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
202
203
204
205
206
207
208
209
210
211
212
213
214
215
|
! $Header$
#include "cctk.h"
subroutine dissipation_4_2 (var, ni, nj, nk, bb, gsize, delta, epsdis, rhs)
implicit none
integer :: ni, nj, nk
CCTK_REAL, dimension(ni,nj,nk), intent(in) :: var
CCTK_REAL, dimension(ni,nj,nk), intent(inout) :: rhs
CCTK_INT, dimension(6), intent(in) :: bb
CCTK_INT, dimension(3), intent(in) :: gsize
CCTK_REAL, dimension(3), intent(in) :: delta
CCTK_REAL, intent(in) :: epsdis
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
integer :: i, j, k
CCTK_REAL, dimension(6,4) :: a
CCTK_REAL :: idel
CCTK_INT :: il, ir, jl, jr, kl, kr
call set_coeff ( a )
idel = epsdis / 16
if ( bb(1) == 0 ) then
il = 1 + gsize(1)
else
rhs(1,:,:) = rhs(1,:,:) + &
( a(1,1) * var(1,:,:) + a(2,1) * var(2,:,:) + &
a(3,1) * var(3,:,:) ) * idel
rhs(2,:,:) = rhs(2,:,:) + &
( a(1,2) * var(1,:,:) + a(2,2) * var(2,:,:) + &
a(3,2) * var(3,:,:) + a(4,2) * var(4,:,:) ) * idel
rhs(3,:,:) = rhs(3,:,:) + &
( a(1,3) * var(1,:,:) + a(2,3) * var(2,:,:) + &
a(3,3) * var(3,:,:) + a(4,3) * var(4,:,:) + &
a(5,3) * var(5,:,:) ) * idel
rhs(4,:,:) = rhs(4,:,:) + &
( a(2,4) * var(2,:,:) + a(3,4) * var(3,:,:) + &
a(4,4) * var(4,:,:) + a(5,4) * var(5,:,:) + &
a(6,4) * var(6,:,:) ) * idel
il = 5
end if
if ( bb(2) == 0 ) then
ir = ni - gsize(1)
else
rhs(ni-3,:,:) = rhs(ni-3,:,:) + &
( a(2,4) * var(ni-1,:,:) + a(3,4) * var(ni-2,:,:) + &
a(4,4) * var(ni-3,:,:) + a(5,4) * var(ni-4,:,:) + &
a(6,4) * var(ni-5,:,:) ) * idel
rhs(ni-2,:,:) = rhs(ni-2,:,:) + &
( a(1,3) * var(ni,:,:) + a(2,3) * var(ni-1,:,:) + &
a(3,3) * var(ni-2,:,:) + a(4,3) * var(ni-3,:,:) + &
a(5,3) * var(ni-4,:,:) ) * idel
rhs(ni-1,:,:) = rhs(ni-1,:,:) + &
( a(1,2) * var(ni,:,:) + a(2,2) * var(ni-1,:,:) + &
a(3,2) * var(ni-2,:,:) + a(4,2) * var(ni-3,:,:) ) * idel
rhs(ni,:,:) = rhs(ni,:,:) + &
( a(1,1) * var(ni,:,:) + a(2,1) * var(ni-1,:,:) + &
a(3,1) * var(ni-2,:,:) ) * idel
ir = ni - 4
end if
rhs(il:ir,:,:) = rhs(il:ir,:,:) + &
( -6.0_wp * var(il:ir,:,:) + &
4.0_wp * ( var(il-1:ir-1,:,:) + &
var(il+1:ir+1,:,:) ) - &
( var(il-2:ir-2,:,:) + &
var(il+2:ir+2,:,:) ) ) * idel
call set_coeff ( a )
idel = epsdis / 16
if ( bb(3) == 0 ) then
jl = 1 + gsize(2)
else
rhs(:,1,:) = rhs(:,1,:) + &
( a(1,1) * var(:,1,:) + a(2,1) * var(:,2,:) + &
a(3,1) * var(:,3,:) ) * idel
rhs(:,2,:) = rhs(:,2,:) + &
( a(1,2) * var(:,1,:) + a(2,2) * var(:,2,:) + &
a(3,2) * var(:,3,:) + a(4,2) * var(:,4,:) ) * idel
rhs(:,3,:) = rhs(:,3,:) + &
( a(1,3) * var(:,1,:) + a(2,3) * var(:,2,:) + &
a(3,3) * var(:,3,:) + a(4,3) * var(:,4,:) + &
a(5,3) * var(:,5,:) ) * idel
rhs(:,4,:) = rhs(:,4,:) + &
( a(2,4) * var(:,2,:) + a(3,4) * var(:,3,:) + &
a(4,4) * var(:,4,:) + a(5,4) * var(:,5,:) + &
a(6,4) * var(:,6,:) ) * idel
jl = 5
end if
if ( bb(4) == 0 ) then
jr = nj - gsize(2)
else
rhs(:,nj-3,:) = rhs(:,nj-3,:) + &
( a(2,4) * var(:,nj-1,:) + a(3,4) * var(:,nj-2,:) + &
a(4,4) * var(:,nj-3,:) + a(5,4) * var(:,nj-4,:) + &
a(6,4) * var(:,nj-5,:) ) * idel
rhs(:,nj-2,:) = rhs(:,nj-2,:) + &
( a(1,3) * var(:,nj,:) + a(2,3) * var(:,nj-1,:) + &
a(3,3) * var(:,nj-2,:) + a(4,3) * var(:,nj-3,:) + &
a(5,3) * var(:,nj-4,:) ) * idel
rhs(:,nj-1,:) = rhs(:,nj-1,:) + &
( a(1,2) * var(:,nj,:) + a(2,2) * var(:,nj-1,:) + &
a(3,2) * var(:,nj-2,:) + a(4,2) * var(:,nj-3,:) ) * idel
rhs(:,nj,:) = rhs(:,nj,:) + &
( a(1,1) * var(:,nj,:) + a(2,1) * var(:,nj-1,:) + &
a(3,1) * var(:,nj-2,:) ) * idel
jr = nj - 4
end if
rhs(:,jl:jr,:) = rhs(:,jl:jr,:) + &
( -6.0_wp * var(:,jl:jr,:) + &
4.0_wp * ( var(:,jl-1:jr-1,:) + &
var(:,jl+1:jr+1,:) ) - &
( var(:,jl-2:jr-2,:) + &
var(:,jl+2:jr+2,:) ) ) * idel
call set_coeff ( a )
idel = epsdis / 16
if ( bb(5) == 0 ) then
kl = 1 + gsize(3)
else
rhs(:,:,1) = rhs(:,:,1) + &
( a(1,1) * var(:,:,1) + a(2,1) * var(:,:,2) + &
a(3,1) * var(:,:,3) ) * idel
rhs(:,:,2) = rhs(:,:,2) + &
( a(1,2) * var(:,:,1) + a(2,2) * var(:,:,2) + &
a(3,2) * var(:,:,3) + a(4,2) * var(:,:,4) ) * idel
rhs(:,:,3) = rhs(:,:,3) + &
( a(1,3) * var(:,:,1) + a(2,3) * var(:,:,2) + &
a(3,3) * var(:,:,3) + a(4,3) * var(:,:,4) + &
a(5,3) * var(:,:,5) ) * idel
rhs(:,:,4) = rhs(:,:,4) + &
( a(2,4) * var(:,:,2) + a(3,4) * var(:,:,3) + &
a(4,4) * var(:,:,4) + a(5,4) * var(:,:,5) + &
a(6,4) * var(:,:,6) ) * idel
kl = 5
end if
if ( bb(6) == 0 ) then
kr = nk - gsize(3)
else
rhs(:,:,nk-3) = rhs(:,:,nk-3) + &
( a(2,4) * var(:,:,nk-1) + a(3,4) * var(:,:,nk-2) + &
a(4,4) * var(:,:,nk-3) + a(5,4) * var(:,:,nk-4) + &
a(6,4) * var(:,:,nk-5) ) * idel
rhs(:,:,nk-2) = rhs(:,:,nk-2) + &
( a(1,3) * var(:,:,nk) + a(2,3) * var(:,:,nk-1) + &
a(3,3) * var(:,:,nk-2) + a(4,3) * var(:,:,nk-3) + &
a(5,3) * var(:,:,nk-4) ) * idel
rhs(:,:,nk-1) = rhs(:,:,nk-1) + &
( a(1,2) * var(:,:,nk) + a(2,2) * var(:,:,nk-1) + &
a(3,2) * var(:,:,nk-2) + a(4,2) * var(:,:,nk-3) ) * idel
rhs(:,:,nk) = rhs(:,:,nk) + &
( a(1,1) * var(:,:,nk) + a(2,1) * var(:,:,nk-1) + &
a(3,1) * var(:,:,nk-2) ) * idel
kr = nk - 4
end if
rhs(:,:,kl:kr) = rhs(:,:,kl:kr) + &
( -6.0_wp * var(:,:,kl:kr) + &
4.0_wp * ( var(:,:,kl-1:kr-1) + &
var(:,:,kl+1:kr+1) ) - &
( var(:,:,kl-2:kr-2) + &
var(:,:,kl+2:kr+2) ) ) * idel
contains
subroutine set_coeff ( a )
implicit none
CCTK_REAL, dimension(6,4), intent(OUT) :: a
CCTK_REAL :: zero = 0.0
integer, parameter :: wp = kind(zero)
a(1,1) = -2.8235294117647058823529411764705882352941176470588_wp
a(2,1) = 5.6470588235294117647058823529411764705882352941176_wp
a(3,1) = -2.8235294117647058823529411764705882352941176470588_wp
a(4,1) = 0.0_wp
a(5,1) = 0.0_wp
a(6,1) = 0.0_wp
a(1,2) = 1.6271186440677966101694915254237288135593220338983_wp
a(2,2) = -4.0677966101694915254237288135593220338983050847458_wp
a(3,2) = 3.2542372881355932203389830508474576271186440677966_wp
a(4,2) = -0.81355932203389830508474576271186440677966101694915_wp
a(5,2) = 0.0_wp
a(6,2) = 0.0_wp
a(1,3) = -1.1162790697674418604651162790697674418604651162791_wp
a(2,3) = 4.4651162790697674418604651162790697674418604651163_wp
a(3,3) = -6.6976744186046511627906976744186046511627906976744_wp
a(4,3) = 4.4651162790697674418604651162790697674418604651163_wp
a(5,3) = -1.1162790697674418604651162790697674418604651162791_wp
a(6,3) = 0.0_wp
a(1,4) = 0.0_wp
a(2,4) = -0.97959183673469387755102040816326530612244897959184_wp
a(3,4) = 3.9183673469387755102040816326530612244897959183673_wp
a(4,4) = -5.8775510204081632653061224489795918367346938775510_wp
a(5,4) = 3.9183673469387755102040816326530612244897959183673_wp
a(6,4) = -0.97959183673469387755102040816326530612244897959184_wp
end subroutine set_coeff
end subroutine dissipation_4_2
|
