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mapb2s.f90
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program mapb2s
use iso_fortran_env, only: real64, int64
use param, only: PI, N_R, N_THETA, N_PHI, TWOPI, DEG_TO_RAD
use mtrx, only: norm2, trilinear
use file_op, only: read_maggrid, write_b1rs
use rksolvers, only: rk4
implicit none
include 'omp_lib.h'
real(kind=real64), parameter :: RSS = 2.5d0
real(kind=real64) :: magfieldgrid(0:N_R, 0:N_THETA, 0:N_PHI, 3)
real(kind=real64) :: gbgrid(0:N_R, 0:N_THETA, 0:N_PHI, 3) ! dummy storage
real(kind=real64) :: b1rs(0:N_R, 0:N_THETA, 0:N_PHI, 2)
real(kind=real64) :: pol
real(kind=real64) :: bmag, bmag0
!real(kind=real64) :: v(3)
real(kind=real64) :: t, dt
real(kind=real64) :: r0(3), r1(3), r(3), b(3)
!real(kind=real64) :: sintheta
!real(kind=real64) :: nan(6), nan1
!real(kind=real64) :: dis
real(kind=real64) :: dr
!real(kind=real64) :: bm
integer :: n, i, j, k
integer :: chunk
!integer :: id
!real(kind=real64) :: ratio
integer :: lr, ltheta, lphi
real(kind=real64) :: rmin(3), rmin1(3)
integer :: map(0:N_R, 0:N_THETA, 0:N_PHI)
integer :: n1
!real(kind=real64) :: r_mhd, theta_mhd, phi_mhd
t = 0d0
dr = 0.01d0
dt = 0.005d0
chunk = 1
! load magnetic field grid
call read_maggrid(magfieldgrid, gbgrid)
b1rs = 0.d0
map = 0
print "('N_R = ',i0,', N_THETA = ',i0,', N_PHI = ',i0)", N_R, N_THETA, N_PHI
!$OMP PARALLEL NUM_THREADS(20) DEFAULT(firstprivate) SHARED(chunk,magfieldgrid,b1rs,map)
!$OMP DO SCHEDULE(static,chunk)
! trace field lines from surface surface back to 1 Rs
do k = 0, N_R
r0(1) = 1.00001d0 + k*0.01d0
do i = 0, N_THETA
r0(2) = i * DEG_TO_RAD
do j = 0, N_PHI
r0(3) = j * DEG_TO_RAD
r = r0
b = magfield(r)
if (b(1) > 0) then
pol = 1.0
else
pol = -1.0
end if
n = 0
bmag0 = norm2(b)
b1rs(k,i,j,2) = bmag0
bmag = bmag0
if (k == 1 .and. i == 1 .and. j == 1) write(*,*) b
rmin(1) = 100000.d0
do while (r(1) > 1.000009d0)
r(2) = acos(cos(r(2)))
r(3) = atan2(sin(r(3)), cos(r(3)))
if (r(3) < 0) r(3) = r(3) + TWOPI
r1 = r
b = magfield(r)
bmag = norm2(b)
!v = -pol*b/bmag
!v(2) = v(2)/r1(1)
!sintheta = sin(r1(2))
!if (sintheta == 0) sintheta = 1.0d-6
!v(3) = v(3) / (r1(1)*sintheta)
dt = dr * 0.1
!r = rk4(r1, v, 3, t, dt, vfunc, pol)
r = rk4(vfunc, t, r1, dt, pol)
n = n + 1
if (r(2) < 0) then
r(2) = -r(2)
r(3) = r(3) + pi
if (r(3) > twopi) r(3) = r(3) - twopi
end if
if (r(1) < rmin(1)) rmin = r
if ((r(1) - rmin(1)) > 2.5 .or. n > 10000) then !wrong direction?
pol = -pol !try back with opposite polarity
n1 = 0
r = r0
rmin1(1) = 100000.0
do while (r(1) > 1.000009d0)
r(2) = acos(cos(r(2)))
r(3) = atan2(sin(r(3)),cos(r(3)))
if (r(3) < 0) r(3) = r(3) + twopi
r1 = r
b = magfield(r)
bmag = norm2(b)
!v = -pol * b / bmag
!v(2) = v(2) / r1(1)
!sintheta = sin(r1(2))
!if (sintheta == 0) sintheta = 1.0d-6
!v(3) = v(3) / (r1(1)*sintheta)
dt = dr * 0.1
!r = rk4(r1, v, 3, t, dt, vfunc, pol)
r = rk4(vfunc, t, r1, dt, pol)
n1 = n1 + 1
if (r(2) < 0) then
r(2) = -r(2)
r(3) = r(3)+pi
if (r(3) > twopi) r(3) = r(3) - twopi
end if
if (r(1) < rmin1(1)) rmin1 = r
! double open field or stuck
if ((r(1) - rmin1(1)) > 2.5 .or. n1 > 10000) then
if (rmin(1) < rmin1(1)) then
pol = -pol
r = rmin ! use rmin to remap
else
pol = pol
r = rmin1
end if
lr = floor((r(1)-1.0d0) / 0.01d0)
ltheta = floor(r(2) / pi * 180.d0)
lphi = floor(r(3) / pi * 180.d0)
if (((lr*(N_THETA+1)+ltheta) * (N_PHI+1) + lphi) < &
((k*(N_THETA+1) + i) * (N_PHI+1) + j)) then
map(k,i,j) = (lr*(N_THETA+1)+ltheta) * (N_PHI+1) + lphi
else
write(*,*) "New x point at", lr, ltheta, lphi
map(k,i,j) = ((lr-1)*(N_THETA+1)+ltheta) * (N_PHI+1) + lphi
end if
bmag = 0.0
exit
end if
end do
exit
end if
end do
!nan1 = -3.0
!nan = sqrt(nan1)
b1rs(k,i,j,1) = pol * bmag
map(k,i,j) = pol * map(k,i,j)
end do
end do
end do
!$OMP BARRIER
!$OMP END PARALLEL
call write_b1rs(b1rs, map)
contains
! velocity function. find dr/dt given r and t (t not really needed)
! v = -sgn(B_r) / |B| (B_r r_hat + B_theta / r theta_hat + B_phi / (r sin theta) phi_hat)
function vfunc(t, r, pol) result(v)
real(kind=real64), intent(in) :: t, r(3), pol
real(kind=real64) :: v(3)
real(kind=real64) :: b(3), bmag, sintheta
b = magfield(r)
bmag = norm2(b)
if (bmag == 0) then
v = 0
return
end if
v = -pol * b / bmag
v(2) = v(2) / r(1)
sintheta = sin(r(2))
if (sintheta == 0) sintheta = 1.0d-6
v(3) = v(3) / (r(1) * sintheta)
end function
! get \vec{B} = \vec{B}(\vec{r})
function magfield(rvec) result(b)
real(kind=real64), intent(in) :: rvec(3)
real(kind=real64) :: b(3)
real(kind=real64) :: r, theta, phi ! input copy
real(kind=real64) :: fc(2,2,2)
real(kind=real64) :: px(3)
integer(kind=int64) :: irr, itheta, iphi ! grid positon
integer(kind=int64) :: m ! iteration variable
b(:) = 0
r = rvec(1)
theta = rvec(2)
phi = rvec(3)
theta = acos(cos(theta))
phi = atan2(sin(phi), cos(phi))
if (phi < 0.0) phi = phi + twopi
! find the grid cell
irr = floor((r-1) / (RSS-1) * N_R)
if (irr >= N_R) irr = N_R - 1
itheta = floor(theta / pi * N_THETA)
if (itheta >= N_THETA) itheta = N_THETA - 1
iphi = floor(phi / twopi * N_PHI)
if (iphi >= N_PHI) iphi = N_PHI - 1
if (irr < 0) then
! going into the sun, stop at the surface
b = magfieldgrid(0, itheta, iphi, :)
return
end if
! relative displacement from lower grids
px(1) = (r-1.0) / (RSS-1.0) * N_R - irr
px(2) = theta / pi * N_THETA - itheta
px(3) = phi / twopi * N_PHI - iphi
!print "(a,':',i3,': ', ' irr = ', i3, ', itheta = ', i3, ', iphi = ', i3)", &
! __FILE__, __LINE__, irr, itheta, iphi
do m = 1, 3
fc(1,1,1) = magfieldgrid(irr, itheta, iphi, m)
fc(2,1,1) = magfieldgrid(irr+1, itheta, iphi, m)
fc(1,2,1) = magfieldgrid(irr, itheta+1, iphi, m)
fc(2,2,1) = magfieldgrid(irr+1, itheta+1, iphi, m)
fc(1,1,2) = magfieldgrid(irr, itheta, iphi+1, m)
fc(2,1,2) = magfieldgrid(irr+1, itheta, iphi+1, m)
fc(1,2,2) = magfieldgrid(irr, itheta+1, iphi+1, m)
fc(2,2,2) = magfieldgrid(irr+1, itheta+1, iphi+1, m)
! interpolate the magnetic field
b(m) = trilinear(fc, px)
end do
end function ! magfield
end program
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!Modification log
!!7/12/21:
! corona data interpolated e.g. l246
! adaptive dt based on dr e.g. l70
! use b1rs from ir-1 if reconnection occurs at ir e.g. l81
! Failed tracing overhaul 7/2/21
! output polarity information in sign of b1rs