work_in_use
implicit none
type(block_data), pointer, intent(inout) :: pdata
real(kind=8) , intent(in) :: time, dt
logical, save :: first = .true.
integer :: j, k, status
real(kind=8) :: fl, fr, fd, fa, fb
integer, save :: nt
!$ integer :: omp_get_thread_num
real(kind=8), dimension(3) :: dh = 1.0d+00
real(kind=8), dimension(nn) :: yc, fc
real(kind=8), dimension(nv,nn) :: q, u
real(kind=8), dimension(:,:,:), pointer, save :: q2
!$omp threadprivate(first, nt, q2)
character(len=*), parameter :: loc = 'USER_PROBLEM:update_user_shapes()'
!-------------------------------------------------------------------------------
!
#if NDIMS == 2
k = 1
#endif /* NDIMS == 2 */
nt = 0
!$ nt = omp_get_thread_num()
if (first) then
j = nn**NDIMS
call resize_workspace(j, status)
if (status /= 0) then
call print_message(loc, "Could not resize the workspace!")
go to 100
end if
#if NDIMS == 3
q2(1:nn,1:nn,1:nn) => work(1:j,nt)
#else /* NDIMS == 3 */
q2(1:nn,1:nn,1: 1) => work(1:j,nt)
#endif /* NDIMS == 3 */
first = .false.
end if
if (work_in_use(nt)) &
call print_message(loc, "Workspace is being used right now! " // &
"Corruptions can occur!")
work_in_use(nt) = .true.
yc(:) = pdata%meta%ymin + ay(pdata%meta%level,:)
if (yc(1) < -yabs .or. yc(nn) > yabs) then
dh(1) = adx(pdata%meta%level)
dh(2) = ady(pdata%meta%level)
#if NDIMS == 3
dh(3) = adz(pdata%meta%level)
#endif /* NDIMS == 3 */
fa = 1.0d+00 - exp(- dt / tabs)
fb = 5.0d-01 * adif * minval(dh(1:NDIMS))**2
call laplace(dh, pdata%q(ivy,:,:,:), q2)
fc(:) = (abs(yc(:)) - yabs) / adec
do j = 1, nn
if (fc(j) > 0.0d+00) then
if (fc(j) < 1.0d+00) then
fr = fa * sin(5.0d-01 * pi * fc(j))**2
else
fr = fa
end if
fl = 1.0d+00 - fr
fd = fr * fb
#if NDIMS == 3
do k = 1, nn
#endif /* NDIMS == 3 */
q(idn,:) = fl * pdata%q(idn,:,j,k) + fr * dens
q(ivx,:) = fl * pdata%q(ivx,:,j,k)
q(ivy,:) = pdata%q(ivy,:,j,k) + fd * q2(:,j,k)
q(ivz,:) = fl * pdata%q(ivz,:,j,k)
q(ibx,:) = fl * pdata%q(ibx,:,j,k) + fr * sign(bamp, yc(j))
q(iby,:) = fl * pdata%q(iby,:,j,k)
q(ibz,:) = fl * pdata%q(ibz,:,j,k) + fr * bgui
q(ibp,:) = fl * pdata%q(ibp,:,j,k)
if (ipr > 0) q(ipr,:) = fl * pdata%q(ipr,:,j,k) + fr * pres
call prim2cons(q(:,:), u(:,:))
pdata%q(:,:,j,k) = q(:,:)
pdata%u(:,:,j,k) = u(:,:)
#if NDIMS == 3
end do
#endif /* NDIMS == 3 */
end if
end do
end if
work_in_use(nt) = .false.
100 continue
!-------------------------------------------------------------------------------
!
end subroutine update_user_shapes
!
!===============================================================================
!
! subroutine USER_BOUNDARY_X:
! --------------------------
!
! Subroutine updates ghost zones within the specific region along
! the X direction.
!
! Arguments:
!
! is - the block side along the X direction for the ghost zone update;
! jl, ju - the cell index limits for the Y direction;
! kl, ku - the cell index limits for the Z direction;
! t, dt - time and time increment;
! x, y, z - the block coordinates;
! qn - the array of variables to update;
!
!===============================================================================
!
subroutine user_boundary_x(is, jl, ju, kl, ku, t, dt, x, y, z, qn)
use coordinates , only : nn => bcells, nb, ne, nbl, neu
use equations , only : magnetized, ivx, ibx, iby, ibp
#if NDIMS == 3
use equations , only : ibz
#endif /* NDIMS == 3 */
implicit none
integer , intent(in) :: is, jl, ju, kl, ku
real(kind=8) , intent(in) :: t, dt
real(kind=8), dimension(:) , intent(in) :: x, y, z
real(kind=8), dimension(:,:,:,:), intent(inout) :: qn
integer :: im2, im1, i , ip1, ip2
integer :: jm2, jm1, j , jp1, jp2
integer :: k
#if NDIMS == 3
integer :: km2, km1, kp1, kp2
#endif /* NDIMS == 3 */
real(kind=8) :: dx, dy, dxy
#if NDIMS == 3
real(kind=8) :: dz, dxz
#endif /* NDIMS == 3 */
!-------------------------------------------------------------------------------
!
if (magnetized) then
#if NDIMS == 2
k = 1
#endif /* NDIMS == 2 */
dx = x(2) - x(1)
dy = y(2) - y(1)
#if NDIMS == 3
dz = z(2) - z(1)
#endif /* NDIMS == 3 */
dxy = dx / dy
#if NDIMS == 3
dxz = dx / dz
#endif /* NDIMS == 3 */
if (is == 1) then
! iterate over left-side ghost layers
!
do i = nbl, 1, -1
! calculate neighbor cell indices
!
ip1 = min(nn, i + 1)
ip2 = min(nn, i + 2)
! iterate over boundary layer
!
#if NDIMS == 3
do k = kl, ku
km2 = max( 1, k - 2)
km1 = max( 1, k - 1)
kp1 = min(nn, k + 1)
kp2 = min(nn, k + 2)
#endif /* NDIMS == 3 */
do j = jl, ju
jm2 = max( 1, j - 2)
jm1 = max( 1, j - 1)
jp1 = min(nn, j + 1)
jp2 = min(nn, j + 2)
! make the normal derivative zero
!
qn(:,i,j,k) = qn(:,nb,j,k)
! prevent the inflow
!
qn(ivx,i,j,k) = min(0.0d+00, qn(ivx,nb,j,k))
! update the normal component of magnetic field from divergence-free condition
!
qn(ibx,i,j,k) = qn(ibx,ip2,j,k) &
+ (qn(iby,ip1,jp1,k) - qn(iby,ip1,jm1,k)) * dxy
#if NDIMS == 3
qn(ibx,i,j,k) = qn(ibx,i ,j,k) &
+ (qn(ibz,ip1,j,kp1) - qn(ibz,ip1,j,km1)) * dxz
#endif /* NDIMS == 3 */
qn(ibp,i,j,k) = 0.0d+00
end do ! j = jl, ju
#if NDIMS == 3
end do ! k = kl, ku
#endif /* NDIMS == 3 */
end do ! i = nbl, 1, -1
else ! is == 1
! iterate over right-side ghost layers
!
do i = neu, nn
! calculate neighbor cell indices
!
im1 = max( 1, i - 1)
im2 = max( 1, i - 2)
! iterate over boundary layer
!
#if NDIMS == 3
do k = kl, ku
km1 = max( 1, k - 1)
kp1 = min(nn, k + 1)
km2 = max( 1, k - 2)
kp2 = min(nn, k + 2)
#endif /* NDIMS == 3 */
do j = jl, ju
jm1 = max( 1, j - 1)
jp1 = min(nn, j + 1)
jm2 = max( 1, j - 2)
jp2 = min(nn, j + 2)
! make the normal derivative zero
!
qn(:,i,j,k) = qn(:,ne,j,k)
! prevent the inflow
!
qn(ivx,i,j,k) = max(0.0d+00, qn(ivx,ne,j,k))
! update the normal component of magnetic field from divergence-free condition
!
qn(ibx,i,j,k) = qn(ibx,im2,j,k) &
+ (qn(iby,im1,jm1,k) - qn(iby,im1,jp1,k)) * dxy
#if NDIMS == 3
qn(ibx,i,j,k) = qn(ibx,i ,j,k) &
+ (qn(ibz,im1,j,km1) - qn(ibz,im1,j,kp1)) * dxz
#endif /* NDIMS == 3 */
qn(ibp,i,j,k) = 0.0d+00
end do ! j = jl, ju
#if NDIMS == 3
end do ! k = kl, ku
#endif /* NDIMS == 3 */
end do ! i = neu, nn
end if ! is == 1
else ! ibx > 0
if (is == 1) then
do i = nbl, 1, -1
#if NDIMS == 3
qn( : ,i,jl:ju,kl:ku) = qn( : ,nb,jl:ju,kl:ku)
qn(ivx,i,jl:ju,kl:ku) = min(qn(ivx,nb,jl:ju,kl:ku), 0.0d+00)
#else /* NDIMS == 3 */
qn( : ,i,jl:ju, : ) = qn( : ,nb,jl:ju, : )
qn(ivx,i,jl:ju, : ) = min(qn(ivx,nb,jl:ju, : ), 0.0d+00)
#endif /* NDIMS == 3 */
end do ! i = nbl, 1, -1
else
do i = neu, nn
#if NDIMS == 3
qn( : ,i,jl:ju,kl:ku) = qn( : ,ne,jl:ju,kl:ku)
qn(ivx,i,jl:ju,kl:ku) = max(qn(ivx,ne,jl:ju,kl:ku), 0.0d+00)
#else /* NDIMS == 3 */
qn( : ,i,jl:ju, : ) = qn( : ,ne,jl:ju, : )
qn(ivx,i,jl:ju, : ) = max(qn(ivx,ne,jl:ju, : ), 0.0d+00)
#endif /* NDIMS == 3 */
end do ! i = neu, nn
end if
end if ! magnetized
!-------------------------------------------------------------------------------
!
end subroutine user_boundary_x
!
!===============================================================================
!
! subroutine USER_BOUNDARY_Y:
! --------------------------
!
! Subroutine updates ghost zones within the specific region along
! the Y direction.
!
! Arguments:
!
! js - the block side along the Y direction for the ghost zone update;
! il, iu - the cell index limits for the X direction;
! kl, ku - the cell index limits for the Z direction;
! t, dt - time and time increment;
! x, y, z - the block coordinates;
! qn - the array of variables to update;
!
!===============================================================================
!
subroutine user_boundary_y(js, il, iu, kl, ku, t, dt, x, y, z, qn)
use coordinates, only : nn => bcells, nb, ne, nbl, neu
use equations , only : magnetized, nv
use equations , only : idn, ivy, ipr, ibx, iby, ibz, ibp
implicit none
integer , intent(in) :: js, il, iu, kl, ku
real(kind=8) , intent(in) :: t, dt
real(kind=8), dimension(:) , intent(in) :: x, y, z
real(kind=8), dimension(:,:,:,:), intent(inout) :: qn
integer :: i, im1, ip1
integer :: j, jm1, jp1, jm2, jp2
integer :: k
#if NDIMS == 3
integer :: km1, kp1
#endif /* NDIMS == 3 */
real(kind=8) :: dx, dy, dyx
#if NDIMS == 3
real(kind=8) :: dz, dyz
#endif /* NDIMS == 3 */
real(kind=8) :: fl, fr
!-------------------------------------------------------------------------------
!
if (magnetized) then
#if NDIMS == 2
k = 1
#endif /* NDIMS == 2 */
dx = x(2) - x(1)
dy = y(2) - y(1)
#if NDIMS == 3
dz = z(2) - z(1)
#endif /* NDIMS == 3 */
dyx = dy / dx
#if NDIMS == 3
dyz = dy / dz
#endif /* NDIMS == 3 */
! process left and right side boundary separatelly
!
if (js == 1) then
! iterate over left-side ghost layers
!
do j = nbl, 1, -1
! calculate neighbor cell indices
!
jp1 = min(nn, j + 1)
jp2 = min(nn, j + 2)
! calculate variable decay coefficients
!
fr = (dy * (nb - j - 5.0d-01)) / blim
fl = 1.0d+00 - fr
! iterate over boundary layer
!
#if NDIMS == 3
do k = kl, ku
km1 = max( 1, k - 1)
kp1 = min(nn, k + 1)
#endif /* NDIMS == 3 */
do i = il, iu
im1 = max( 1, i - 1)
ip1 = min(nn, i + 1)
! make normal derivatives zero
!
qn(1:nv,i,j,k) = qn(1:nv,i,nb,k)
! decay density and pressure to their limits
!
qn(idn,i,j,k) = fl * qn(idn,i,nb,k) + fr * dens
if (ipr > 0) qn(ipr,i,j,k) = fl * qn(ipr,i,nb,k) + fr * pres
! decay magnetic field to its limit
!
qn(ibx,i,j,k) = fl * qn(ibx,i,nb,k) - fr * bamp
qn(ibz,i,j,k) = fl * qn(ibz,i,nb,k) + fr * bgui
! update By from div(B)=0
!
qn(iby,i,j,k) = qn(iby,i,jp2,k) &
+ (qn(ibx,ip1,jp1,k) - qn(ibx,im1,jp1,k)) * dyx
#if NDIMS == 3
qn(iby,i,j,k) = qn(iby,i,j ,k) &
+ (qn(ibz,i,jp1,kp1) - qn(ibz,i,jp1,km1)) * dyz
#endif /* NDIMS == 3 */
qn(ibp,i,j,k) = 0.0d+00
end do ! i = il, iu
#if NDIMS == 3
end do ! k = kl, ku
#endif /* NDIMS == 3 */
end do ! j = nbl, 1, -1
else ! js = 1
! iterate over right-side ghost layers
!
do j = neu, nn
! calculate neighbor cell indices
!
jm1 = max( 1, j - 1)
jm2 = max( 1, j - 2)
! calculate variable decay coefficients
!
fr = (dy * (j - ne - 5.0d-01)) / blim
fl = 1.0d+00 - fr
! iterate over boundary layer
!
#if NDIMS == 3
do k = kl, ku
km1 = max( 1, k - 1)
kp1 = min(nn, k + 1)
#endif /* NDIMS == 3 */
do i = il, iu
im1 = max( 1, i - 1)
ip1 = min(nn, i + 1)
! make normal derivatives zero
!
qn(1:nv,i,j,k) = qn(1:nv,i,ne,k)
! decay density and pressure to their limits
!
qn(idn,i,j,k) = fl * qn(idn,i,ne,k) + fr * dens
if (ipr > 0) qn(ipr,i,j,k) = fl * qn(ipr,i,ne,k) + fr * pres
! decay magnetic field to its limit
!
qn(ibx,i,j,k) = fl * qn(ibx,i,ne,k) + fr * bamp
qn(ibz,i,j,k) = fl * qn(ibz,i,ne,k) + fr * bgui
! update By from div(B)=0
!
qn(iby,i,j,k) = qn(iby,i,jm2,k) &
+ (qn(ibx,im1,jm1,k) - qn(ibx,ip1,jm1,k)) * dyx
#if NDIMS == 3
qn(iby,i,j,k) = qn(iby,i,j ,k) &
+ (qn(ibz,i,jm1,km1) - qn(ibz,i,jm1,kp1)) * dyz
#endif /* NDIMS == 3 */
qn(ibp,i,j,k) = 0.0d+00
end do ! i = il, iu
#if NDIMS == 3
end do ! k = kl, ku
#endif /* NDIMS == 3 */
end do ! j = neu, nn
end if ! js = 1
else ! ibx > 0
if (js == 1) then
do j = nbl, 1, -1
#if NDIMS == 3
qn(1:nv,il:iu,j,kl:ku) = qn(1:nv,il:iu,nb,kl:ku)
qn(ivy ,il:iu,j,kl:ku) = min(0.0d+00, qn(ivy,il:iu,nb,kl:ku))
#else /* NDIMS == 3 */
qn(1:nv,il:iu,j, : ) = qn(1:nv,il:iu,nb, : )
qn(ivy ,il:iu,j, : ) = min(0.0d+00, qn(ivy,il:iu,nb, : ))
#endif /* NDIMS == 3 */
end do ! j = nbl, 1, -1
else
do j = neu, nn
#if NDIMS == 3
qn(1:nv,il:iu,j,kl:ku) = qn(1:nv,il:iu,ne,kl:ku)
qn(ivy ,il:iu,j,kl:ku) = max(0.0d+00, qn(ivy,il:iu,ne,kl:ku))
#else /* NDIMS == 3 */
qn(1:nv,il:iu,j, : ) = qn(1:nv,il:iu,ne, : )
qn(ivy ,il:iu,j, : ) = max(0.0d+00, qn(ivy,il:iu,ne, : ))
#endif /* NDIMS == 3 */
end do ! j = neu, nn
end if
end if ! ibx > 0
!-------------------------------------------------------------------------------
!
end subroutine user_boundary_y
!
!===============================================================================
!
! subroutine USER_BOUNDARY_Z:
! --------------------------
!
! Subroutine updates ghost zones within the specific region along
! the Z direction.
!
! Arguments:
!
! ks - the block side along the Z direction for the ghost zone update;
! il, iu - the cell index limits for the X direction;
! jl, ju - the cell index limits for the Y direction;
! t, dt - time and time increment;
! x, y, z - the block coordinates;
! qn - the array of variables to update;
!
!===============================================================================
!
subroutine user_boundary_z(ks, il, iu, jl, ju, t, dt, x, y, z, qn)
implicit none
integer , intent(in) :: ks, il, iu,jl, ju
real(kind=8) , intent(in) :: t, dt
real(kind=8), dimension(:) , intent(in) :: x, y, z
real(kind=8), dimension(:,:,:,:), intent(inout) :: qn
!-------------------------------------------------------------------------------
!
!-------------------------------------------------------------------------------
!
end subroutine user_boundary_z
!
!===============================================================================
!
! subroutine USER_STATISTICS:
! -------------------------------
!
! Subroutine can be use to store user defined time statistics. The file to
! store these statistics should be properly created in subroutine
! initialize_user_problem() and closed in finalize_user_problem().
!
! Arguments:
!
! time - the current simulation time;
!
!===============================================================================
!
subroutine user_statistics(time)
use blocks , only : block_meta, block_data, list_data
use coordinates, only : nn => bcells, nb, ne
use coordinates, only : adx, ady, adz, advol, ay, yarea
use equations , only : ivx, ivy, ivz, ibx, iby, ibz, ibp
use helpers , only : print_message, flush_and_sync
#ifdef MPI
use mpitools , only : reduce_sum
#endif /* MPI */
use operators , only : curl, gradient
use workspace , only : resize_workspace, work, work_in_use
implicit none
real(kind=8), intent(in) :: time
logical, save :: first = .true.
type(block_meta), pointer :: pmeta
type(block_data), pointer :: pdata
integer, save :: nt
!$ integer :: omp_get_thread_num
integer :: ni, nl, nu, nm, np, status
real(kind=8) :: dvol, dxz
real(kind=8), dimension(3) :: dh
real(kind=8), dimension(nn) :: yc
real(kind=8), dimension(32) :: rterms
real(kind=8), dimension(:,:,:,:), pointer, save :: cur
!$omp threadprivate(first, nt, cur)
character(len=*), parameter :: loc = 'USER_PROBLEM:user_time_statistics()'
!-------------------------------------------------------------------------------
!
nt = 0
!$ nt = omp_get_thread_num()
if (first) then
ni = 3 * nn**NDIMS
call resize_workspace(ni, status)
if (status /= 0) then
call print_message(loc, "Could not resize the workspace!")
go to 100
end if
#if NDIMS == 3
cur(1:3,1:nn,1:nn,1:nn) => work(1:ni,nt)
#else /* NDIMS == 3 */
cur(1:3,1:nn,1:nn,1: 1) => work(1:ni,nt)
#endif /* NDIMS == 3 */
first = .false.
end if
rterms(:) = 0.0d+00
if (work_in_use(nt)) &
call print_message(loc, &
"Workspace is being used right now! Corruptions can occur!")
work_in_use(nt) = .true.
pdata => list_data
do while(associated(pdata))
pmeta => pdata%meta
dh(1) = adx(pmeta%level)
dh(2) = ady(pmeta%level)
dh(3) = adz(pmeta%level)
dvol = advol(pmeta%level)
dxz = adx(pmeta%level) * adz(pmeta%level)
yc(:) = pmeta%ymin + ay(pmeta%level,:)
ni = -1
nl = nb
nu = ne
do while (yc(nl) < ylo .and. nl < ne)
nl = nl + 1
end do
do while (yc(nu) > yup .and. nu > nb)
nu = nu - 1
end do
if (nl < nu) then
! calculate current density (J = ∇xB)
!
call curl(dh(:), pdata%q(ibx:ibz,:,:,:), cur(1:3,:,:,:))
! the integral of |Bx|
!
rterms(1) = rterms(1) &
#if NDIMS == 3
+ sum(abs(pdata%q(ibx,nb:ne,nl:nu,nb:ne))) * dvol
#else /* NDIMS == 3 */
+ sum(abs(pdata%q(ibx,nb:ne,nl:nu, : ))) * dvol
#endif /* NDIMS == 3 */
! the integral of magnetic energy
!
rterms(12) = rterms(12) &
#if NDIMS == 3
+ sum(pdata%u(ibx:ibz,nb:ne,nl:nu,nb:ne)**2) * dvol
#else /* NDIMS == 3 */
+ sum(pdata%u(ibx:ibz,nb:ne,nl:nu, : )**2) * dvol
#endif /* NDIMS == 3 */
if (pmeta%ymin <= ylo .and. ylo < pmeta%ymax) then
ni = nl
nm = ni - 1
! get the inflow speed
!
rterms(10) = rterms(10) &
#if NDIMS == 3
+ sum(pdata%q(ivy,nb:ne,ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
+ sum(pdata%q(ivy,nb:ne,ni, : )) * dxz
#endif /* NDIMS == 3 */
! mean Bx at boundary
!
rterms(2) = rterms(2) &
#if NDIMS == 3
+ sum(abs(pdata%q(ibx,nb:ne,nm:ni,nb:ne))) * dxz
#else /* NDIMS == 3 */
+ sum(abs(pdata%q(ibx,nb:ne,nm:ni, : ))) * dxz
#endif /* NDIMS == 3 */
! advection of Bx along Y
!
rterms(3) = rterms(3) &
#if NDIMS == 3
+ sum(abs(pdata%q(ibx,nb:ne,nm:ni,nb:ne)) &
* pdata%q(ivy,nb:ne,nm:ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
+ sum(abs(pdata%q(ibx,nb:ne,nm:ni, : )) &
* pdata%q(ivy,nb:ne,nm:ni, : )) * dxz
#endif /* NDIMS == 3 */
! shear of By along X
!
rterms(5) = rterms(5) &
#if NDIMS == 3
- sum(sign(pdata%q(iby,nb:ne,nm:ni,nb:ne) &
* pdata%q(ivx,nb:ne,nm:ni,nb:ne), &
pdata%q(ibx,nb:ne,nm:ni,nb:ne))) * dxz
#else /* NDIMS == 3 */
- sum(sign(pdata%q(iby,nb:ne,nm:ni, : ) &
* pdata%q(ivx,nb:ne,nm:ni, : ), &
pdata%q(ibx,nb:ne,nm:ni, : ))) * dxz
#endif /* NDIMS == 3 */
! mean magnetic energy
!
rterms(13) = rterms(13) &
#if NDIMS == 3
+ sum(pdata%q(ibx:ibz,nb:ne,nm:ni,nb:ne)**2) * dxz
#else /* NDIMS == 3 */
+ sum(pdata%q(ibx:ibz,nb:ne,nm:ni, : )**2) * dxz
#endif /* NDIMS == 3 */
! advection of magnetic energy
!
rterms(15) = rterms(15) &
#if NDIMS == 3
+ sum(sum(pdata%q(ibx:ibz,nb:ne,nm:ni,nb:ne)**2,1) &
* pdata%q(ivy ,nb:ne,nm:ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
+ sum(sum(pdata%q(ibx:ibz,nb:ne,nm:ni, : )**2,1) &
* pdata%q(ivy ,nb:ne,nm:ni, : )) * dxz
#endif /* NDIMS == 3 */
! advection of magnetic energy
!
rterms(18) = rterms(18) &
#if NDIMS == 3
- sum(sum(pdata%q(ivx:ivz,nb:ne,nm:ni,nb:ne) &
* pdata%q(ibx:ibz,nb:ne,nm:ni,nb:ne),1) &
* pdata%q(iby ,nb:ne,nm:ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
- sum(sum(pdata%q(ivx:ivz,nb:ne,nm:ni, : ) &
* pdata%q(ibx:ibz,nb:ne,nm:ni, : ),1) &
* pdata%q(iby ,nb:ne,nm:ni, : )) * dxz
#endif /* NDIMS == 3 */
if (resistive) then
! diffusion of Bx through
!
rterms(7) = rterms(7) &
#if NDIMS == 3
+ sum(sign(cur(3,nb:ne,nm:ni,nb:ne), &
pdata%q(ibx,nb:ne,nm:ni,nb:ne))) * dxz
#else /* NDIMS == 3 */
+ sum(sign(cur(3,nb:ne,nm:ni, : ), &
pdata%q(ibx,nb:ne,nm:ni, : ))) * dxz
#endif /* NDIMS == 3 */
! diffusion of magnetic energy through the lower Y boundary
!
rterms(21) = rterms(21) &
#if NDIMS == 3
+ sum(cur(3,nb:ne,nm:ni,nb:ne) &
* pdata%q(ibx,nb:ne,nm:ni,nb:ne) &
- cur(1,nb:ne,nm:ni,nb:ne) &
* pdata%q(ibz,nb:ne,nm:ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
+ sum(cur(3,nb:ne,nm:ni, : ) &
* pdata%q(ibx,nb:ne,nm:ni, : ) &
- cur(1,nb:ne,nm:ni, : ) &
* pdata%q(ibz,nb:ne,nm:ni, : )) * dxz
#endif /* NDIMS == 3 */
end if ! resistivity
end if
if (pmeta%ymin < yup .and. yup <= pmeta%ymax) then
ni = nu
np = ni + 1
! get the inflow speed
!
rterms(11) = rterms(11) &
#if NDIMS == 3
- sum(pdata%q(ivy,nb:ne,ni,nb:ne)) * dxz
#else /* NDIMS == 3 */
- sum(pdata%q(ivy,nb:ne,ni, : )) * dxz
#endif /* NDIMS == 3 */
! mean Bx at boundary
!
rterms(2) = rterms(2) &
#if NDIMS == 3
+ sum(abs(pdata%q(ibx,nb:ne,ni:np,nb:ne))) * dxz
#else /* NDIMS == 3 */
+ sum(abs(pdata%q(ibx,nb:ne,ni:np, : ))) * dxz
#endif /* NDIMS == 3 */
! advection of Bx along Y
!
rterms(3) = rterms(3) &
#if NDIMS == 3
- sum(abs(pdata%q(ibx,nb:ne,ni:np,nb:ne)) &
* pdata%q(ivy,nb:ne,ni:np,nb:ne)) * dxz
#else /* NDIMS == 3 */
- sum(abs(pdata%q(ibx,nb:ne,ni:np, : )) &
* pdata%q(ivy,nb:ne,ni:np, : )) * dxz
#endif /* NDIMS == 3 */
! shear of By along X
!
rterms(5) = rterms(5) &
#if NDIMS == 3
+ sum(sign(pdata%q(iby,nb:ne,ni:np,nb:ne) &
* pdata%q(ivx,nb:ne,ni:np,nb:ne), &
pdata%q(ibx,nb:ne,ni:np,nb:ne))) * dxz
#else /* NDIMS == 3 */
+ sum(sign(pdata%q(iby,nb:ne,ni:np, : ) &
* pdata%q(ivx,nb:ne,ni:np, : ), &
pdata%q(ibx,nb:ne,ni:np, : ))) * dxz
#endif /* NDIMS == 3 */
! mean magnetic energy
!
rterms(13) = rterms(13) &
#if NDIMS == 3
+ sum(pdata%q(ibx:ibz,nb:ne,ni:np,nb:ne)**2) * dxz
#else /* NDIMS == 3 */
+ sum(pdata%q(ibx:ibz,nb:ne,ni:np, : )**2) * dxz
#endif /* NDIMS == 3 */
! advection of magnetic energy
!
rterms(15) = rterms(15) &
#if NDIMS == 3
- sum(sum(pdata%q(ibx:ibz,nb:ne,ni:np,nb:ne)**2,1) &
* pdata%q(ivy ,nb:ne,ni:np,nb:ne)) * dxz
#else /* NDIMS == 3 */
- sum(sum(pdata%q(ibx:ibz,nb:ne,ni:np, : )**2,1) &
* pdata%q(ivy ,nb:ne,ni:np, : )) * dxz
#endif /* NDIMS == 3 */
rterms(18) = rterms(18) &
#if NDIMS == 3
+ sum(sum(pdata%q(ivx:ivz,nb:ne,ni:np,nb:ne) &
* pdata%q(ibx:ibz,nb:ne,ni:np,nb:ne),1) &
* pdata%q(iby ,nb:ne,ni:np,nb:ne)) * dxz
#else /* NDIMS == 3 */
+ sum(sum(pdata%q(ivx:ivz,nb:ne,ni:np, : ) &
* pdata%q(ibx:ibz,nb:ne,ni:np, : ),1) &
* pdata%q(iby ,nb:ne,ni:np, : )) * dxz
#endif /* NDIMS == 3 */
if (resistive) then
! diffusion of Bx
!
rterms(7) = rterms(7) &
#if NDIMS == 3
- sum(sign(cur(3,nb:ne,ni:np,nb:ne), &
pdata%q(ibx,nb:ne,ni:np,nb:ne))) * dxz
#else /* NDIMS == 3 */
- sum(sign(cur(3,nb:ne,ni:np, : ), &
pdata%q(ibx,nb:ne,ni:np, : ))) * dxz
#endif /* NDIMS == 3 */
! diffusion of magnetic energy
!
rterms(21) = rterms(21) &
#if NDIMS == 3
- sum(cur(3,nb:ne,ni:np,nb:ne) &
* pdata%q(ibx,nb:ne,ni:np,nb:ne) &
- cur(1,nb:ne,ni:np,nb:ne) &
* pdata%q(ibz,nb:ne,ni:np,nb:ne)) * dxz
#else /* NDIMS == 3 */
- sum(cur(3,nb:ne,ni:np, : ) &
* pdata%q(ibx,nb:ne,ni:np, : ) &
- cur(1,nb:ne,ni:np, : ) &
* pdata%q(ibz,nb:ne,ni:np, : )) * dxz
#endif /* NDIMS == 3 */
end if ! resistivity
end if
! get the conversion between the magnetic energy and kinetic and
! internal energies
!
rterms(23) = rterms(23) &
#if NDIMS == 3
+ sum((pdata%q(ivy,nb:ne,nl:nu,nb:ne) &
* pdata%q(ibz,nb:ne,nl:nu,nb:ne) &
- pdata%q(ivz,nb:ne,nl:nu,nb:ne) &
* pdata%q(iby,nb:ne,nl:nu,nb:ne)) &
* cur(1,nb:ne,nl:nu,nb:ne)) * dvol
#else /* NDIMS == 3 */
+ sum((pdata%q(ivy,nb:ne,nl:nu, : ) &
* pdata%q(ibz,nb:ne,nl:nu, : ) &
- pdata%q(ivz,nb:ne,nl:nu, : ) &
* pdata%q(iby,nb:ne,nl:nu, : )) &
* cur(1,nb:ne,nl:nu, : )) * dvol
#endif /* NDIMS == 3 */
rterms(23) = rterms(23) &
#if NDIMS == 3
+ sum((pdata%q(ivz,nb:ne,nl:nu,nb:ne) &
* pdata%q(ibx,nb:ne,nl:nu,nb:ne) &
- pdata%q(ivx,nb:ne,nl:nu,nb:ne) &
* pdata%q(ibz,nb:ne,nl:nu,nb:ne)) &
* cur(2,nb:ne,nl:nu,nb:ne)) * dvol
#else /* NDIMS == 3 */
+ sum((pdata%q(ivz,nb:ne,nl:nu, : ) &
* pdata%q(ibx,nb:ne,nl:nu, : ) &
- pdata%q(ivx,nb:ne,nl:nu, : ) &
* pdata%q(ibz,nb:ne,nl:nu, : )) &
* cur(2,nb:ne,nl:nu, : )) * dvol
#endif /* NDIMS == 3 */
rterms(23) = rterms(23) &
#if NDIMS == 3
+ sum((pdata%q(ivx,nb:ne,nl:nu,nb:ne) &
* pdata%q(iby,nb:ne,nl:nu,nb:ne) &
- pdata%q(ivy,nb:ne,nl:nu,nb:ne) &
* pdata%q(ibx,nb:ne,nl:nu,nb:ne)) &
* cur(3,nb:ne,nl:nu,nb:ne)) * dvol
#else /* NDIMS == 3 */
+ sum((pdata%q(ivx,nb:ne,nl:nu, : ) &
* pdata%q(iby,nb:ne,nl:nu, : ) &
- pdata%q(ivy,nb:ne,nl:nu, : ) &
* pdata%q(ibx,nb:ne,nl:nu, : )) &
* cur(3,nb:ne,nl:nu, : )) * dvol
#endif /* NDIMS == 3 */
if (resistive) then
rterms(24) = rterms(24) &
#if NDIMS == 3
- sum(cur(1:3,nb:ne,nl:nu,nb:ne)**2) * dvol
#else /* NDIMS == 3 */
- sum(cur(1:3,nb:ne,nl:nu, : )**2) * dvol
#endif /* NDIMS == 3 */
end if
! calculate gradient (∇ψ)
!
call gradient(dh(:), pdata%q(ibp,:,:,:), cur(1:3,:,:,:))
rterms(25) = rterms(25) &
#if NDIMS == 3
- sum(pdata%q(ibx:ibz,nb:ne,nl:nu,nb:ne) &
* cur(1:3,nb:ne,nl:nu,nb:ne)) * dvol
#else /* NDIMS == 3 */
- sum(pdata%q(ibx:ibz,nb:ne,nl:nu, : ) &
* cur(1:3,nb:ne,nl:nu, : )) * dvol
#endif /* NDIMS == 3 */
! contribution to |Bx| from ∇ψ
!
rterms(9) = rterms(9) &
#if NDIMS == 3
- sum(sign(cur(1,nb:ne,nl:nu,nb:ne), &
pdata%q(ibx,nb:ne,nl:nu,nb:ne))) * dvol
#else /* NDIMS == 3 */
- sum(sign(cur(1,nb:ne,nl:nu, : ), &
pdata%q(ibx,nb:ne,nl:nu, : ))) * dvol
#endif /* NDIMS == 3 */
end if ! nl < nu
pdata => pdata%next
end do
work_in_use(nt) = .false.
#ifdef MPI
call reduce_sum(rterms(:))
#endif /* MPI */
rterms(2) = 2.50d-01 * rterms(2) / yarea
rterms(12) = 5.00d-01 * rterms(12)
rterms(13) = 1.25d-01 * rterms(13) / yarea
rterms(3:6) = 5.00d-01 * rterms(3:6)
rterms(14:19) = 5.00d-01 * rterms(14:19)
rterms(7:8) = 5.00d-01 * eta * rterms(7:8)
rterms(20:22) = 5.00d-01 * eta * rterms(20:22)
rterms(24) = eta * rterms(24)
write(runit,"(26es25.15e3)") time, rterms(1:25)
call flush_and_sync(runit)
100 continue
!-------------------------------------------------------------------------------
!
end subroutine user_statistics
!
!===============================================================================
!
! subroutine LOG_COSH:
! -------------------
!
! Function calculates the logarithm of the hyperbolic cosine, which is
! the result of the integration of tanh(x). Direct calculation using
! Fortran intrinsic subroutines fails for large values of x, therefore
! the logarithm of cosh is approximated as |x| + log(1/2) for
! |x| > threshold.
!
! Arguments:
!
! x - function argument;
!
!===============================================================================
!
function log_cosh(x) result(y)
implicit none
real(kind=8), intent(in) :: x
real(kind=8) :: y
real(kind=8), parameter :: th = acosh(huge(x)), lh = log(0.5d+00)
!-------------------------------------------------------------------------------
!
if (abs(x) < th) then
y = log(cosh(x))
else
y = abs(x) + lh
end if
!-------------------------------------------------------------------------------
!
end function log_cosh
!===============================================================================
!
end module user_problem