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
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
#include "cctk.h"
c ========================================================================
SUBROUTINE momentum_integrand3D(origin,Dx,Dy,Dz,x,y,z,gxx,gxy,gxz,
& gyy,gyz,gzz,hxx,hxy,hxz,hyy,hyz,hzz,
& momentum_int,Psi,Psi_power,conformal_state)
c ------------------------------------------------------------------------
c
c Estimates the momentum at a given radius using Equation (11.2.14) from
c Walds General Relativity
c
c -----------------------------------------------------------------------
IMPLICIT NONE
c Input variables
INTEGER,INTENT(IN) ::
& Psi_power,conformal_state
CCTK_REAL,INTENT(IN) ::
& Dx,Dy,Dz,origin(3)
CCTK_REAL,DIMENSION(:),INTENT(IN) ::
& x,y,z
CCTK_REAL,DIMENSION(:,:,:),INTENT(IN) ::
& gxx,gxy,gxz,gyy,gyz,gzz,Psi,
& hxx,hxy,hxz,hyy,hyz,hzz
c Output variables
CCTK_REAL,DIMENSION(:,:,:),INTENT(OUT) ::
& momentum_int
c Local variables, here only
INTEGER ::
& i,j,k,ip,count
CCTK_REAL,PARAMETER ::
& half = 0.5D0
CCTK_REAL ::
& rad,ux,uy,uz,det,dxx,dxy,dxz,dyy,dyz,dzz,uxx,uxy,uxz,uyy,
& uyz,uzz,
& Pi,idet,p,term1,
& tracek
data count / 1 /
save count
c ------------------------------------------------------------------------
Pi = ACOS(-1D0)
c Because other codes evolve Psi**4
SELECT CASE (Psi_power)
CASE (1)
ip = 4
CASE (4)
ip = 1
CASE DEFAULT
WRITE(*,*) "This value of Psi_power is not supported"
END SELECT
DO k = 2, SIZE(z)-1
DO j = 2, SIZE(y)-1
DO i = 2, SIZE(x)-1
rad = SQRT((x(i)-origin(1))**2
& +(y(j)-origin(2))**2
& +(z(k)-origin(3))**2)
IF (rad.NE.0) THEN
ux = (x(i)-origin(1))/rad
uy = (y(j)-origin(2))/rad
uz = (z(k)-origin(3))/rad
c Abbreviations for metric coefficients
c -------------------------------------
if (conformal_state > 0) then
p = psi(i,j,k)**ip
dxx = p*gxx(i,j,k); dxy = p*gxy(i,j,k)
dxz = p*gxz(i,j,k); dyy = p*gyy(i,j,k)
dyz = p*gyz(i,j,k); dzz = p*gzz(i,j,k)
else
p = 1.0d0
dxx = gxx(i,j,k); dxy = gxy(i,j,k)
dxz = gxz(i,j,k); dyy = gyy(i,j,k)
dyz = gyz(i,j,k); dzz = gzz(i,j,k)
end if
c Determinant of 3-metric
c -----------------------
det = (dxx*dyy*dzz + 2.0D0*dxy*dxz*dyz
& - (dxx*dyz**2 + dyy*dxz**2 + dzz*dxy**2))
idet = 1.0/det
c Inverse 3-metric
c ----------------
uxx = idet*(dyy*dzz - dyz**2)
uyy = idet*(dxx*dzz - dxz**2)
uzz = idet*(dxx*dyy - dxy**2)
uxy = idet*(dxz*dyz - dzz*dxy)
uxz = idet*(dxy*dyz - dyy*dxz)
uyz = idet*(dxy*dxz - dxx*dyz)
c Trace of extrinsic curvature
c ----------------------------
tracek = uxx*hxx(i,j,k) + uyy*hyy(i,j,k) +
& uzz*hzz(i,j,k)
c Integrands
c ----------
if (count.eq.1) then
term1 = ux*hxx(i,j,k)+uy*hxy(i,j,k)+uz*hxz(i,j,k)
c momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
c & (term1 - tracek*ux)*rad**2
momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
& (term1 - tracek*(dxx*ux+dxy*uy+dxz*uz))*rad**2
else if (count.eq.2) then
term1 = ux*hxy(i,j,k)+uy*hyy(i,j,k)+uz*hyz(i,j,k)
c momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
c & (term1 - tracek*uy)*rad**2
momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
& (term1 - tracek*(dxy*ux+dyy*uy+dyz*uz))*rad**2
else if (count.eq.3) then
term1 = ux*hxz(i,j,k)+uy*hyz(i,j,k)+uz*hzz(i,j,k)
c momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
c & (term1 - tracek*uz)*rad**2
momentum_int(i,j,k) = 1.0D0/8.0D0/Pi*
& (term1 - tracek*(dxz*ux+dyz*uy+dzz*uz))*rad**2
end if
ELSE
momentum_int(i,j,k) = 0.0D0
ENDIF
ENDDO
ENDDO
ENDDO
c This is needed when the grid is an octant, but it does not hurt
c if it is not
DO k = 2, size(z)-1
DO j = 2, size(y)-1
momentum_int(1,j,k) = momentum_int(2,j,k)
ENDDO
ENDDO
DO k = 2, size(z)-1
DO i = 1, size(x)-1
momentum_int(i,1,k) = momentum_int(i,2,k)
ENDDO
ENDDO
DO j = 1, size(y)-1
DO i = 1, size(x)-1
momentum_int(i,j,1) = momentum_int(i,j,2)
ENDDO
ENDDO
c setting counter
c ---------------
if (count.eq.3) then
count = 1
else
count = count + 1
end if
c end
c ---
END SUBROUTINE momentum_integrand3D
|
