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
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
|
*DECK NSSFL3
SUBROUTINE NSSFL3(IPFLX,NUN,NG,NEL,NMIX,NALB,EPSNOD,MAXNOD,
1 EPSOUT,MAXOUT,MAT,XX,XXX,IDL,IQFR,QFR,DIFF,SIGR,CHI,SIGF,SCAT,
2 BETA,FD,IMPX)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Flux calculation for the analytic nodal method in Cartesian 1D
* geometry using the nodal correction iteration strategy.
*
*Copyright:
* Copyright (C) 2022 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* IPFLX nodal flux.
* NUN number of unknowns per energy group (=4*NEL+1).
* NG number of energy groups.
* NEL number of nodes in the nodal calculation.
* NMIX number of mixtures in the nodal calculation.
* NALB number of physical albedos.
* EPSNOD nodal correction epsilon.
* MAXNOD maximum number of nodal correction iterations.
* EPSOUT convergence epsilon for the power method.
* MAXOUT maximum number of iterations for the power method.
* MAT material mixtures.
* XX mesh spacings.
* XXX Cartesian coordinates along the X axis.
* IDL position of averaged fluxes in unknown vector.
* IQFR boundary condition information.
* QFR albedo function information.
* DIFF diffusion coefficients
* SIGR removal cross sections.
* CHI fission spectra.
* SIGF nu times fission cross section.
* SCAT scattering cross section.
* BETA albedos.
* FD discontinuity factors.
* IMPX edition flag.
*
*-----------------------------------------------------------------------
*
USE GANLIB
*----
* SUBROUTINE ARGUMENTS
*----
TYPE(C_PTR) IPFLX
INTEGER NUN,NG,NEL,NMIX,NALB,MAXNOD,MAXOUT,IMPX,MAT(NEL),IDL(NEL),
1 IQFR(6,NEL)
REAL EPSNOD,EPSOUT,XX(NEL),XXX(NEL+1),QFR(6,NEL),DIFF(NMIX,NG),
1 SIGR(NMIX,NG),CHI(NMIX,NG),SIGF(NMIX,NG),SCAT(NMIX,NG,NG),
2 BETA(NALB,NG,NG),FD(NMIX,2,NG,NG)
*----
* LOCAL VARIABLES
*----
TYPE(C_PTR) JPFLX
INTEGER, PARAMETER :: NY=1,NZ=1,NDIM=1
REAL :: COEF(6),CODR(6),KEFF,KEFF_OLD
*----
* ALLOCATABLE ARRAYS
*----
REAL, ALLOCATABLE, DIMENSION(:) :: YY,ZZ,EVECT
REAL, ALLOCATABLE, DIMENSION(:,:) :: A,SAVG
REAL, ALLOCATABLE, DIMENSION(:,:,:) :: QFR2,DRIFT
*
ALB(X)=0.5*(1.0-X)/(1.0+X)
*----
* SCRATCH STORAGE ALLOCATION
*----
N=NEL*NG
ALLOCATE(QFR2(6,NEL,NG),YY(NEL),ZZ(NEL),A(N,2*N),EVECT(N))
ALLOCATE(DRIFT(6,NEL,NG),SAVG(NUN,NG))
*----
* ALBEDO PROCESSING
*----
QFR2(:6,:NEL,:NG)=0.0
DO IG=1,NG
DO IQW=1,2
DO IEL=1,NEL
IALB=IQFR(IQW,IEL)
IF(IALB > 0) THEN
IF(IALB.GT.NALB) CALL XABORT('NSSFL3: BETA OVERFLOW.')
QFR2(IQW,IEL,IG)=QFR(IQW,IEL)*ALB(BETA(IALB,IG,IG))
ELSE
QFR2(IQW,IEL,IG)=QFR(IQW,IEL)
ENDIF
ENDDO
ENDDO
ENDDO
*----
* INITIALIZATIONS
*----
KEFF_OLD=0.0
KEFF=1.0
CALL LCMLEN(IPFLX,'FLUX',ILONG,ITYLCM)
IF(ILONG == 0) THEN
JPFLX=LCMLID(IPFLX,'FLUX',NG)
SAVG(:NUN,:NG)=1.0
ELSE
JPFLX=LCMGID(IPFLX,'FLUX')
DO IG=1,NG
CALL LCMLEL(JPFLX,IG,ILONG,ITYLCM)
IF(ILONG /= NUN) CALL XABORT('NSSFL3: INVALID FLUX.')
CALL LCMGDL(JPFLX,IG,SAVG(1,IG))
ENDDO
CALL LCMGET(IPFLX,'K-EFFECTIVE',KEFF)
ENDIF
CALL LCMLEN(IPFLX,'DRIFT',ILONG,ITYLCM)
IF(ILONG == 0) THEN
JPFLX=LCMLID(IPFLX,'DRIFT',6*NEL)
DRIFT(:6,:NEL,:NG)=0.0
ELSE
JPFLX=LCMGID(IPFLX,'DRIFT')
DO IG=1,NG
CALL LCMLEL(JPFLX,IG,ILONG,ITYLCM)
IF(ILONG /= 6*NEL) CALL XABORT('NSSFL3: INVALID DRIFT.')
CALL LCMGDL(JPFLX,IG,DRIFT(1,1,IG))
ENDDO
ENDIF
DO IEL=1,NEL
DO IG=1,NG
EVECT((IG-1)*NEL+IEL)=SAVG(IEL,IG)
ENDDO
ENDDO
*----
* NODAL CORRECTION LOOP
*----
YY(:NEL)=1.0
ZZ(:NEL)=1.0
JTER=0
DO WHILE((ABS(KEFF_OLD-KEFF) >= EPSNOD).OR.(JTER==0))
JTER=JTER+1
IF(IMPX > 0) THEN
WRITE(6,'(36H NSSFL3: Nodal correction iteration=,I5)')
1 JTER
ENDIF
IF(JTER > MAXNOD) THEN
WRITE(6,'(/22H ACCURACY AT ITERATION,I4,2H =,1P,E12.5)')
1 JTER,ABS(KEFF_OLD-KEFF)
CALL XABORT('NSSFL3: NODAL ITERATION FAILURE')
ENDIF
!
! set CMFD matrix for x-directed couplings
A(:N,:2*N)=0.D0
IOF=0
DO IG=1,NG
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM <= 0) CYCLE
KEL=IDL(IEL)
IF(KEL == 0) CYCLE
VOL0=XX(IEL)
CALL NSSCO(NX,NY,NZ,NMIX,IEL,1,1,MAT,XX,YY,ZZ,DIFF(1,IG),
> IQFR(1,IEL),QFR2(1,IEL,IG),COEF)
COEF(1:2)=COEF(1:2)*VOL0/XX(IEL)
CODR(1:2)=DRIFT(1:2,IEL,IG)*VOL0/XX(IEL)
KEL2=0
KK1=IQFR(1,IEL)
IF(KK1 == -4) THEN
KEL2=IDL(NX)
ELSE IF(KK1 == 0) THEN
KEL2=IDL(IEL-1)
ENDIF
IF(KEL2 /= 0) THEN
A(IOF+KEL,IOF+KEL2)=A(IOF+KEL,IOF+KEL2)-COEF(1)+CODR(1)
ENDIF
KEL2=0
KK2=IQFR(2,IEL)
IF(KK2 == -4) THEN
KEL2=IDL(1)
ELSE IF(KK2 == 0) THEN
KEL2=IDL(IEL+1)
ENDIF
IF(KEL2 /= 0) THEN
A(IOF+KEL,IOF+KEL2)=A(IOF+KEL,IOF+KEL2)-COEF(2)-CODR(2)
ENDIF
A(IOF+KEL,IOF+KEL)=A(IOF+KEL,IOF+KEL)+COEF(1)+CODR(1)+
> COEF(2)-CODR(2)
A(IOF+KEL,IOF+KEL)=A(IOF+KEL,IOF+KEL)+SIGR(IBM,IG)*VOL0
ENDDO
JOF=0
DO JG=1,NG ! IG <-- JG
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM <= 0) CYCLE
KEL=IDL(IEL)
IF(KEL == 0) CYCLE
IF(IG /= JG) A(IOF+KEL,JOF+KEL)=-XX(IEL)*SCAT(IBM,IG,JG)
A(IOF+KEL,N+JOF+KEL)=XX(IEL)*CHI(IBM,IG)*SIGF(IBM,JG)
ENDDO
JOF=JOF+NEL
ENDDO
IOF=IOF+NEL
ENDDO
CALL ALSB(N,N,A,IER,N)
IF(IER /= 0) CALL XABORT('NSSFL3: SINGULAR MATRIX.')
!
! CMFD power iteration (use double precision)
DELTA=ABS(KEFF_OLD-KEFF)
KEFF_OLD=KEFF
CALL AL1EIG(N,A(1,N+1),EPSOUT,MAXOUT,ITER,EVECT,KEFF,IMPX)
*----
* FLUX NORMALIZATION
*----
FMAX=MAXVAL(EVECT(:N))
EVECT(:N)=EVECT(:N)/FMAX
IF(IMPX > 0) WRITE(6,10) JTER,KEFF,ITER,DELTA
IF(IMPX > 2) THEN
WRITE(6,'(1X,A)') 'NSSFL3: EVECT='
IOF=0
DO IG=1,NG
WRITE(6,'(1X,1P,14E12.4)') EVECT(IOF+1:IOF+NEL)
IOF=IOF+NEL
ENDDO
ENDIF
!
! begin construct SAVG
IF(NUN /= 4*NEL+1) CALL XABORT('NSSFL3: INVALID NUN.')
SAVG(:NUN,:NG)=0.0
DO IEL=1,NEL
DO IG=1,NG
SAVG(IEL,IG)=EVECT((IG-1)*NEL+IEL)
ENDDO
ENDDO
!
! one- and two-node anm relations
CALL NSSANM1(NEL,NG,NMIX,IQFR,QFR2,MAT,XXX,KEFF,DIFF,SIGR,CHI,
1 SIGF,SCAT,FD,SAVG)
!
! compute new drift coefficients
DO IG=1,NG
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM == 0) CYCLE
CALL NSSCO(NX,NY,NZ,NMIX,IEL,1,1,MAT,XX,YY,ZZ,DIFF(1,IG),
1 IQFR(1,IEL),QFR2(1,IEL,IG),COEF)
IF(IEL == 1) THEN
DRIFT(1,IEL,IG)=-(SAVG(3*NEL+IEL,IG)+COEF(1)*SAVG(IEL,IG))
1 /SAVG(IEL,IG)
DRIFT(2,IEL,IG)=-(SAVG(3*NEL+IEL+1,IG)+COEF(2)*
1 (SAVG(IEL+1,IG)-SAVG(IEL,IG)))/(SAVG(IEL+1,IG)+
2 SAVG(IEL,IG))
ELSE IF(IEL < NEL) THEN
DRIFT(1,IEL,IG)=-(SAVG(3*NEL+IEL,IG)+COEF(1)*(SAVG(IEL,IG)
1 -SAVG(IEL-1,IG)))/(SAVG(IEL,IG)+SAVG(IEL-1,IG))
DRIFT(2,IEL,IG)=-(SAVG(3*NEL+IEL+1,IG)+COEF(2)*
1 (SAVG(IEL+1,IG)-SAVG(IEL,IG)))/(SAVG(IEL+1,IG)+
2 SAVG(IEL,IG))
ELSE
DRIFT(1,IEL,IG)=-(SAVG(3*NEL+IEL,IG)+COEF(1)*(SAVG(IEL,IG)
1 -SAVG(IEL-1,IG)))/(SAVG(IEL,IG)+SAVG(IEL-1,IG))
DRIFT(2,IEL,IG)=-(SAVG(3*NEL+IEL+1,IG)-COEF(2)*
1 SAVG(IEL,IG))/SAVG(IEL,IG)
ENDIF
ENDDO
ENDDO
ENDDO
*----
* END OF NODAL CORRECTION LOOP
*----
IF(IMPX.GT.0) WRITE(6,20) KEFF,JTER
IF(IMPX > 2) THEN
WRITE(6,'(/21H NSSFL3: UNKNOWNS----)')
DO IG=1,NG
WRITE(6,'(14H NSSFL3: SAVG(,I4,2H)=)') IG
WRITE(6,'(1P,12E12.4)') SAVG(:NEL,IG)
WRITE(6,'(19H X-BOUNDARY FLUXES:)')
WRITE(6,'(1P,12E12.4)') SAVG(NEL+1:2*NEL,IG)
WRITE(6,'(1P,12E12.4)') SAVG(2*NEL+1:3*NEL,IG)
WRITE(6,'(12H X-CURRENTS:)')
WRITE(6,'(1P,12E12.4)') SAVG(3*NEL+1:,IG)
WRITE(6,'(5H ----)')
ENDDO
ENDIF
*----
* SAVE SOLUTION
*----
JPFLX=LCMGID(IPFLX,'FLUX')
DO IG=1,NG
CALL LCMPDL(JPFLX,IG,NUN,2,SAVG(1,IG))
ENDDO
JPFLX=LCMGID(IPFLX,'DRIFT')
DO IG=1,NG
CALL LCMPDL(JPFLX,IG,6*NEL,2,DRIFT(1,1,IG))
ENDDO
CALL LCMPUT(IPFLX,'K-EFFECTIVE',1,2,KEFF)
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(SAVG,DRIFT)
DEALLOCATE(EVECT,A,ZZ,YY,QFR2)
RETURN
*
10 FORMAT(14H NSSFL3: JTER=,I4,11H CMFD KEFF=,1P E13.6,
1 12H OBTAINED IN,I4,28H CMFD ITERATIONS WITH ERROR=,
2 1P,E11.4,1H.)
20 FORMAT(18H NSSFL3: ANM KEFF=,F11.8,12H OBTAINED IN,I5,
1 28H NODAL CORRECTION ITERATIONS)
END
|
