-
Notifications
You must be signed in to change notification settings - Fork 1
/
Ra_loop_no_opt.f90
executable file
·655 lines (573 loc) · 21.7 KB
/
Ra_loop_no_opt.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
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
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
program Ra_loop
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
use global
use strings
use write_pack
use interpolation_pack
use allocate_vars
use statistics
use jacobians
use gmres_pack
use mesh_pack
use time_integrators
use nonlinear_solvers
implicit none
integer :: ntokens, ios
integer :: Nxc, Nyc, Nzc
integer :: nRa, ii, jj, n_flm, alphai
integer :: ext
integer, parameter :: alphai_max = 3
integer :: refine_flag_x, refine_flag_y, refine_flag_z
integer :: vtk_flag, rstrt_flag, opt_flag
integer :: nl_iter_data
integer, parameter :: iprint = 1
integer, dimension(1) :: imin
logical :: wvtk, save_restart, calc_opt, physical
logical :: refine_x, refine_y, refine_z, refine_xy
logical :: fTexist, fuyexist
logical :: ex_Tptrb
real(dp) :: temp, eta
real(dp) :: gmres_iter_data
real(dp) :: dxc
real(dp) :: Ra, dRa, Nu, dalpha
real(dp) :: Lmax, Numax, alphamax
real(dp), dimension(3) :: Nui, Li
real(dp), allocatable, dimension(:) :: Nus, Ras, Especu, EspecT
real(dp), allocatable, dimension(:) :: Numaxs, Lmaxs
real(dp), allocatable, dimension(:) :: xpc, ypc, zpc
complex(C_DOUBLE_COMPLEX), allocatable, dimension(:,:) :: uyc, Tc
character(10) :: citer
character(9) :: fiter
character(80) :: line
character(80) :: tokens(80)
open(2,file="input.data", status="old")
do ii = 1,7
read(2,'(A)') line
call parse(line,' ,', tokens, ntokens)
if (ntokens > 0) then
select case(ii)
case (1)
call value(tokens(1), Pr, ios)
call value(tokens(2), alpha, ios)
call value(tokens(3), dalpha, ios)
case (2)
call value(tokens(1), Ra, ios)
call value(tokens(2), nRa, ios)
call value(tokens(3), dRa, ios)
case (3)
call value(tokens(1), t_final, ios)
call value(tokens(2), dt, ios)
dt_init = dt
case (4)
call value(tokens(1), ybot, ios)
call value(tokens(2), ytop, ios)
case (5)
call value(tokens(1), Nx, ios)
call value(tokens(2), Ny, ios)
call value(tokens(3), Nz, ios)
case (6)
call value(tokens(1), refine_flag_x, ios)
call value(tokens(2), refine_flag_y, ios)
call value(tokens(3), refine_flag_z, ios)
if (refine_flag_x == 1) then
if (refine_flag_y == 1) then
refine_xy = .true.
refine_x = .false.
refine_y = .false.
else
refine_x = .true.
refine_y = .false.
refine_xy = .false.
end if
else if (refine_flag_y == 1) then
refine_x = .false.
refine_y = .true.
refine_xy = .false.
else if (refine_flag_z == 1) then
write(*,*) "Refinement in z-direction not available yet!"
stop
else
refine_x = .false.
refine_y = .false.
refine_z = .false.
refine_xy = .false.
end if
case (7)
call value(tokens(1), vtk_flag, ios)
call value(tokens(2), rstrt_flag, ios)
call value(tokens(2), opt_flag, ios)
if (vtk_flag == 1) then
wvtk = .true.
else
wvtk = .false.
end if
if (rstrt_flag == 1) then
save_restart = .true.
else
save_restart = .false.
end if
if (opt_flag == 1) then
calc_opt = .true.
else
calc_opt = .false.
end if
end select
end if
end do
close(unit=2)
! Create FFT plans
planuy = fftw_plan_dft_1d(Nx,tuy,tuy, FFTW_FORWARD,FFTW_ESTIMATE)
iplanuy = fftw_plan_dft_1d(Nx,tuy,tuy, FFTW_BACKWARD,FFTW_ESTIMATE)
planux = fftw_plan_dft_1d(Nx,tux,tux, FFTW_FORWARD,FFTW_ESTIMATE)
iplanux = fftw_plan_dft_1d(Nx,tux,tux, FFTW_BACKWARD,FFTW_ESTIMATE)
planphi = fftw_plan_dft_1d(Nx,tphi,tphi, FFTW_FORWARD,FFTW_ESTIMATE)
iplanphi = fftw_plan_dft_1d(Nx,tphi,tphi, FFTW_BACKWARD,FFTW_ESTIMATE)
planT = fftw_plan_dft_1d(Nx,tT,tT, FFTW_FORWARD,FFTW_ESTIMATE)
iplanT = fftw_plan_dft_1d(Nx,tT,tT, FFTW_BACKWARD,FFTW_ESTIMATE)
plannlT = fftw_plan_dft_1d(Nx,tnlT,tnlT, FFTW_FORWARD,FFTW_ESTIMATE)
iplannlT = fftw_plan_dft_1d(Nx,tnlT,tnlT, FFTW_BACKWARD,FFTW_ESTIMATE)
plannlphi = fftw_plan_dft_1d(Nx,tnlphi,tnlphi, FFTW_FORWARD,FFTW_ESTIMATE)
iplannlphi = fftw_plan_dft_1d(Nx,tnlphi,tnlphi, FFTW_BACKWARD,FFTW_ESTIMATE)
call global_params
call global_allocations
! Allocate some local arrays
allocate(Especu(kmax), EspecT(kmax), stat=alloc_err)
allocate(Nus(nRa), Ras(nRa), stat=alloc_err)
allocate(Numaxs(nRa), Lmaxs(nRa), stat=alloc_err)
call check_alloc_err(alloc_err)
Nus = 0.0_dp
Ras = 0.0_dp
Especu = 0.0_dp
EspecT = 0.0_dp
inquire(file="uy", exist=fuyexist)
if (fuyexist) then
open(unit=2,file="uy",action="read", status="old", form="unformatted")
if (refine_x) then
Nxc = Nx / 2
allocate(uyc(Ny,Nxc), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nxc
do jj = 1,Ny
read(2) temp
uyc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else if (refine_y) then
Nyc = (Ny+1) / 2
allocate(uyc(Nyc,Nx), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nx
do jj = 1,Nyc
read(2) temp
uyc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else if (refine_xy) then
Nxc = Nx / 2
Nyc = (Ny+1) / 2
Nzc = Nz
allocate(uyc(Nyc,Nxc), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nxc
do jj = 1,Nyc
read(2) temp
uyc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else
do ii = 1,Nx
do jj = 1,Ny
read(2) temp
uy(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
end if
close(unit=2)
end if
inquire(file="temperature", exist=fTexist)
if (fTexist) then
open(unit=3,file="temperature",action="read", status="old", form="unformatted")
if (refine_x) then
Nxc = Nx / 2
allocate(Tc(Ny,Nxc), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nxc
do jj = 1,Ny
read(3) temp
Tc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else if (refine_y) then
Nyc = (Ny+1) / 2
allocate(Tc(Nyc,Nx), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nx
do jj = 1,Nyc
read(3) temp
Tc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else if (refine_xy) then
Nxc = Nx / 2
Nyc = (Ny+1) / 2
Nzc = Nz
allocate(Tc(Nyc,Nxc), stat=alloc_err)
call check_alloc_err(alloc_err)
do ii = 1,Nxc
do jj = 1,Nyc
read(3) temp
Tc(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
else
do ii = 1,Nx
do jj = 1,Ny
read(3) temp
T(jj,ii) = cmplx(temp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end do
end do
end if
close(unit=3)
end if
xR = pi / alpha
xL = -pi / alpha
Lx = xR - xL
if (Nx == 1) then
dx = 1.0_dp
else
dx = Lx / (real(Nx,kind=dp))
end if
! Create the grid
call cosine_mesh(xp,yp,zp, Nx,Ny,Nz) ! get coordinates
call dxdydz(dynu, xp,yp,zp) ! get mesh spacing for nonuniform grids
call y_mesh_params ! get metric coefficients for nonuniform grids
dymin = minval(dynu)
dxmin = sqrt(dx**2.0_dp + dymin**2.0_dp)
if (refine_xy) then
if (fuyexist) then
if (fTexist) then
allocate(xpc(Nxc), stat=alloc_err)
allocate(ypc(Nyc), stat=alloc_err)
allocate(zpc(Nzc), stat=alloc_err)
call check_alloc_err(alloc_err)
dxc = Lx / real(Nxc,kind=dp)
call cosine_mesh(xpc,ypc,zpc, Nxc,Nyc,Nzc, dxc)
call bilinear_interp(xpc,ypc,uyc,Tc)
else if (.not. fTexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Only have data from uy."
stop
end if
else if (.not. fuyexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Not able to find uy data."
stop
end if
else if (refine_x) then
if (fuyexist) then
if (fTexist) then
allocate(xpc(Nxc), stat=alloc_err)
allocate(ypc(Ny), stat=alloc_err)
allocate(zpc(Nz), stat=alloc_err)
call check_alloc_err(alloc_err)
dxc = Lx / real(Nxc,kind=dp)
call cosine_mesh(xpc,ypc,zpc, Nxc,Ny,Nz, dxc)
call linear_interp_x(xpc,uyc,Tc)
else if (.not. fTexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Only have data from uy."
stop
end if
else if (.not. fuyexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Not able to find uy data."
stop
end if
else if (refine_y) then
if (fuyexist) then
if (fTexist) then
allocate(xpc(Nx), stat=alloc_err)
allocate(ypc(Nyc), stat=alloc_err)
allocate(zpc(Nz), stat=alloc_err)
call check_alloc_err(alloc_err)
call cosine_mesh(xpc,ypc,zpc, Nx,Nyc,Nz, dx)
call linear_interp_y(ypc,uyc,Tc)
else if (.not. fTexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Only have data from uy."
stop
end if
else if (.not. fuyexist) then
write(*,*) "ERROR: Need input data from uy and temperature. Not able to find uy data."
stop
end if
end if
do ii = 1,Nx/2
kx_modes(ii) = real(ii,kind=dp) - 1.0_dp
end do
do ii = Nx/2+1, Nx
kx_modes(ii) = real(ii-Nx,kind=dp) - 1.0_dp
end do
kx = alpha*kx_modes
! Write initial field to vtk
if (wvtk) then
call write_to_vtk(int(Ra), .true.) ! true = already in physical space
end if
! Initialize fields.
call init_fields(ex_Tptrb, fTexist, Ra)
call init_to_fourier(ex_Tptrb)
! Allocate space for flow map variables
n_flm = 2*2*Ny*Nx ! # of fields X real/imag X Ny X Nx
! Form x0 and GT (flow map)
allocate(x0(n_flm), GT(n_flm), stat=alloc_err)
if (alloc_err /= 0) then
write(*,*) "ERROR: Allocation of x0 and GT incomplete."
stop
end if
x0 = 0.0_dp
GT = 0.0_dp
! p points to the boundaries. Will be used to ensure that
! Delta_x is zero on the boundaries.
b_pntr(1) = 1
b_pntr(2) = Ny
b_pntr(3) = Ny+1
b_pntr(4) = 2*Ny
b_pntr(5) = 2*Ny+1
b_pntr(6) = 3*Ny
b_pntr(7) = 3*Ny+1
b_pntr(8) = 4*Ny
write(*,'(A70)') ' '
write(*,'(A70)') '*********************************************************************|'
write(*,'(A70)') ' TWO-DIMENSIONAL THERMAL CONVECTION |'
write(*,'(A70)') '*********************************************************************|'
write(*,'(5X,A,47X,A)') 'COMPUTATION SIZE:', '|'
write(*,'(A69,A)') ' ','|'
write(*,'(20X,A23,I5,21X,A)') 'Nx = ', Nx, '|'
write(*,'(20X,A23,I5,21X,A)') 'Ny = ', Ny, '|'
write(*,'(20X,A23,I5,21X,A)') 'Nz = ', Nz, '|'
write(*,'(20X,A23,I5,21X,A)') 'Number of time steps = ', nt, '|'
write(*,'(20X,A23,I5,21X,A)') 'Number of Fourier modes = ', Nf, '|'
write(*,'(A69,A)') ' ','|'
write(*,'(A70)') '*********************************************************************|'
write(*,'(5X,A,45X,A)') 'PROBLEM PARAMETERS:', '|'
write(*,'(A69,A)') ' ','|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Prandtl number (Pr) = ', Pr, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Initial Rayleigh number (Ra) = ', Ra, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Initial Reynolds number (Re) = ', sqrt(Ra/(16.0_dp*Pr)), '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Ra Gradation (dRa) = ', dRa, '|'
write(*,'(10X,A32,I5, 21X,A)') 'Number of steps (nRa) = ', nRa, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Final Rayleigh Number = ', (dRa**(nRa-1))*Ra, '|'
write(*,'(A69,A)') ' ','|'
write(*,'(A70)') '*********************************************************************|'
write(*,'(5X,A,42X,A)') 'PHYSICAL PROBLEM SIZE:', '|'
write(*,'(A69,A)') ' ','|'
write(*,'(10X,A32,ES16.8,11X,A)') 'alpha = ', alpha, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Left coordinate of box = ', xL, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Right coordinate of box = ', xR, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Coordinate of bottom wall = ', ybot, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Coordinate of top wall = ', ytop, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Box width = ', Lx, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Box height = ', Ly, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Aspect Ratio = ', Lx/Ly, '|'
write(*,'(A69,A)') ' ','|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Integration time (T) = ', t_final, '|'
write(*,'(10X,A32,ES16.8,11X,A)') 'Time step size (Delta t) = ', dt, '|'
write(*,'(A69,A)') ' ','|'
write(*,'(A70)') '*********************************************************************|'
write(*,'(A70)') '*********************************************************************|'
write(*,'(A70)') ' '
flush(6)
open(unit=8000, file="Nu_data.txt", action="write", status="unknown", position="append")
Raloop: do ii = 1, nRa
Ras(ii) = Ra
Ra_global = Ra
if (mod((ii-1),iprint) == 0) then
if (ii == 1) then
write(*,*) " "
write(*,*) "Ra, dt = ", Ra, dt
write(*,*) " "
else
write(*,*) " "
write(*,*)"::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::"
write(*,*) "Ra, dt = ", Ra, dt
write(*,*) " "
end if
end if
! Get nu0 and kappa0
call global_params_Ra(Ra)
! Populate x0
call packx(x0)
! Get solution with flow map
call flow_map(Nu, nl_iter_data, temp)
write(*,*) " "
flush(6)
if (save_restart) then
call write_restart(.false.) ! false = Fourier space
end if
if (wvtk) then
call write_to_vtk(int(Ra), .false.) ! false = Fourier space
end if
! Increment Ra
Ra = dRa * Ra
end do Raloop
close(unit=8000)
if (save_restart) then
call write_restart(.false.) ! false = Fourier space
end if
if (wvtk) then
call write_to_vtk(int(Ra), .false.) ! false = Fourier space
end if
write(*,*) " "
write(*,*) "Done."
1000 format(E25.16E3 )
2000 format(E25.16E3,E25.16E3 )
3000 format(E25.16E3,E25.16E3,E25.16E3 )
4000 format(E25.16E3,E25.16E3,E25.16E3,E25.16E3)
end program Ra_loop
!::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
subroutine init_fields(ex_Tptrb, fTexist,Ra)
use global
implicit none
logical, intent(in) :: fTexist
logical, intent(out) :: ex_Tptrb
real(dp), intent(in) :: Ra
integer :: ii
! Initialize fields.
if (.not. fTexist) then
if (Ra < 1710.0_dp) then
ex_Tptrb = .true.
do ii = 1,Nx
Tptrb(:,ii) = 0.5_dp*2.0_dp*cos(alpha*xp(ii))*cos(pi*yp/2.0_dp)
T(:,ii) = -yp + Tptrb(:,ii)
end do
else
ex_Tptrb = .false.
do ii = 1,Nx
T(:,ii) = -yp + 0.5_dp*2.0_dp*cos(alpha*xp(ii))*cos(pi*yp/2.0_dp)
end do
end if
else if (fTexist) then
if (Ra < 1710.0_dp) then
ex_Tptrb = .true.
do ii = 1,Nx
Tptrb(:,ii) = 0.5_dp*2.0_dp*cos(alpha*xp(ii))*cos(pi*yp/2.0_dp)
end do
else
ex_Tptrb = .false.
end if
end if
end subroutine init_fields
!::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
subroutine init_to_fourier(ex_Tptrb)
use global
implicit none
logical, intent(in) :: ex_Tptrb
integer :: ii, jj
! Bring temperature and velocity to Fourier space.
do jj = 1,Ny
tT = T(jj,:)
tuy = uy(jj,:)
call fftw_execute_dft(planT, tT, tT)
call fftw_execute_dft(planuy, tuy, tuy)
! Truncate modes
do ii = 1,Nx
if (abs(kx(ii))/alpha >= Nf/2) then
tT(ii) = cmplx(0.0_dp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
tuy(ii) = cmplx(0.0_dp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end if
end do
T(jj,:) = tT
uy(jj,:) = tuy
! If temperature perturbation needed.
if (ex_Tptrb) then
tT = Tptrb(jj,:)
call fftw_execute_dft(planT, tT, tT)
! Truncate modes
do ii = 1,Nx
if (abs(kx(ii))/alpha >= Nf/2) then
tT(ii) = cmplx(0.0_dp, 0.0_dp, kind=C_DOUBLE_COMPLEX)
end if
end do
Tptrb(jj,:) = tT
end if
end do
T = T / real(Nx, kind=dp)
uy = uy / real(Nx, kind=dp)
if (ex_Tptrb) then
Tptrb = Tptrb / real(Nx, kind=dp)
end if
! Calculate phi and ux from uy
do ii = 1,Nx
if (kx(ii) /= 0.0_dp) then
tmp_uy = uy(:,ii)
!ux(:,ii) = -CI*d1y(tmp_uy)/kx(ii)
ux(:,ii) = CI*d1y(tmp_uy)/kx(ii)
else if (kx(ii) == 0.0_dp) then
ux(:,ii) = cmplx(0.0_dp, 0.0_dp, kind=C_DOUBLE_COMPLEX) ! Zero mean flow!
end if
phi(:,ii) = -kx(ii)**2.0_dp*uy(:,ii) + d2y(uy(:,ii))
end do
end subroutine init_to_fourier
!::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
subroutine fit_parab(xstar,ystar, x, y)
use global
use write_pack
implicit none
real(dp), dimension(3), intent(in) :: x, y
real(dp), intent(out) :: xstar, ystar
real(dp) :: den1, den2, den3
real(dp) :: c1, c2, c3
real(dp) :: x1,x2,x3,y1,y2,y3
x1 = x(1)
x2 = x(2)
x3 = x(3)
y1 = y(1)
y2 = y(2)
y3 = y(3)
den1 = (x1 - x2) * (x1 - x3)
den2 = (x2 - x1) * (x2 - x3)
den3 = (x3 - x1) * (x3 - x2)
c1 = y1 / den1 + y2 / den2 + y3 / den3
c2 = y1 * (x2 + x3) / den1 + &
& y2 * (x1 + x3) / den2 + &
& y3 * (x1 + x2) / den3
c3 = y1 * x2 * x3 / den1 + &
& y2 * x1 * x3 / den2 + &
& y3 * x1 * x2 / den3
xstar = c2 / (2.0_dp * c1)
ystar = c1 * xstar**2.0_dp - c2 * xstar + c3
end subroutine fit_parab
! :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
subroutine calc_optimal(ave_num_gmres, alphain)
use global
use mesh_pack
use nonlinear_solvers
implicit none
integer :: jj
integer :: num_nonlinear
real(dp) :: temp
real(dp), intent(in) :: alphain
real(dp), intent(out) :: ave_num_gmres
alpha = alphain
xR = pi / alpha
xL = -pi / alpha
Lx = xR - xL
if (Nx == 1) then
dx = 1.0_dp
else
dx = Lx / (real(Nx,kind=dp))
end if
kx = alpha * kx_modes
call cosine_mesh(xp,yp,zp, Nx,Ny,Nz) ! get coordinates
! Calculate phi and ux from uy
do jj = 1,Nx
if (kx(jj) /= 0.0_dp) then
tmp_uy = uy(:,jj)
!ux(:,jj) = -CI*d1y(tmp_uy)/kx(jj)
ux(:,jj) = CI*d1y(tmp_uy)/kx(jj)
else if (kx(jj) == 0.0_dp) then
ux(:,jj) = cmplx(0.0_dp, 0.0_dp, kind=C_DOUBLE_COMPLEX) ! Zero mean flow!
end if
phi(:,jj) = -kx(jj)**2.0_dp*uy(:,jj) + d2y(uy(:,jj))
end do
! Populate x0
call packx(x0)
! Get solution with flow map
call flow_map(temp, num_nonlinear, ave_num_gmres)
end subroutine calc_optimal