-
Notifications
You must be signed in to change notification settings - Fork 6
/
regcoil_evaluate_coil_surface.f90
170 lines (146 loc) · 9.15 KB
/
regcoil_evaluate_coil_surface.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
subroutine regcoil_evaluate_coil_surface()
! This subroutine takes the arrays rmnc_coil, zmns_coil, etc, and evaluates the position vector r_coil
! and its first and second derivatives with respect to theta and zeta.
use regcoil_variables
use stel_kinds
implicit none
integer :: imn, m, n, iflag, j
real(dp) :: rmnc, rmns, zmnc, zmns
real(dp) :: angle, sinangle, cosangle, dsinangledtheta, dcosangledtheta, dsinangledzeta, dcosangledzeta
real(dp) :: d2sinangledtheta2, d2sinangledthetadzeta, d2sinangledzeta2, d2cosangledtheta2, d2cosangledthetadzeta, d2cosangledzeta2
real(dp) :: angle2, sinangle2, cosangle2, dsinangle2dzeta, dcosangle2dzeta, d2sinangle2dzeta2, d2cosangle2dzeta2
real(dp), dimension(:,:), allocatable :: major_R_squared
integer :: itheta, izeta
integer :: tic, toc, countrate
real(dp), dimension(:,:), allocatable :: sin_m_theta, cos_m_theta, sin_n_zeta, cos_n_zeta
call system_clock(tic,countrate)
allocate(sin_m_theta(mnmax_coil,ntheta_coil))
allocate(cos_m_theta(mnmax_coil,ntheta_coil))
allocate(sin_n_zeta( mnmax_coil,nzetal_coil))
allocate(cos_n_zeta( mnmax_coil,nzetal_coil))
do itheta = 1,ntheta_coil
sin_m_theta(:,itheta) = sin(xm_coil * theta_coil(itheta))
cos_m_theta(:,itheta) = cos(xm_coil * theta_coil(itheta))
end do
do izeta = 1,nzetal_coil
sin_n_zeta(:, izeta) = sin(xn_coil * zetal_coil(izeta))
cos_n_zeta(:, izeta) = cos(xn_coil * zetal_coil(izeta))
end do
r_coil = 0
drdtheta_coil = 0
drdzeta_coil = 0
d2rdtheta2_coil = 0
d2rdthetadzeta_coil = 0
d2rdzeta2_coil = 0
do izeta = 1,nzetal_coil
angle2 = zetal_coil(izeta)
sinangle2 = sin(angle2)
cosangle2 = cos(angle2)
dsinangle2dzeta = cosangle2
dcosangle2dzeta = -sinangle2
d2sinangle2dzeta2 = -sinangle2
d2cosangle2dzeta2 = -cosangle2
do imn = 1, mnmax_coil
m = xm_coil(imn)
n = xn_coil(imn)
rmnc = rmnc_coil(imn)
rmns = rmns_coil(imn)
zmnc = zmnc_coil(imn)
zmns = zmns_coil(imn)
do itheta = 1,ntheta_coil
!angle = m*theta_coil(itheta) - n*zetal_coil(izeta)
!sinangle = sin(angle)
!cosangle = cos(angle)
! Trig angle sum formulae for angle = m*theta_coil(itheta) - n*zetal_coil(izeta):
sinangle = sin_m_theta(imn,itheta) * cos_n_zeta(imn,izeta) - cos_m_theta(imn,itheta) * sin_n_zeta(imn,izeta)
cosangle = cos_m_theta(imn,itheta) * cos_n_zeta(imn,izeta) + sin_m_theta(imn,itheta) * sin_n_zeta(imn,izeta)
!if (abs(sinangle - sin(angle)) > 1d-10) stop "Error sin"
!if (abs(cosangle - cos(angle)) > 1d-10) stop "Error cos"
dsinangledtheta = cosangle*m
dcosangledtheta = -sinangle*m
dsinangledzeta = -cosangle*n
dcosangledzeta = sinangle*n
r_coil(1,itheta,izeta) = r_coil(1,itheta,izeta) + rmnc * cosangle * cosangle2 + rmns * sinangle * cosangle2
r_coil(2,itheta,izeta) = r_coil(2,itheta,izeta) + rmnc * cosangle * sinangle2 + rmns * sinangle * sinangle2
r_coil(3,itheta,izeta) = r_coil(3,itheta,izeta) + zmns * sinangle + zmnc * cosangle
drdtheta_coil(1,itheta,izeta) = drdtheta_coil(1,itheta,izeta) + rmnc * dcosangledtheta * cosangle2 + rmns * dsinangledtheta * cosangle2
drdtheta_coil(2,itheta,izeta) = drdtheta_coil(2,itheta,izeta) + rmnc * dcosangledtheta * sinangle2 + rmns * dsinangledtheta * sinangle2
drdtheta_coil(3,itheta,izeta) = drdtheta_coil(3,itheta,izeta) + zmns * dsinangledtheta + zmnc * dcosangledtheta
drdzeta_coil(1,itheta,izeta) = drdzeta_coil(1,itheta,izeta) + rmnc * (dcosangledzeta * cosangle2 + cosangle * dcosangle2dzeta) &
+ rmns * (dsinangledzeta * cosangle2 + sinangle * dcosangle2dzeta)
drdzeta_coil(2,itheta,izeta) = drdzeta_coil(2,itheta,izeta) + rmnc * (dcosangledzeta * sinangle2 + cosangle * dsinangle2dzeta) &
+ rmns * (dsinangledzeta * sinangle2 + sinangle * dsinangle2dzeta)
drdzeta_coil(3,itheta,izeta) = drdzeta_coil(3,itheta,izeta) + zmns * dsinangledzeta + zmnc * dcosangledzeta
! 2nd derivatives are only constructed on 1 field period.
if (izeta > nzeta_coil) cycle
d2sinangledtheta2 = -m*m*sinangle
d2sinangledthetadzeta = m*n*sinangle
d2sinangledzeta2 = -n*n*sinangle
d2cosangledtheta2 = -m*m*cosangle
d2cosangledthetadzeta = m*n*cosangle
d2cosangledzeta2 = -n*n*cosangle
d2rdtheta2_coil(1,itheta,izeta) = d2rdtheta2_coil(1,itheta,izeta) + rmnc * d2cosangledtheta2 * cosangle2 + rmns * d2sinangledtheta2 * cosangle2
d2rdtheta2_coil(2,itheta,izeta) = d2rdtheta2_coil(2,itheta,izeta) + rmnc * d2cosangledtheta2 * sinangle2 + rmns * d2sinangledtheta2 * sinangle2
d2rdtheta2_coil(3,itheta,izeta) = d2rdtheta2_coil(3,itheta,izeta) + zmns * d2sinangledtheta2 + zmnc * d2cosangledtheta2
d2rdthetadzeta_coil(1,itheta,izeta) = d2rdthetadzeta_coil(1,itheta,izeta) + rmnc * (d2cosangledthetadzeta * cosangle2 + dcosangledtheta * dcosangle2dzeta) &
+ rmns * (d2sinangledthetadzeta * cosangle2 + dsinangledtheta * dcosangle2dzeta)
d2rdthetadzeta_coil(2,itheta,izeta) = d2rdthetadzeta_coil(2,itheta,izeta) + rmnc * (d2cosangledthetadzeta * sinangle2 + dcosangledtheta * dsinangle2dzeta) &
+ rmns * (d2sinangledthetadzeta * sinangle2 + dsinangledtheta * dsinangle2dzeta)
d2rdthetadzeta_coil(3,itheta,izeta) = d2rdthetadzeta_coil(3,itheta,izeta) + zmns * d2sinangledthetadzeta + zmnc * d2cosangledthetadzeta
d2rdzeta2_coil(1,itheta,izeta) = d2rdzeta2_coil(1,itheta,izeta) + rmnc * (d2cosangledzeta2 * cosangle2 + dcosangledzeta * dcosangle2dzeta &
+ dcosangledzeta * dcosangle2dzeta + cosangle * d2cosangle2dzeta2) &
+ rmns * (d2sinangledzeta2 * cosangle2 + dsinangledzeta * dcosangle2dzeta &
+ dsinangledzeta * dcosangle2dzeta + sinangle * d2cosangle2dzeta2)
d2rdzeta2_coil(2,itheta,izeta) = d2rdzeta2_coil(2,itheta,izeta) + rmnc * (d2cosangledzeta2 * sinangle2 + dcosangledzeta * dsinangle2dzeta &
+ dcosangledzeta * dsinangle2dzeta + cosangle * d2sinangle2dzeta2) &
+ rmns * (d2sinangledzeta2 * sinangle2 + dsinangledzeta * dsinangle2dzeta &
+ dsinangledzeta * dsinangle2dzeta + sinangle * d2sinangle2dzeta2)
d2rdzeta2_coil(3,itheta,izeta) = d2rdzeta2_coil(3,itheta,izeta) + zmns * d2sinangledzeta2 + zmnc * d2cosangledzeta2
end do
end do
end do
deallocate(sin_m_theta, cos_m_theta, sin_n_zeta, cos_n_zeta)
call system_clock(toc)
if (verbose) print *," Evaluating coil surface & derivatives:",real(toc-tic)/countrate," sec."
!!$ print *,"mnmax_coil:",mnmax_coil
!!$ print *,"xm_coil:",xm_coil
!!$ print *,"xn_coil:",xn_coil
!!$ print *,"rmnc_coil:",rmnc_coil
!!$ print *,"zmns_coil:",zmns_coil
!!$ print *,"r_coil(1,:,:):"
!!$ do j = 1,ntheta_coil
!!$ print *,r_coil(1,j,:)
!!$ end do
!!$ print *,"r_coil(2,:,:):"
!!$ do j = 1,ntheta_coil
!!$ print *,r_coil(2,j,:)
!!$ end do
!!$ print *,"r_coil(3,:,:):"
!!$ do j = 1,ntheta_coil
!!$ print *,r_coil(3,j,:)
!!$ end do
! Evaluate cross product:
normal_coil(1,:,:) = drdzeta_coil(2,:,:) * drdtheta_coil(3,:,:) - drdtheta_coil(2,:,:) * drdzeta_coil(3,:,:)
normal_coil(2,:,:) = drdzeta_coil(3,:,:) * drdtheta_coil(1,:,:) - drdtheta_coil(3,:,:) * drdzeta_coil(1,:,:)
normal_coil(3,:,:) = drdzeta_coil(1,:,:) * drdtheta_coil(2,:,:) - drdtheta_coil(1,:,:) * drdzeta_coil(2,:,:)
if (allocated(norm_normal_coil)) deallocate(norm_normal_coil)
allocate(norm_normal_coil(ntheta_coil, nzeta_coil),stat=iflag)
if (iflag .ne. 0) stop 'Allocation error! regcoil_init_coil_surface 11'
norm_normal_coil = sqrt(normal_coil(1,:,1:nzeta_coil)**2 + normal_coil(2,:,1:nzeta_coil)**2 &
+ normal_coil(3,:,1:nzeta_coil)**2)
area_coil = nfp * dtheta_coil * dzeta_coil * sum(norm_normal_coil)
! Compute coil surface volume using \int (1/2) R^2 dZ dzeta.
! These quantities will be evaluated on the half theta grid, which is the natural grid for dZ,
! but we will need to interpolate R^2 from the full to half grid.
allocate(major_R_squared(ntheta_coil,nzetal_coil))
major_R_squared = r_coil(1,:,:)*r_coil(1,:,:) + r_coil(2,:,:)*r_coil(2,:,:)
! First handle the interior of the theta grid:
volume_coil = sum((major_R_squared(1:ntheta_coil-1,:) + major_R_squared(2:ntheta_coil,:)) * (0.5d+0) & ! R^2, interpolated from full to half grid
* (r_coil(3,2:ntheta_coil,:)-r_coil(3,1:ntheta_coil-1,:))) ! dZ
! Add the contribution from the ends of the theta grid:
volume_coil = volume_coil + sum((major_R_squared(1,:) + major_R_squared(ntheta_coil,:)) * (0.5d+0) & ! R^2, interpolated from full to half grid
* (r_coil(3,1,:)-r_coil(3,ntheta_coil,:))) ! dZ
volume_coil = abs(volume_coil * dzeta_coil / 2) ! r includes all nfp periods already, so no factor of nfp needed.
deallocate(major_R_squared)
if (verbose) print "(a,es10.3,a,es10.3,a)"," Coil surface area:",area_coil," m^2. Volume:",volume_coil," m^3."
end subroutine regcoil_evaluate_coil_surface