Grzegorz Kowal
f99a1fb0bf
Add a flag to select only the perturbation modes which are stable for tearing mode instability. Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
2235 lines
68 KiB
Fortran
2235 lines
68 KiB
Fortran
!!******************************************************************************
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!!
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!! This file is part of the AMUN source code, a program to perform
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!! Newtonian or relativistic magnetohydrodynamical simulations on uniform or
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!! adaptive mesh.
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!!
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!! Copyright (C) 2017-2024 Grzegorz Kowal <grzegorz@amuncode.org>
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!!
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!! This program is free software: you can redistribute it and/or modify
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!! it under the terms of the GNU General Public License as published by
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!! the Free Software Foundation, either version 3 of the License, or
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!! (at your option) any later version.
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!!
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!! This program is distributed in the hope that it will be useful,
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!! but WITHOUT ANY WARRANTY; without even the implied warranty of
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!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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!! GNU General Public License for more details.
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!!
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!! You should have received a copy of the GNU General Public License
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!! along with this program. If not, see <http://www.gnu.org/licenses/>.
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!!
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!!*****************************************************************************
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!!
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!! module: USER_PROBLEM
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!!
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!! This module provides subroutines to set up a custom problem.
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!!
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!!*****************************************************************************
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!
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module user_problem
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implicit none
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real(kind=8), save :: alpha = 5.00d-01
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real(kind=8), save :: beta = 1.00d+00
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real(kind=8), save :: zeta = 0.00d+00
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real(kind=8), save :: eta = 0.00d+00
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real(kind=8), save :: nu = 0.00d+00
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real(kind=8), save :: dens = 1.00d+00
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real(kind=8), save :: bamp = 1.00d+00
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real(kind=8), save :: btra = 0.00d+00
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real(kind=8), save :: bgui = 0.00d+00
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real(kind=8), save :: pres = 5.00d-01
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real(kind=8), save :: pmag = 5.00d-01
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real(kind=8), save :: ptot = 1.00d+00
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real(kind=8), save :: valf = 1.00d+00
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real(kind=8), save :: lund = 1.00d+00
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real(kind=8), save :: prdl = 0.00d+00
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real(kind=8), save :: dlta = 1.00d-16
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real(kind=8), save :: tdec = 1.00d+00
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integer , save :: pert = 0
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integer , save :: nper = 16
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real(kind=8), save :: kper = 1.00d+00
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real(kind=8), save :: kdel = 1.00d+00
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real(kind=8), save :: bper = 0.00d+00
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real(kind=8), save :: vper = 0.00d+00
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real(kind=8), save :: kvec = 1.00d+00
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real(kind=8), save :: xcut = 1.00d+99
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real(kind=8), save :: ycut = 1.00d+99
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real(kind=8), save :: xdec = 1.00d-01
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real(kind=8), save :: ydec = 1.00d-01
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real(kind=8), save :: ylo = -9.00d+99
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real(kind=8), save :: yup = 9.00d+99
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real(kind=8), save :: tabs = 1.00d+00
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real(kind=8), save :: adif = 5.00d-01
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real(kind=8), save :: acut = 1.00d+00
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real(kind=8), save :: adec = 1.00d+00
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real(kind=8), save :: yabs = 9.00d+99
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integer(kind=4), save :: runit = 33
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logical, save :: absorption = .false.
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logical, save :: resistive = .false.
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real(kind=8), dimension(:), allocatable :: kx, ky, kz, ux, uy, uz, ph
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private
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public :: initialize_user_problem, finalize_user_problem
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public :: user_statistics
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!- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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!
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contains
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!
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!===============================================================================
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!
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! subroutine INITIALIZE_USER_PROBLEM:
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! ----------------------------------
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!
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! Subroutine initializes the user problem. It can read problem parameters
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! that are used in all subroutines defining this specific problem.
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!
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! Arguments:
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!
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! problem - the problem name
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! rcount - the run count for restarted jobs
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! verbose - a logical flag turning on information printing;
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! status - an integer flag for error return value;
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!
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!===============================================================================
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!
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subroutine initialize_user_problem(problem, rcount, verbose, status)
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use boundaries , only : custom_boundary_x, custom_boundary_y
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use constants , only : pi, pi2
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use coordinates, only : xlen, zlen, ymax
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use equations , only : magnetized, csnd, csnd2, qpbnd
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use equations , only : idn, ivx, ivy, ivz, ibx, iby, ibz, ibp, ipr
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use helpers , only : print_section, print_parameter, print_message
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use mesh , only : setup_problem
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use parameters , only : get_parameter
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use random , only : randuni, randsym
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use shapes , only : update_shapes
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implicit none
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character(len=64), intent(in) :: problem
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integer , intent(in) :: rcount
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logical , intent(in) :: verbose
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integer , intent(out) :: status
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logical :: perturb_tearing = .true.
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character(len=32) :: stmp
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character(len=64) :: perturbation = "noise", append = "off", fname
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character(len=64) :: enable_absorption = "off"
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logical :: flag
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integer :: n, kd, ki, kj, kk, kv, ks
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real(kind=8) :: kl2, ku2, kv2, ka, fc, ydis = 9.00d+99
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real(kind=8) :: thv, thh, tx, ty, tz
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character(len=*), parameter :: &
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loc = 'USER_PROBLEM::initialize_user_problem()'
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!-------------------------------------------------------------------------------
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!
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status = 0
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if (.not. magnetized) then
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if (verbose) &
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call print_message(loc, &
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"The reconnection problem does not work without magnetic field.")
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status = 1
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return
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end if
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! get the reconnection equilibrium parameters
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!
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call get_parameter("beta", beta)
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if (beta <= 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Plasma-beta must be positive (beta > 0.0)!")
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status = 1
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return
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end if
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call get_parameter("zeta", zeta)
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if (zeta < 0.0d+00 .or. zeta > 1.0d+00) then
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if (verbose) &
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call print_message(loc, "Parameter 'zeta' must be between 0.0 and 1.0!")
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status = 1
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return
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end if
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call get_parameter("viscosity" , nu )
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call get_parameter("resistivity", eta)
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if (eta < 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Resistivity cannot be negative!")
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status = 1
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return
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else
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resistive = .true.
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end if
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call get_parameter("dens", dens)
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if (dens <= 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Density must be positive (dens > 0.0)!")
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status = 1
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return
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end if
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call get_parameter("bamp", bamp)
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call get_parameter("btra", btra)
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call get_parameter("bgui", bgui)
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call get_parameter("boundary_decay_time", tdec)
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if (tdec <= 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Boundary decay time must be larger than zero!")
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status = 1
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return
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end if
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! get the index for the current sheet thickness scaling
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!
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call get_parameter("alpha", alpha)
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if (alpha <= 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Current sheet thickness scaling index " // &
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"(alpha) must be larger than zero! " // &
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"Resetting it to the default value of 1/2.")
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alpha = 5.0d-01
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end if
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! calculate the maximum magnetic pressure, thermal pressure from the plasma-β
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! parameters, and the sound speed in the case of isothermal equations of state
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!
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pmag = 0.5d+00 * (bamp**2 + bgui**2)
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pres = beta * pmag
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ptot = pres + pmag
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csnd2 = pres / dens
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csnd = sqrt(csnd2)
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valf = sqrt(bamp**2 / dens)
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lund = valf / max(tiny(eta), eta)
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prdl = nu / max(tiny(eta), eta)
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dlta = lund**(-alpha)
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! fill up the boundary values
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!
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qpbnd(idn,2,:) = dens
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qpbnd(ivx,2,:) = 0.0d+00
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qpbnd(ivy,2,:) = 0.0d+00
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qpbnd(ivz,2,:) = 0.0d+00
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qpbnd(ibx,2,:) = [ - bamp, bamp ]
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qpbnd(iby,2,:) = btra
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qpbnd(ibz,2,:) = bgui
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qpbnd(ibp,2,:) = 0.0d+00
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if (ipr > 0) qpbnd(ipr,2,:) = pres
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! get the geometry parameters
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!
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call get_parameter("delta", dlta)
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if (dlta < 0.0d+00) then
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if (verbose) &
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call print_message(loc, "Density must be positive (dens > 0.0)!")
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status = 1
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return
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end if
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ycut = 2 * dlta
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ydec = dlta
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! get the perturbation parameters
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!
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call get_parameter("perturbation", perturbation)
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call get_parameter("nper" , nper)
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call get_parameter("bper" , bper)
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call get_parameter("vper" , vper)
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call get_parameter("kper" , kper)
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call get_parameter("kdel" , kdel)
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call get_parameter("xcut" , xcut)
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call get_parameter("ycut" , ycut)
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call get_parameter("xdec" , xdec)
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call get_parameter("ydec" , ydec)
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! choose the perturbation type
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!
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select case(perturbation)
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case('noise', 'random')
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pert = 0
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case('mode', 'one mode', 'one-mode', 'one_mode')
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pert = 1
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case('multi-wave', 'random waves', 'random-waves', 'random_waves')
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pert = 2
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case('wave-spectrum', 'wave spectrum', 'wave_spectrum')
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pert = 3
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case('external')
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pert = 4
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case default
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perturbation = 'mode'
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pert = 1
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end select
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! enable or disable tearing modes perturbation
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!
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stmp = 'on'
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call get_parameter("perturb_tearing", stmp)
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select case(stmp)
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case ("on", "ON", "t", "T", "y", "Y", "true", "TRUE", "yes", "YES")
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perturb_tearing = .true.
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case default
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perturb_tearing = .false.
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end select
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! prepare the wave vector of the perturbation
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!
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kvec = pi2 * kper
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! prepare the wave vectors for multi-wave perturbation
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!
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if (pert == 2) then
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kl2 = max(0.0d+00, kper - kdel)**2
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ku2 = (kper + kdel)**2
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kv = int(kper)
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ks = int(ceiling(1.0d+00 / (pi2 * dlta)))
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if (perturb_tearing) ks = 0
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n = 0
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#if NDIMS == 3
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kd = int(xlen / zlen)
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do kk = - kv + mod(kv, kd), kv - mod(kv, kd), kd
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#else /* NDIMS == 3 */
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kk = 0
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#endif /* NDIMS == 3 */
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do kj = - kv, kv
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do ki = ks, kv
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kv2 = 1.0d+00 * (ki**2 + kj**2 + kk**2)
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if (kl2 <= kv2 .and. kv2 <= ku2) then
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if (.not. (ki == 0 .and. kj == 0 .and. kk < 0) .and. &
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.not. (ki == 0 .and. kj < 0)) then
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n = n + 1
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end if
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end if
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end do
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end do
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#if NDIMS == 3
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end do
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#endif /* NDIMS == 3 */
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if (n > 0) nper = n
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! allocate phase and wave vector components
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!
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allocate(kx(nper), ky(nper), kz(nper), ux(nper), uy(nper), uz(nper), &
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ph(nper), stat = status)
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if (status == 0) then
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! choose random wave vector directions
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!
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n = 0
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#if NDIMS == 3
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do kk = - kv + mod(kv, kd), kv - mod(kv, kd), kd
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#else /* NDIMS == 3 */
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kk = 0
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#endif /* NDIMS == 3 */
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do kj = - kv, kv
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do ki = ks, kv
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kv2 = 1.0d+00 * (ki**2 + kj**2 + kk**2)
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if (kl2 <= kv2 .and. kv2 <= ku2) then
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if (.not. (ki == 0 .and. kj == 0 .and. kk < 0) .and. &
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.not. (ki == 0 .and. kj < 0)) then
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n = n + 1
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kx(n) = pi2 * ki
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ky(n) = pi2 * kj
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kz(n) = pi2 * kk
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if (kk == 0) then
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ka = sqrt(kx(n)**2 + ky(n)**2)
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ux(n) = ky(n) / ka
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uy(n) = - kx(n) / ka
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uz(n) = 0.0d+00
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else
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ka = 0.0d+00
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do while(ka < 1.0d-08)
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thh = pi2 * randuni()
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thv = pi * randsym()
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tx = cos(thh) * cos(thv)
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ty = sin(thh) * cos(thv)
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tz = sin(thv)
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ux(n) = ty * kz(n) - tz * ky(n)
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uy(n) = tz * kx(n) - tx * kz(n)
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uz(n) = tx * ky(n) - ty * kx(n)
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ka = sqrt(ux(n)**2 + uy(n)**2 + uz(n)**2)
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end do
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ux(n) = ux(n) / ka
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uy(n) = uy(n) / ka
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uz(n) = uz(n) / ka
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end if
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ph(n) = pi2 * randuni()
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end if
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end if
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end do
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end do
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#if NDIMS == 3
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end do
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#endif /* NDIMS == 3 */
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else
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if (verbose) &
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call print_message(loc, &
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"Could not allocate space for perturbation vectors!")
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return
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end if
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end if ! pert = 2
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! prepare the wave vectors for wave-spectrum perturbation
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!
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if (pert == 3) then
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! allocate phase and wave vector components
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!
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allocate(kx(nper), ph(nper), stat = status)
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if (status == 0) then
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do n = 1, nper
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kx(n) = pi2 * n / xlen
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ph(n) = pi2 * randuni()
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end do
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else
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if (verbose) &
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call print_message(loc, &
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"Could not allocate space for perturbation vectors!")
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return
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end if
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end if ! pert = 3
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! determine if to append or create another file
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!
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call get_parameter("reconnection_append", append)
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select case(trim(append))
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case ("on", "ON", "t", "T", "y", "Y", "true", "TRUE", "yes", "YES")
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write(fname, "('reconnection.dat')")
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inquire(file = fname, exist = flag)
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case default
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write(fname, "('reconnection_',i2.2,'.dat')") rcount
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flag = .false.
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end select
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! check if the file exists; if not, create a new one, otherwise move to the end
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!
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if (flag .and. rcount > 1) then
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#ifdef __INTEL_COMPILER
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open(newunit = runit, file = fname, form = 'formatted', status = 'old' &
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, position = 'append', buffered = 'yes')
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#else /* __INTEL_COMPILER */
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open(newunit = runit, file = fname, form = 'formatted', status = 'old' &
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, position = 'append')
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#endif /* __INTEL_COMPILER */
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write(runit,"('#')")
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else
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#ifdef __INTEL_COMPILER
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open(newunit = runit, file = fname, form = 'formatted' &
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, status = 'replace', buffered = 'yes')
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#else /* __INTEL_COMPILER */
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open(newunit = runit, file = fname, form = 'formatted' &
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, status = 'replace')
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#endif /* __INTEL_COMPILER */
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end if
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! write the integral file header
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!
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write(runit,'("#",a24,26a25)') &
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'time', '|Bx| int', '|Bx| inf' &
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, '|Bx| y-adv', '|Bx| z-adv', '|Bx| y-shr', '|Bx| z-shr' &
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, '|Bx| y-dif', '|Bx| z-dif', '|Bx| Psi' &
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, 'Vin lower' , 'Vin upper' &
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, 'Emag', 'Emag inf' &
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, 'Emag x-adv', 'Emag y-adv', 'Emag z-adv' &
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, 'Emag x-v.b', 'Emag y-v.b', 'Emag z-v.b' &
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, 'Emag x-dif', 'Emag y-dif', 'Emag z-dif' &
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, 'Emag-Ekin', 'Emag-Eint', 'Emag-Psi'
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write(runit,"('#')")
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call get_parameter("ydistance", ydis)
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ydis = min(ydis, ymax)
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ylo = - ydis
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yup = ydis
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! absorption parameters
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!
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call get_parameter("enable_shapes", enable_absorption)
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select case(trim(enable_absorption))
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case ("on", "ON", "t", "T", "y", "Y", "true", "TRUE", "yes", "YES")
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absorption = .true.
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case default
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absorption = .false.
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end select
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call get_parameter("tabs", tabs)
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call get_parameter("adif", adif)
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call get_parameter("acut", acut)
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call get_parameter("adec", adec)
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yabs = ymax - abs(acut)
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! print information about the user problem setup
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!
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call print_section(verbose, "Parameters (* - set, otherwise calculated)")
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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, '(*) btra (transverse)' , btra)
|
|
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, '( ) P (Prandtl number)', prdl)
|
|
call print_parameter(verbose, '(*) delta (thickness)', dlta)
|
|
call print_parameter(verbose, '(*) perturbation', perturbation)
|
|
if (pert == 2) then
|
|
if (perturb_tearing) then
|
|
call print_parameter(verbose, '(*) perturb tearing modes', 'on')
|
|
else
|
|
call print_parameter(verbose, '(*) perturb tearing modes', 'off')
|
|
end if
|
|
end if
|
|
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, '(*) kdel' , kdel)
|
|
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, '(*) boundary decay time', tdec)
|
|
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
|
|
custom_boundary_x => user_boundary_x
|
|
custom_boundary_y => user_boundary_y
|
|
if (absorption) &
|
|
update_shapes => update_user_shapes
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
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
|
|
if (pert == 3) then
|
|
deallocate(kx, 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, nc => ncells, ng => nghosts
|
|
use coordinates, only : ax, ay, adx, ady, ymin, 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.
|
|
|
|
character(len=64) :: filename
|
|
|
|
integer :: i, j, k, n, io, status, jl, ju, p
|
|
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
|
|
!$omp threadprivate(first, nt, qpert, pot)
|
|
|
|
real(kind=8), dimension(nv,nn) :: q, u, qprof
|
|
real(kind=8), dimension(nn) :: xl, xu, xc, fx
|
|
real(kind=8), dimension(nn) :: yl, yu, yc, fy
|
|
#if NDIMS == 3
|
|
real(kind=8), dimension(nn) :: zc
|
|
#endif /* NDIMS == 3 */
|
|
real(kind=8), dimension(3) :: dh
|
|
real(kind=8), dimension(:) , allocatable :: yt
|
|
real(kind=8), dimension(:,:), allocatable :: qr, qi
|
|
|
|
character(len=*), parameter :: loc = 'USER_PROBLEM:setup_user_problem()'
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
#if NDIMS == 2
|
|
k = 1
|
|
#endif /* NDIMS == 2 */
|
|
|
|
nt = 0
|
|
!$ 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,:) = btra
|
|
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 = 5.0d-01 * 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 * 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 velocity components from stream function
|
|
!
|
|
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 * 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
|
|
|
|
! prepare the spectrum of waves
|
|
!
|
|
if (pert == 3) then
|
|
|
|
! of velocity
|
|
!
|
|
if (abs(vper) > 0.0d+00) then
|
|
|
|
pot(:,:,:,:) = 0.0d+00
|
|
|
|
do n = 1, nper
|
|
do j = 1, nn
|
|
yp = sqrt(max(0.0d+00, 1.0d+00 - tanh(yc(j) / dlta)**2))
|
|
do i = 1, nn
|
|
pot(3,i,j,:) = pot(3,i,j,:) &
|
|
+ vper / kx(n) * cos(kx(n) * xc(i) + ph(n)) * yp
|
|
end do ! i = 1, nn
|
|
end do ! j = 1, nn
|
|
end do ! n = 1, nper
|
|
|
|
call curl(dh(1:3), pot(:,:,:,:), qpert(ivx:ivz,:,:,:))
|
|
|
|
end if ! vper /= 0.0
|
|
|
|
! of magnetic field
|
|
!
|
|
if (abs(bper) > 0.0d+00) then
|
|
|
|
pot(:,:,:,:) = 0.0d+00
|
|
|
|
do n = 1, nper
|
|
do j = 1, nn
|
|
yp = sqrt(max(0.0d+00, 1.0d+00 - tanh(yc(j) / dlta)**2))
|
|
do i = 1, nn
|
|
pot(3,i,j,:) = pot(3,i,j,:) &
|
|
+ bper / kx(n) * cos(kx(n) * xc(i) + ph(n)) * yp
|
|
end do ! i = 1, nn
|
|
end do ! j = 1, nn
|
|
end do ! n = 1, nper
|
|
|
|
call curl(dh(1:3), pot(:,:,:,:), qpert(ibx:ibz,:,:,:))
|
|
|
|
end if ! bper /= 0.0
|
|
|
|
end if ! pert == 3
|
|
|
|
! load the external perturbation
|
|
!
|
|
if (pert == 4) then
|
|
|
|
write(filename, "('perturbations-',i2.2,'-',i2.2,'.dat')") &
|
|
nc, pdata%meta%level
|
|
open(newunit=io, file=filename)
|
|
read(io, *, iostat=status) kvec
|
|
read(io, *, iostat=status) n
|
|
read(io, *, iostat=status) ypl
|
|
|
|
allocate(yt(n), qr(nv,n), qi(nv,n))
|
|
qr = 0.0d+00
|
|
qi = 0.0d+00
|
|
|
|
do p = 1, n
|
|
read(io, *, iostat=status) yt(p), qr(ivx, p), qi(ivx, p), &
|
|
qr(ivy, p), qi(ivy, p), &
|
|
qr(ibx, p), qi(ibx, p), &
|
|
qr(iby, p), qi(iby, p)
|
|
if (status /= 0) exit
|
|
end do
|
|
|
|
close(io)
|
|
|
|
jl = (pdata%meta%ymin - ypl) / dh(2) - ng + 1
|
|
ju = jl + nn - 1
|
|
|
|
do p = jl, ju
|
|
j = p - jl + 1
|
|
do i = 1, nn
|
|
qpert(ivx,i,j,:) = qr(ivx,p) * cos(kvec * xc(i)) &
|
|
+ qi(ivx,p) * sin(kvec * xc(i))
|
|
qpert(ivy,i,j,:) = qr(ivy,p) * cos(kvec * xc(i)) &
|
|
+ qi(ivy,p) * sin(kvec * xc(i))
|
|
qpert(ibx,i,j,:) = qr(ibx,p) * cos(kvec * xc(i)) &
|
|
+ qi(ibx,p) * sin(kvec * xc(i))
|
|
qpert(iby,i,j,:) = qr(iby,p) * cos(kvec * xc(i)) &
|
|
+ qi(iby,p) * sin(kvec * xc(i))
|
|
end do
|
|
end do
|
|
|
|
deallocate(yt, qr, qi)
|
|
|
|
end if ! pert == 4
|
|
|
|
! 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:
|
|
!
|
|
! t, dt - the time and time increment;
|
|
! pdata - the pointer to a data block;
|
|
!
|
|
!===============================================================================
|
|
!
|
|
subroutine update_user_sources(t, dt, pdata)
|
|
|
|
use blocks, only : block_data
|
|
|
|
implicit none
|
|
|
|
real(kind=8) , intent(in) :: t, dt
|
|
type(block_data), pointer, intent(inout) :: pdata
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
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
|
|
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) + fr * btra
|
|
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, ivy, qpbnd
|
|
|
|
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, j, k, jm, jp
|
|
real(kind=8) :: fl, fr
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
if (magnetized) then
|
|
|
|
#if NDIMS == 2
|
|
k = 1
|
|
#endif /* NDIMS == 2 */
|
|
|
|
fl = exp(- dt / tdec)
|
|
fr = 1.0d+00 - fl
|
|
|
|
if (js == 1) then
|
|
|
|
do j = nbl, 1, -1
|
|
jp = j + 1
|
|
#if NDIMS == 3
|
|
do k = kl, ku
|
|
#endif /* NDIMS == 3 */
|
|
do i = il, iu
|
|
qn( : ,i,j,k) = fl * qn( : ,i,jp,k) + fr * qpbnd(:,2,1)
|
|
qn(ivy,i,j,k) = qn(ivy,i,jp,k)
|
|
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
|
|
|
|
do j = neu, nn
|
|
jm = j - 1
|
|
#if NDIMS == 3
|
|
do k = kl, ku
|
|
#endif /* NDIMS == 3 */
|
|
do i = il, iu
|
|
qn( : ,i,j,k) = fl * qn( : ,i,jm,k) + fr * qpbnd(:,2,2)
|
|
qn(ivy,i,j,k) = qn(ivy,i,jm,k)
|
|
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 ! magnetized
|
|
|
|
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 ! magnetized
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
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, nbm, nep, periodic
|
|
use coordinates, only : xmin, xmax
|
|
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, dyz, 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)
|
|
|
|
dyz = ady(pmeta%level) * adz(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 (.not. periodic(1)) then
|
|
if (pmeta%xmin <= xmin) then
|
|
|
|
! advection of magnetic energy across the lower X-boundary
|
|
!
|
|
rterms(14) = rterms(14) &
|
|
#if NDIMS == 3
|
|
+ sum(sum(pdata%q(ibx:ibz,nbm:nb,nl:nu,nb:ne)**2,1) &
|
|
* pdata%q(ivx ,nbm:nb,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
+ sum(sum(pdata%q(ibx:ibz,nbm:nb,nl:nu, : )**2,1) &
|
|
* pdata%q(ivx ,nbm:nb,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
rterms(17) = rterms(17) &
|
|
#if NDIMS == 3
|
|
- sum(sum(pdata%q(ivx:ivz,nbm:nb,nl:nu,nb:ne) &
|
|
* pdata%q(ibx:ibz,nbm:nb,nl:nu,nb:ne),1) &
|
|
* pdata%q(ibx ,nbm:nb,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
- sum(sum(pdata%q(ivx:ivz,nbm:nb,nl:nu, : ) &
|
|
* pdata%q(ibx:ibz,nbm:nb,nl:nu, : ),1) &
|
|
* pdata%q(ibx ,nbm:nb,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
if (resistive) then
|
|
|
|
! diffusion of magnetic energy across the lower X-boundary
|
|
!
|
|
rterms(20) = rterms(20) &
|
|
#if NDIMS == 3
|
|
- sum(cur(2,nbm:nb,nl:nu,nb:ne) &
|
|
* pdata%q(ibz,nbm:nb,nl:nu,nb:ne) &
|
|
- cur(3,nbm:nb,nl:nu,nb:ne) &
|
|
* pdata%q(iby,nbm:nb,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
- sum(cur(2,nbm:nb,nl:nu, : ) &
|
|
* pdata%q(ibz,nbm:nb,nl:nu, : ) &
|
|
- cur(3,nbm:nb,nl:nu, : ) &
|
|
* pdata%q(iby,nbm:nb,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
end if ! resistivity
|
|
|
|
end if
|
|
|
|
if (pmeta%xmax >= xmax) then
|
|
|
|
! advection of magnetic energy across the upper X-boundary
|
|
!
|
|
rterms(14) = rterms(14) &
|
|
#if NDIMS == 3
|
|
- sum(sum(pdata%q(ibx:ibz,ne:nep,nl:nu,nb:ne)**2,1) &
|
|
* pdata%q(ivx ,ne:nep,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
- sum(sum(pdata%q(ibx:ibz,ne:nep,nl:nu, : )**2,1) &
|
|
* pdata%q(ivx ,ne:nep,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
rterms(17) = rterms(17) &
|
|
#if NDIMS == 3
|
|
+ sum(sum(pdata%q(ivx:ivz,ne:nep,nl:nu,nb:ne) &
|
|
* pdata%q(ibx:ibz,ne:nep,nl:nu,nb:ne),1) &
|
|
* pdata%q(ibx ,ne:nep,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
+ sum(sum(pdata%q(ivx:ivz,ne:nep,nl:nu, : ) &
|
|
* pdata%q(ibx:ibz,ne:nep,nl:nu, : ),1) &
|
|
* pdata%q(ibx ,ne:nep,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
if (resistive) then
|
|
|
|
! diffusion of magnetic energy across the upper X-boundary
|
|
!
|
|
rterms(20) = rterms(20) &
|
|
#if NDIMS == 3
|
|
+ sum(cur(2,ne:nep,nl:nu,nb:ne) &
|
|
* pdata%q(ibz,ne:nep,nl:nu,nb:ne) &
|
|
- cur(3,ne:nep,nl:nu,nb:ne) &
|
|
* pdata%q(iby,ne:nep,nl:nu,nb:ne)) * dyz
|
|
#else /* NDIMS == 3 */
|
|
+ sum(cur(2,ne:nep,nl:nu, : ) &
|
|
* pdata%q(ibz,ne:nep,nl:nu, : ) &
|
|
- cur(3,ne:nep,nl:nu, : ) &
|
|
* pdata%q(iby,ne:nep,nl:nu, : )) * dyz
|
|
#endif /* NDIMS == 3 */
|
|
|
|
end if ! resistivity
|
|
|
|
end if
|
|
end if
|
|
|
|
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 across the lower Y-boundary
|
|
!
|
|
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
|
|
!
|
|
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
|
|
!
|
|
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(10:11) = rterms(10:11) / 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:
|
|
! -------------------
|
|
!
|
|
! The function calculates the logarithm of the hyperbolic cosine of x, which
|
|
! is the result of integrating the hyperbolic tangent function, tanh(x).
|
|
! Direct calculation using Fortran intrinsic subroutines can fail for
|
|
! large values of x due to overflow issues. To handle this, the function
|
|
! approximates log(cosh(x)) for large values of |x| using the asymptotic
|
|
! expansion when |x| exceeds a certain threshold. This ensures accurate and
|
|
! stable results across the entire range of input values.
|
|
!
|
|
! Arguments:
|
|
!
|
|
! x - function argument;
|
|
!
|
|
!===============================================================================
|
|
!
|
|
function log_cosh(x) result(y)
|
|
|
|
implicit none
|
|
|
|
real(kind=8), intent(in) :: x
|
|
real(kind=8) :: y, d
|
|
|
|
real(kind=8), parameter :: th = 2.0d+01, lh = log(5.0d-01)
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
if (abs(x) > th) then
|
|
d = exp(-2.0d+00 * abs(x))
|
|
y = abs(x) + lh + d * (1.0d+00 - 5.0d-01 * d)
|
|
else
|
|
y = log(cosh(x))
|
|
end if
|
|
|
|
!-------------------------------------------------------------------------------
|
|
!
|
|
end function log_cosh
|
|
|
|
!===============================================================================
|
|
!
|
|
end module user_problem
|