Neko  0.9.99
A portable framework for high-order spectral element flow simulations
sx_cfl.f90
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34 submodule(opr_sx) sx_cfl
35  implicit none
36 
37 contains
38 
39  module function opr_sx_cfl(dt, u, v, w, xh, coef, nelv) result(cfl)
40  type(space_t), intent(in) :: Xh
41  type(coef_t), intent(in) :: coef
42  integer, intent(in) :: nelv
43  real(kind=rp), intent(in) :: dt
44  real(kind=rp), dimension(Xh%lx, Xh%ly, Xh%lz, nelv) :: u, v, w
45  real(kind=rp) :: cfl
46 
47  select case (xh%lx)
48  case (14)
49  cfl = sx_cfl_lx14(dt, u, v, w, &
50  coef%drdx, coef%dsdx, coef%dtdx, &
51  coef%drdy, coef%dsdy, coef%dtdy, &
52  coef%drdz, coef%dsdz, coef%dtdz, &
53  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
54  coef%jacinv, nelv)
55  case (13)
56  cfl = sx_cfl_lx13(dt, u, v, w, &
57  coef%drdx, coef%dsdx, coef%dtdx, &
58  coef%drdy, coef%dsdy, coef%dtdy, &
59  coef%drdz, coef%dsdz, coef%dtdz, &
60  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
61  coef%jacinv, nelv)
62  case (12)
63  cfl = sx_cfl_lx12(dt, u, v, w, &
64  coef%drdx, coef%dsdx, coef%dtdx, &
65  coef%drdy, coef%dsdy, coef%dtdy, &
66  coef%drdz, coef%dsdz, coef%dtdz, &
67  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
68  coef%jacinv, nelv)
69  case (11)
70  cfl = sx_cfl_lx11(dt, u, v, w, &
71  coef%drdx, coef%dsdx, coef%dtdx, &
72  coef%drdy, coef%dsdy, coef%dtdy, &
73  coef%drdz, coef%dsdz, coef%dtdz, &
74  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
75  coef%jacinv, nelv)
76  case (10)
77  cfl = sx_cfl_lx10(dt, u, v, w, &
78  coef%drdx, coef%dsdx, coef%dtdx, &
79  coef%drdy, coef%dsdy, coef%dtdy, &
80  coef%drdz, coef%dsdz, coef%dtdz, &
81  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
82  coef%jacinv, nelv)
83  case (9)
84  cfl = sx_cfl_lx9(dt, u, v, w, &
85  coef%drdx, coef%dsdx, coef%dtdx, &
86  coef%drdy, coef%dsdy, coef%dtdy, &
87  coef%drdz, coef%dsdz, coef%dtdz, &
88  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
89  coef%jacinv, nelv)
90  case (8)
91  cfl = sx_cfl_lx8(dt, u, v, w, &
92  coef%drdx, coef%dsdx, coef%dtdx, &
93  coef%drdy, coef%dsdy, coef%dtdy, &
94  coef%drdz, coef%dsdz, coef%dtdz, &
95  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
96  coef%jacinv, nelv)
97  case (7)
98  cfl = sx_cfl_lx7(dt, u, v, w, &
99  coef%drdx, coef%dsdx, coef%dtdx, &
100  coef%drdy, coef%dsdy, coef%dtdy, &
101  coef%drdz, coef%dsdz, coef%dtdz, &
102  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
103  coef%jacinv, nelv)
104  case (6)
105  cfl = sx_cfl_lx6(dt, u, v, w, &
106  coef%drdx, coef%dsdx, coef%dtdx, &
107  coef%drdy, coef%dsdy, coef%dtdy, &
108  coef%drdz, coef%dsdz, coef%dtdz, &
109  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
110  coef%jacinv, nelv)
111  case (5)
112  cfl = sx_cfl_lx5(dt, u, v, w, &
113  coef%drdx, coef%dsdx, coef%dtdx, &
114  coef%drdy, coef%dsdy, coef%dtdy, &
115  coef%drdz, coef%dsdz, coef%dtdz, &
116  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
117  coef%jacinv, nelv)
118  case (4)
119  cfl = sx_cfl_lx4(dt, u, v, w, &
120  coef%drdx, coef%dsdx, coef%dtdx, &
121  coef%drdy, coef%dsdy, coef%dtdy, &
122  coef%drdz, coef%dsdz, coef%dtdz, &
123  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
124  coef%jacinv, nelv)
125  case (3)
126  cfl = sx_cfl_lx3(dt, u, v, w, &
127  coef%drdx, coef%dsdx, coef%dtdx, &
128  coef%drdy, coef%dsdy, coef%dtdy, &
129  coef%drdz, coef%dsdz, coef%dtdz, &
130  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
131  coef%jacinv, nelv)
132  case (2)
133  cfl = sx_cfl_lx2(dt, u, v, w, &
134  coef%drdx, coef%dsdx, coef%dtdx, &
135  coef%drdy, coef%dsdy, coef%dtdy, &
136  coef%drdz, coef%dsdz, coef%dtdz, &
137  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
138  coef%jacinv, nelv)
139  case default
140  cfl = sx_cfl_lx(dt, u, v, w, &
141  coef%drdx, coef%dsdx, coef%dtdx, &
142  coef%drdy, coef%dsdy, coef%dtdy, &
143  coef%drdz, coef%dsdz, coef%dtdz, &
144  xh%dr_inv, xh%ds_inv, xh%dt_inv, &
145  coef%jacinv, nelv, xh%lx)
146  end select
147 
148  end function opr_sx_cfl
149 
150  function sx_cfl_lx(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
151  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
152  jacinv, nelv, lx) result(cfl)
153  integer, intent(in) :: nelv, lx
154  real(kind=rp), intent(in) :: dt
155  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
156  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
157  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
158  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
159  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
160  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
161  real(kind=rp) :: cflr, cfls, cflt, cflm
162  real(kind=rp) :: ur, us, ut
163  real(kind=rp) :: cfl
164  integer :: i, j, k, e
165  cfl = 0d0
166 
167  do k = 1, lx
168  do j = 1, lx
169  do i = 1, lx
170  do e = 1, nelv
171  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
172  + v(i,j,k,e)*drdy(i,j,k,e) &
173  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
174  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
175  + v(i,j,k,e)*dsdy(i,j,k,e) &
176  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
177  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
178  + v(i,j,k,e)*dtdy(i,j,k,e) &
179  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
180 
181  cflr = abs(dt*ur*dr_inv(i))
182  cfls = abs(dt*us*ds_inv(j))
183  cflt = abs(dt*ut*dt_inv(k))
184 
185  cflm = cflr + cfls + cflt
186  cfl = max(cfl, cflm)
187  end do
188  end do
189  end do
190  end do
191 
192  end function sx_cfl_lx
193 
194  function sx_cfl_lx14(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
195  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
196  jacinv, nelv) result(cfl)
197  integer, parameter :: lx = 14
198  integer, intent(in) :: nelv
199  real(kind=rp), intent(in) :: dt
200  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
201  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
202  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
203  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
204  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
205  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
206  real(kind=rp) :: cflr, cfls, cflt, cflm
207  real(kind=rp) :: ur, us, ut
208  real(kind=rp) :: cfl
209  integer :: i, j, k, e
210  cfl = 0d0
211 
212  do k = 1, lx
213  do j = 1, lx
214  do i = 1, lx
215  do e = 1, nelv
216  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
217  + v(i,j,k,e)*drdy(i,j,k,e) &
218  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
219  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
220  + v(i,j,k,e)*dsdy(i,j,k,e) &
221  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
222  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
223  + v(i,j,k,e)*dtdy(i,j,k,e) &
224  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
225 
226  cflr = abs(dt*ur*dr_inv(i))
227  cfls = abs(dt*us*ds_inv(j))
228  cflt = abs(dt*ut*dt_inv(k))
229 
230  cflm = cflr + cfls + cflt
231  cfl = max(cfl, cflm)
232  end do
233  end do
234  end do
235  end do
236 
237  end function sx_cfl_lx14
238 
239  function sx_cfl_lx13(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
240  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
241  jacinv, nelv) result(cfl)
242  integer, parameter :: lx = 13
243  integer, intent(in) :: nelv
244  real(kind=rp), intent(in) :: dt
245  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
246  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
247  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
248  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
249  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
250  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
251  real(kind=rp) :: cflr, cfls, cflt, cflm
252  real(kind=rp) :: ur, us, ut
253  real(kind=rp) :: cfl
254  integer :: i, j, k, e
255  cfl = 0d0
256 
257  do k = 1, lx
258  do j = 1, lx
259  do i = 1, lx
260  do e = 1, nelv
261  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
262  + v(i,j,k,e)*drdy(i,j,k,e) &
263  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
264  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
265  + v(i,j,k,e)*dsdy(i,j,k,e) &
266  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
267  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
268  + v(i,j,k,e)*dtdy(i,j,k,e) &
269  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
270 
271  cflr = abs(dt*ur*dr_inv(i))
272  cfls = abs(dt*us*ds_inv(j))
273  cflt = abs(dt*ut*dt_inv(k))
274 
275  cflm = cflr + cfls + cflt
276  cfl = max(cfl, cflm)
277  end do
278  end do
279  end do
280  end do
281 
282  end function sx_cfl_lx13
283 
284  function sx_cfl_lx12(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
285  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
286  jacinv, nelv) result(cfl)
287  integer, parameter :: lx = 12
288  integer, intent(in) :: nelv
289  real(kind=rp), intent(in) :: dt
290  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
291  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
292  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
293  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
294  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
295  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
296  real(kind=rp) :: cflr, cfls, cflt, cflm
297  real(kind=rp) :: ur, us, ut
298  real(kind=rp) :: cfl
299  integer :: i, j, k, e
300  cfl = 0d0
301 
302  do k = 1, lx
303  do j = 1, lx
304  do i = 1, lx
305  do e = 1, nelv
306  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
307  + v(i,j,k,e)*drdy(i,j,k,e) &
308  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
309  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
310  + v(i,j,k,e)*dsdy(i,j,k,e) &
311  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
312  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
313  + v(i,j,k,e)*dtdy(i,j,k,e) &
314  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
315 
316  cflr = abs(dt*ur*dr_inv(i))
317  cfls = abs(dt*us*ds_inv(j))
318  cflt = abs(dt*ut*dt_inv(k))
319 
320  cflm = cflr + cfls + cflt
321  cfl = max(cfl, cflm)
322  end do
323  end do
324  end do
325  end do
326 
327  end function sx_cfl_lx12
328 
329  function sx_cfl_lx11(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
330  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
331  jacinv, nelv) result(cfl)
332  integer, parameter :: lx = 11
333  integer, intent(in) :: nelv
334  real(kind=rp), intent(in) :: dt
335  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
336  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
337  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
338  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
339  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
340  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
341  real(kind=rp) :: cflr, cfls, cflt, cflm
342  real(kind=rp) :: ur, us, ut
343  real(kind=rp) :: cfl
344  integer :: i, j, k, e
345  cfl = 0d0
346 
347  do k = 1, lx
348  do j = 1, lx
349  do i = 1, lx
350  do e = 1, nelv
351  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
352  + v(i,j,k,e)*drdy(i,j,k,e) &
353  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
354  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
355  + v(i,j,k,e)*dsdy(i,j,k,e) &
356  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
357  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
358  + v(i,j,k,e)*dtdy(i,j,k,e) &
359  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
360 
361  cflr = abs(dt*ur*dr_inv(i))
362  cfls = abs(dt*us*ds_inv(j))
363  cflt = abs(dt*ut*dt_inv(k))
364 
365  cflm = cflr + cfls + cflt
366  cfl = max(cfl, cflm)
367  end do
368  end do
369  end do
370  end do
371 
372  end function sx_cfl_lx11
373 
374  function sx_cfl_lx10(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
375  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
376  jacinv, nelv) result(cfl)
377  integer, parameter :: lx = 10
378  integer, intent(in) :: nelv
379  real(kind=rp), intent(in) :: dt
380  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
381  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
382  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
383  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
384  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
385  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
386  real(kind=rp) :: cflr, cfls, cflt, cflm
387  real(kind=rp) :: ur, us, ut
388  real(kind=rp) :: cfl
389  integer :: i, j, k, e
390  cfl = 0d0
391 
392  do k = 1, lx
393  do j = 1, lx
394  do i = 1, lx
395  do e = 1, nelv
396  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
397  + v(i,j,k,e)*drdy(i,j,k,e) &
398  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
399  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
400  + v(i,j,k,e)*dsdy(i,j,k,e) &
401  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
402  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
403  + v(i,j,k,e)*dtdy(i,j,k,e) &
404  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
405 
406  cflr = abs(dt*ur*dr_inv(i))
407  cfls = abs(dt*us*ds_inv(j))
408  cflt = abs(dt*ut*dt_inv(k))
409 
410  cflm = cflr + cfls + cflt
411  cfl = max(cfl, cflm)
412  end do
413  end do
414  end do
415  end do
416 
417  end function sx_cfl_lx10
418 
419  function sx_cfl_lx9(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
420  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
421  jacinv, nelv) result(cfl)
422  integer, parameter :: lx = 9
423  integer, intent(in) :: nelv
424  real(kind=rp), intent(in) :: dt
425  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
426  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
427  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
428  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
429  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
430  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
431  real(kind=rp) :: cflr, cfls, cflt, cflm
432  real(kind=rp) :: ur, us, ut
433  real(kind=rp) :: cfl
434  integer :: i, j, k, e
435  cfl = 0d0
436 
437  do k = 1, lx
438  do j = 1, lx
439  do i = 1, lx
440  do e = 1, nelv
441  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
442  + v(i,j,k,e)*drdy(i,j,k,e) &
443  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
444  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
445  + v(i,j,k,e)*dsdy(i,j,k,e) &
446  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
447  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
448  + v(i,j,k,e)*dtdy(i,j,k,e) &
449  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
450 
451  cflr = abs(dt*ur*dr_inv(i))
452  cfls = abs(dt*us*ds_inv(j))
453  cflt = abs(dt*ut*dt_inv(k))
454 
455  cflm = cflr + cfls + cflt
456  cfl = max(cfl, cflm)
457  end do
458  end do
459  end do
460  end do
461 
462  end function sx_cfl_lx9
463 
464  function sx_cfl_lx8(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
465  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
466  jacinv, nelv) result(cfl)
467  integer, parameter :: lx = 8
468  integer, intent(in) :: nelv
469  real(kind=rp), intent(in) :: dt
470  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
471  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
472  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
473  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
474  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
475  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
476  real(kind=rp) :: cflr, cfls, cflt, cflm
477  real(kind=rp) :: ur, us, ut
478  real(kind=rp) :: cfl
479  integer :: i, j, k, e
480  cfl = 0d0
481 
482  do k = 1, lx
483  do j = 1, lx
484  do i = 1, lx
485  do e = 1, nelv
486  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
487  + v(i,j,k,e)*drdy(i,j,k,e) &
488  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
489  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
490  + v(i,j,k,e)*dsdy(i,j,k,e) &
491  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
492  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
493  + v(i,j,k,e)*dtdy(i,j,k,e) &
494  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
495 
496  cflr = abs(dt*ur*dr_inv(i))
497  cfls = abs(dt*us*ds_inv(j))
498  cflt = abs(dt*ut*dt_inv(k))
499 
500  cflm = cflr + cfls + cflt
501  cfl = max(cfl, cflm)
502  end do
503  end do
504  end do
505  end do
506 
507  end function sx_cfl_lx8
508 
509  function sx_cfl_lx7(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
510  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
511  jacinv, nelv) result(cfl)
512  integer, parameter :: lx = 7
513  integer, intent(in) :: nelv
514  real(kind=rp), intent(in) :: dt
515  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
516  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
517  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
518  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
519  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
520  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
521  real(kind=rp) :: cflr, cfls, cflt, cflm
522  real(kind=rp) :: ur, us, ut
523  real(kind=rp) :: cfl
524  integer :: i, j, k, e
525  cfl = 0d0
526 
527  do k = 1, lx
528  do j = 1, lx
529  do i = 1, lx
530  do e = 1, nelv
531  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
532  + v(i,j,k,e)*drdy(i,j,k,e) &
533  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
534  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
535  + v(i,j,k,e)*dsdy(i,j,k,e) &
536  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
537  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
538  + v(i,j,k,e)*dtdy(i,j,k,e) &
539  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
540 
541  cflr = abs(dt*ur*dr_inv(i))
542  cfls = abs(dt*us*ds_inv(j))
543  cflt = abs(dt*ut*dt_inv(k))
544 
545  cflm = cflr + cfls + cflt
546  cfl = max(cfl, cflm)
547  end do
548  end do
549  end do
550  end do
551 
552  end function sx_cfl_lx7
553 
554  function sx_cfl_lx6(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
555  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
556  jacinv, nelv) result(cfl)
557  integer, parameter :: lx = 6
558  integer, intent(in) :: nelv
559  real(kind=rp), intent(in) :: dt
560  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
561  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
562  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
563  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
564  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
565  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
566  real(kind=rp) :: cflr, cfls, cflt, cflm
567  real(kind=rp) :: ur, us, ut
568  real(kind=rp) :: cfl
569  integer :: i, j, k, e
570  cfl = 0d0
571 
572  do k = 1, lx
573  do j = 1, lx
574  do i = 1, lx
575  do e = 1, nelv
576  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
577  + v(i,j,k,e)*drdy(i,j,k,e) &
578  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
579  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
580  + v(i,j,k,e)*dsdy(i,j,k,e) &
581  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
582  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
583  + v(i,j,k,e)*dtdy(i,j,k,e) &
584  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
585 
586  cflr = abs(dt*ur*dr_inv(i))
587  cfls = abs(dt*us*ds_inv(j))
588  cflt = abs(dt*ut*dt_inv(k))
589 
590  cflm = cflr + cfls + cflt
591  cfl = max(cfl, cflm)
592  end do
593  end do
594  end do
595  end do
596 
597  end function sx_cfl_lx6
598 
599  function sx_cfl_lx5(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
600  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
601  jacinv, nelv) result(cfl)
602  integer, parameter :: lx = 5
603  integer, intent(in) :: nelv
604  real(kind=rp), intent(in) :: dt
605  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
606  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
607  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
608  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
609  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
610  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
611  real(kind=rp) :: cflr, cfls, cflt, cflm
612  real(kind=rp) :: ur, us, ut
613  real(kind=rp) :: cfl
614  integer :: i, j, k, e
615  cfl = 0d0
616 
617  do k = 1, lx
618  do j = 1, lx
619  do i = 1, lx
620  do e = 1, nelv
621  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
622  + v(i,j,k,e)*drdy(i,j,k,e) &
623  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
624  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
625  + v(i,j,k,e)*dsdy(i,j,k,e) &
626  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
627  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
628  + v(i,j,k,e)*dtdy(i,j,k,e) &
629  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
630 
631  cflr = abs(dt*ur*dr_inv(i))
632  cfls = abs(dt*us*ds_inv(j))
633  cflt = abs(dt*ut*dt_inv(k))
634 
635  cflm = cflr + cfls + cflt
636  cfl = max(cfl, cflm)
637  end do
638  end do
639  end do
640  end do
641 
642  end function sx_cfl_lx5
643 
644  function sx_cfl_lx4(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
645  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
646  jacinv, nelv) result(cfl)
647  integer, parameter :: lx = 4
648  integer, intent(in) :: nelv
649  real(kind=rp), intent(in) :: dt
650  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
651  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
652  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
653  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
654  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
655  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
656  real(kind=rp) :: cflr, cfls, cflt, cflm
657  real(kind=rp) :: ur, us, ut
658  real(kind=rp) :: cfl
659  integer :: i, j, k, e
660  cfl = 0d0
661 
662  do k = 1, lx
663  do j = 1, lx
664  do i = 1, lx
665  do e = 1, nelv
666  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
667  + v(i,j,k,e)*drdy(i,j,k,e) &
668  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
669  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
670  + v(i,j,k,e)*dsdy(i,j,k,e) &
671  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
672  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
673  + v(i,j,k,e)*dtdy(i,j,k,e) &
674  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
675 
676  cflr = abs(dt*ur*dr_inv(i))
677  cfls = abs(dt*us*ds_inv(j))
678  cflt = abs(dt*ut*dt_inv(k))
679 
680  cflm = cflr + cfls + cflt
681  cfl = max(cfl, cflm)
682  end do
683  end do
684  end do
685  end do
686 
687  end function sx_cfl_lx4
688 
689  function sx_cfl_lx3(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
690  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
691  jacinv, nelv) result(cfl)
692  integer, parameter :: lx = 3
693  integer, intent(in) :: nelv
694  real(kind=rp), intent(in) :: dt
695  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
696  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
697  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
698  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
699  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
700  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
701  real(kind=rp) :: cflr, cfls, cflt, cflm
702  real(kind=rp) :: ur, us, ut
703  real(kind=rp) :: cfl
704  integer :: i, j, k, e
705  cfl = 0d0
706 
707  do k = 1, lx
708  do j = 1, lx
709  do i = 1, lx
710  do e = 1, nelv
711  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
712  + v(i,j,k,e)*drdy(i,j,k,e) &
713  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
714  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
715  + v(i,j,k,e)*dsdy(i,j,k,e) &
716  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
717  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
718  + v(i,j,k,e)*dtdy(i,j,k,e) &
719  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
720 
721  cflr = abs(dt*ur*dr_inv(i))
722  cfls = abs(dt*us*ds_inv(j))
723  cflt = abs(dt*ut*dt_inv(k))
724 
725  cflm = cflr + cfls + cflt
726  cfl = max(cfl, cflm)
727  end do
728  end do
729  end do
730  end do
731 
732  end function sx_cfl_lx3
733 
734  function sx_cfl_lx2(dt, u, v, w, drdx, dsdx, dtdx, drdy, dsdy, dtdy, &
735  drdz, dsdz, dtdz, dr_inv, ds_inv, dt_inv, &
736  jacinv, nelv) result(cfl)
737  integer, parameter :: lx = 2
738  integer, intent(in) :: nelv
739  real(kind=rp), intent(in) :: dt
740  real(kind=rp), dimension(lx, lx, lx, nelv) :: u, v, w
741  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdx, dsdx, dtdx
742  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdy, dsdy, dtdy
743  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: drdz, dsdz, dtdz
744  real(kind=rp), dimension(lx), intent(in) :: dr_inv, ds_inv, dt_inv
745  real(kind=rp), dimension(lx, lx, lx, nelv), intent(in) :: jacinv
746  real(kind=rp) :: cflr, cfls, cflt, cflm
747  real(kind=rp) :: ur, us, ut
748  real(kind=rp) :: cfl
749  integer :: i, j, k, e
750  cfl = 0d0
751 
752  do k = 1, lx
753  do j = 1, lx
754  do i = 1, lx
755  do e = 1, nelv
756  ur = ( u(i,j,k,e)*drdx(i,j,k,e) &
757  + v(i,j,k,e)*drdy(i,j,k,e) &
758  + w(i,j,k,e)*drdz(i,j,k,e) ) * jacinv(i,j,k,e)
759  us = ( u(i,j,k,e)*dsdx(i,j,k,e) &
760  + v(i,j,k,e)*dsdy(i,j,k,e) &
761  + w(i,j,k,e)*dsdz(i,j,k,e) ) * jacinv(i,j,k,e)
762  ut = ( u(i,j,k,e)*dtdx(i,j,k,e) &
763  + v(i,j,k,e)*dtdy(i,j,k,e) &
764  + w(i,j,k,e)*dtdz(i,j,k,e) ) * jacinv(i,j,k,e)
765 
766  cflr = abs(dt*ur*dr_inv(i))
767  cfls = abs(dt*us*ds_inv(j))
768  cflt = abs(dt*ut*dt_inv(k))
769 
770  cflm = cflr + cfls + cflt
771  cfl = max(cfl, cflm)
772  end do
773  end do
774  end do
775  end do
776 
777  end function sx_cfl_lx2
778 
779 end submodule sx_cfl
opr_sx
Operators SX-Aurora backend.
Definition: opr_sx.f90:2
max
#define max(a, b)
Definition: tensor.cu:40