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traadv_fct.F90 @ 13149

Last change on this file since 13149 was 13149, checked in by andmirek, 4 years ago
Ticket #2482: Dissable restart and use allocatable arrays
File size: 33.8 KB

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[5770]	1	MODULE traadv_fct
[3]	2	!!==============================================================================
[5770]	3	!! * MODULE traadv_fct *
	4	!! Ocean tracers: horizontal & vertical advective trend (2nd/4th order Flux Corrected Transport method)
[3]	5	!!==============================================================================
[5770]	6	!! History : 3.7 ! 2015-09 (L. Debreu, G. Madec) original code (inspired from traadv_tvd.F90)
[503]	7	!!----------------------------------------------------------------------
[3]	8
	9	!!----------------------------------------------------------------------
[5770]	10	!! tra_adv_fct : update the tracer trend with a 3D advective trends using a 2nd or 4th order FCT scheme
	11	!! with sub-time-stepping in the vertical direction
	12	!! nonosc : compute monotonic tracer fluxes by a non-oscillatory algorithm
	13	!! interp_4th_cpt : 4th order compact scheme for the vertical component of the advection
[3]	14	!!----------------------------------------------------------------------
[3625]	15	USE oce ! ocean dynamics and active tracers
	16	USE dom_oce ! ocean space and time domain
[4990]	17	USE trc_oce ! share passive tracers/Ocean variables
	18	USE trd_oce ! trends: ocean variables
[3625]	19	USE trdtra ! tracers trends
[4990]	20	USE diaptr ! poleward transport diagnostics
[7646]	21	USE diaar5 ! AR5 diagnostics
[9019]	22	USE phycst , ONLY : rau0_rcp
[4990]	23	!
[5770]	24	USE in_out_manager ! I/O manager
[9019]	25	USE iom !
[3625]	26	USE lib_mpp ! MPP library
	27	USE lbclnk ! ocean lateral boundary condition (or mpp link)
[5770]	28	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
[3]	29
	30	IMPLICIT NONE
	31	PRIVATE
	32
[9019]	33	PUBLIC tra_adv_fct ! called by traadv.F90
	34	PUBLIC interp_4th_cpt ! called by traadv_cen.F90
[3]	35
[5770]	36	LOGICAL :: l_trd ! flag to compute trends
[7646]	37	LOGICAL :: l_ptr ! flag to compute poleward transport
	38	LOGICAL :: l_hst ! flag to compute heat/salt transport
[5770]	39	REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6
[2528]	40
[7646]	41	! ! tridiag solver associated indices:
	42	INTEGER, PARAMETER :: np_NH = 0 ! Neumann homogeneous boundary condition
	43	INTEGER, PARAMETER :: np_CEN2 = 1 ! 2nd order centered boundary condition
[13149]	44	REAL(wp), DIMENSION(:, :, :), ALLOCATABLE :: zbetup, zbetdo, zbup, zbdo
	45	REAL(wp), DIMENSION(:, :, :), ALLOCATABLE :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
[7646]	46
[3]	47	!! * Substitutions
	48	# include "vectopt_loop_substitute.h90"
	49	!!----------------------------------------------------------------------
[9598]	50	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
[1152]	51	!! $Id$
[10068]	52	!! Software governed by the CeCILL license (see ./LICENSE)
[3]	53	!!----------------------------------------------------------------------
	54	CONTAINS
	55
[5770]	56	SUBROUTINE tra_adv_fct( kt, kit000, cdtype, p2dt, pun, pvn, pwn, &
	57	& ptb, ptn, pta, kjpt, kn_fct_h, kn_fct_v )
[3]	58	!!----------------------------------------------------------------------
[5770]	59	!! * ROUTINE tra_adv_fct *
[3]	60	!!
[6140]	61	!! ** Purpose : Compute the now trend due to total advection of tracers
	62	!! and add it to the general trend of tracer equations
[3]	63	!!
[5770]	64	!! ** Method : - 2nd or 4th FCT scheme on the horizontal direction
	65	!! (choice through the value of kn_fct)
[6140]	66	!! - on the vertical the 4th order is a compact scheme
[5770]	67	!! - corrected flux (monotonic correction)
[3]	68	!!
[6140]	69	!! ** Action : - update pta with the now advective tracer trends
[9019]	70	!! - send trends to trdtra module for further diagnostics (l_trdtra=T)
[6140]	71	!! - htr_adv, str_adv : poleward advective heat and salt transport (ln_diaptr=T)
[503]	72	!!----------------------------------------------------------------------
[2528]	73	INTEGER , INTENT(in ) :: kt ! ocean time-step index
[3294]	74	INTEGER , INTENT(in ) :: kit000 ! first time step index
[2528]	75	CHARACTER(len=3) , INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator)
	76	INTEGER , INTENT(in ) :: kjpt ! number of tracers
[5770]	77	INTEGER , INTENT(in ) :: kn_fct_h ! order of the FCT scheme (=2 or 4)
	78	INTEGER , INTENT(in ) :: kn_fct_v ! order of the FCT scheme (=2 or 4)
[6140]	79	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	80	REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ) :: pun, pvn, pwn ! 3 ocean velocity components
	81	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: ptb, ptn ! before and now tracer fields
	82	REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(inout) :: pta ! tracer trend
[2715]	83	!
[5770]	84	INTEGER :: ji, jj, jk, jn ! dummy loop indices
[6140]	85	REAL(wp) :: ztra ! local scalar
[5770]	86	REAL(wp) :: zfp_ui, zfp_vj, zfp_wk, zC2t_u, zC4t_u ! - -
	87	REAL(wp) :: zfm_ui, zfm_vj, zfm_wk, zC2t_v, zC4t_v ! - -
[13149]	88	! REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi, zwx, zwy, zwz, ztu, ztv, zltu, zltv, ztw
[9019]	89	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ztrdx, ztrdy, ztrdz, zptry
[3]	90	!!----------------------------------------------------------------------
[3294]	91	!
	92	IF( kt == kit000 ) THEN
[2528]	93	IF(lwp) WRITE(numout,*)
[5770]	94	IF(lwp) WRITE(numout,*) 'tra_adv_fct : FCT advection scheme on ', cdtype
[2528]	95	IF(lwp) WRITE(numout,*) '~~~~~~~~~~~'
[13149]	96	ALLOCATE (zbetup(jpi,jpj,jpk), zbetdo(jpi,jpj,jpk), zbup(jpi,jpj,jpk), zbdo(jpi,jpj,jpk) )
	97	ALLOCATE (zwi(jpi,jpj,jpk), zwx(jpi,jpj,jpk), zwy(jpi,jpj,jpk), zwz(jpi,jpj,jpk), &
	98	ztu(jpi,jpj,jpk), ztv(jpi,jpj,jpk), zltu(jpi,jpj,jpk), zltv(jpi,jpj,jpk), &
	99	ztw(jpi,jpj,jpk))
[3]	100	ENDIF
[2528]	101	!
[9019]	102	l_trd = .FALSE. ! set local switches
[7646]	103	l_hst = .FALSE.
	104	l_ptr = .FALSE.
[9019]	105	IF( ( cdtype =='TRA' .AND. l_trdtra ) .OR. ( cdtype =='TRC' .AND. l_trdtrc ) ) l_trd = .TRUE.
	106	IF( cdtype =='TRA' .AND. ln_diaptr ) l_ptr = .TRUE.
	107	IF( cdtype =='TRA' .AND. ( iom_use("uadv_heattr") .OR. iom_use("vadv_heattr") .OR. &
	108	& iom_use("uadv_salttr") .OR. iom_use("vadv_salttr") ) ) l_hst = .TRUE.
[5770]	109	!
[7646]	110	IF( l_trd .OR. l_hst ) THEN
[9019]	111	ALLOCATE( ztrdx(jpi,jpj,jpk), ztrdy(jpi,jpj,jpk), ztrdz(jpi,jpj,jpk) )
[7753]	112	ztrdx(:,:,:) = 0._wp ; ztrdy(:,:,:) = 0._wp ; ztrdz(:,:,:) = 0._wp
[3294]	113	ENDIF
[2528]	114	!
[7646]	115	IF( l_ptr ) THEN
[9019]	116	ALLOCATE( zptry(jpi,jpj,jpk) )
[7753]	117	zptry(:,:,:) = 0._wp
[7646]	118	ENDIF
[6140]	119	! ! surface & bottom value : flux set to zero one for all
[7753]	120	zwz(:,:, 1 ) = 0._wp
	121	zwx(:,:,jpk) = 0._wp ; zwy(:,:,jpk) = 0._wp ; zwz(:,:,jpk) = 0._wp
[2528]	122	!
[7753]	123	zwi(:,:,:) = 0._wp
	124	!
[6140]	125	DO jn = 1, kjpt !== loop over the tracers ==!
[5770]	126	!
	127	! !== upstream advection with initial mass fluxes & intermediate update ==!
	128	! !* upstream tracer flux in the i and j direction
[2528]	129	DO jk = 1, jpkm1
	130	DO jj = 1, jpjm1
	131	DO ji = 1, fs_jpim1 ! vector opt.
	132	! upstream scheme
	133	zfp_ui = pun(ji,jj,jk) + ABS( pun(ji,jj,jk) )
	134	zfm_ui = pun(ji,jj,jk) - ABS( pun(ji,jj,jk) )
	135	zfp_vj = pvn(ji,jj,jk) + ABS( pvn(ji,jj,jk) )
	136	zfm_vj = pvn(ji,jj,jk) - ABS( pvn(ji,jj,jk) )
	137	zwx(ji,jj,jk) = 0.5 * ( zfp_ui * ptb(ji,jj,jk,jn) + zfm_ui * ptb(ji+1,jj ,jk,jn) )
	138	zwy(ji,jj,jk) = 0.5 * ( zfp_vj * ptb(ji,jj,jk,jn) + zfm_vj * ptb(ji ,jj+1,jk,jn) )
	139	END DO
[3]	140	END DO
	141	END DO
[5770]	142	! !* upstream tracer flux in the k direction *!
[6140]	143	DO jk = 2, jpkm1 ! Interior value ( multiplied by wmask)
[4990]	144	DO jj = 1, jpj
	145	DO ji = 1, jpi
[2528]	146	zfp_wk = pwn(ji,jj,jk) + ABS( pwn(ji,jj,jk) )
	147	zfm_wk = pwn(ji,jj,jk) - ABS( pwn(ji,jj,jk) )
[5120]	148	zwz(ji,jj,jk) = 0.5 * ( zfp_wk * ptb(ji,jj,jk,jn) + zfm_wk * ptb(ji,jj,jk-1,jn) ) * wmask(ji,jj,jk)
[2528]	149	END DO
[3]	150	END DO
	151	END DO
[6140]	152	IF( ln_linssh ) THEN ! top ocean value (only in linear free surface as zwz has been w-masked)
[5770]	153	IF( ln_isfcav ) THEN ! top of the ice-shelf cavities and at the ocean surface
[5120]	154	DO jj = 1, jpj
	155	DO ji = 1, jpi
	156	zwz(ji,jj, mikt(ji,jj) ) = pwn(ji,jj,mikt(ji,jj)) * ptb(ji,jj,mikt(ji,jj),jn) ! linear free surface
	157	END DO
	158	END DO
[5770]	159	ELSE ! no cavities: only at the ocean surface
[7753]	160	zwz(:,:,1) = pwn(:,:,1) * ptb(:,:,1,jn)
[5770]	161	ENDIF
[5120]	162	ENDIF
[5770]	163	!
	164	DO jk = 1, jpkm1 !* trend and after field with monotonic scheme
[216]	165	DO jj = 2, jpjm1
	166	DO ji = fs_2, fs_jpim1 ! vector opt.
[6691]	167	! ! total intermediate advective trends
[5770]	168	ztra = - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	169	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
[6691]	170	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) * r1_e1e2t(ji,jj)
	171	! ! update and guess with monotonic sheme
	172	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra / e3t_n(ji,jj,jk) * tmask(ji,jj,jk)
	173	zwi(ji,jj,jk) = ( e3t_b(ji,jj,jk) * ptb(ji,jj,jk,jn) + p2dt * ztra ) / e3t_a(ji,jj,jk) * tmask(ji,jj,jk)
[216]	174	END DO
	175	END DO
	176	END DO
[5770]	177	!
[7646]	178	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics (contribution of upstream fluxes)
[7753]	179	ztrdx(:,:,:) = zwx(:,:,:) ; ztrdy(:,:,:) = zwy(:,:,:) ; ztrdz(:,:,:) = zwz(:,:,:)
[2528]	180	END IF
[5770]	181	! ! "Poleward" heat and salt transports (contribution of upstream fluxes)
[9019]	182	IF( l_ptr ) zptry(:,:,:) = zwy(:,:,:)
[5770]	183	!
	184	! !== anti-diffusive flux : high order minus low order ==!
	185	!
[6140]	186	SELECT CASE( kn_fct_h ) !* horizontal anti-diffusive fluxes
[5770]	187	!
[6140]	188	CASE( 2 ) !- 2nd order centered
[5770]	189	DO jk = 1, jpkm1
	190	DO jj = 1, jpjm1
	191	DO ji = 1, fs_jpim1 ! vector opt.
	192	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji+1,jj,jk,jn) ) - zwx(ji,jj,jk)
	193	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( ptn(ji,jj,jk,jn) + ptn(ji,jj+1,jk,jn) ) - zwy(ji,jj,jk)
	194	END DO
[503]	195	END DO
	196	END DO
[5770]	197	!
[6140]	198	CASE( 4 ) !- 4th order centered
[7753]	199	zltu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	200	zltv(:,:,jpk) = 0._wp
[6140]	201	DO jk = 1, jpkm1 ! Laplacian
	202	DO jj = 1, jpjm1 ! 1st derivative (gradient)
[5770]	203	DO ji = 1, fs_jpim1 ! vector opt.
	204	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	205	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	206	END DO
[503]	207	END DO
[6140]	208	DO jj = 2, jpjm1 ! 2nd derivative * 1/ 6
[5770]	209	DO ji = fs_2, fs_jpim1 ! vector opt.
	210	zltu(ji,jj,jk) = ( ztu(ji,jj,jk) + ztu(ji-1,jj,jk) ) * r1_6
	211	zltv(ji,jj,jk) = ( ztv(ji,jj,jk) + ztv(ji,jj-1,jk) ) * r1_6
	212	END DO
	213	END DO
[503]	214	END DO
[10425]	215	CALL lbc_lnk_multi( 'traadv_fct', zltu, 'T', 1. , zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn)
[5770]	216	!
[6140]	217	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	218	DO jj = 1, jpjm1
	219	DO ji = 1, fs_jpim1 ! vector opt.
	220	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points
	221	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	222	! ! C4 minus upstream advective fluxes
	223	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * ( zC2t_u + zltu(ji,jj,jk) - zltu(ji+1,jj,jk) ) - zwx(ji,jj,jk)
	224	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * ( zC2t_v + zltv(ji,jj,jk) - zltv(ji,jj+1,jk) ) - zwy(ji,jj,jk)
	225	END DO
[5120]	226	END DO
[5770]	227	END DO
	228	!
[6140]	229	CASE( 41 ) !- 4th order centered ==>> !!gm coding attempt need to be tested
[7753]	230	ztu(:,:,jpk) = 0._wp ! Bottom value : flux set to zero
	231	ztv(:,:,jpk) = 0._wp
[6140]	232	DO jk = 1, jpkm1 ! 1st derivative (gradient)
	233	DO jj = 1, jpjm1
[5770]	234	DO ji = 1, fs_jpim1 ! vector opt.
	235	ztu(ji,jj,jk) = ( ptn(ji+1,jj ,jk,jn) - ptn(ji,jj,jk,jn) ) * umask(ji,jj,jk)
	236	ztv(ji,jj,jk) = ( ptn(ji ,jj+1,jk,jn) - ptn(ji,jj,jk,jn) ) * vmask(ji,jj,jk)
	237	END DO
	238	END DO
[5120]	239	END DO
[10425]	240	CALL lbc_lnk_multi( 'traadv_fct', ztu, 'U', -1. , ztv, 'V', -1. ) ! Lateral boundary cond. (unchanged sgn)
[5770]	241	!
[6140]	242	DO jk = 1, jpkm1 ! Horizontal advective fluxes
[5770]	243	DO jj = 2, jpjm1
	244	DO ji = 2, fs_jpim1 ! vector opt.
	245	zC2t_u = ptn(ji,jj,jk,jn) + ptn(ji+1,jj ,jk,jn) ! 2 x C2 interpolation of T at u- & v-points (x2)
	246	zC2t_v = ptn(ji,jj,jk,jn) + ptn(ji ,jj+1,jk,jn)
	247	! ! C4 interpolation of T at u- & v-points (x2)
	248	zC4t_u = zC2t_u + r1_6 * ( ztu(ji-1,jj ,jk) - ztu(ji+1,jj ,jk) )
	249	zC4t_v = zC2t_v + r1_6 * ( ztv(ji ,jj-1,jk) - ztv(ji ,jj+1,jk) )
	250	! ! C4 minus upstream advective fluxes
	251	zwx(ji,jj,jk) = 0.5_wp * pun(ji,jj,jk) * zC4t_u - zwx(ji,jj,jk)
	252	zwy(ji,jj,jk) = 0.5_wp * pvn(ji,jj,jk) * zC4t_v - zwy(ji,jj,jk)
	253	END DO
	254	END DO
	255	END DO
	256	!
	257	END SELECT
[6140]	258	!
	259	SELECT CASE( kn_fct_v ) !* vertical anti-diffusive fluxes (w-masked interior values)
[5770]	260	!
[6140]	261	CASE( 2 ) !- 2nd order centered
[5770]	262	DO jk = 2, jpkm1
	263	DO jj = 2, jpjm1
	264	DO ji = fs_2, fs_jpim1
[6140]	265	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * 0.5_wp * ( ptn(ji,jj,jk,jn) + ptn(ji,jj,jk-1,jn) ) &
	266	& - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
[5770]	267	END DO
	268	END DO
	269	END DO
	270	!
[6140]	271	CASE( 4 ) !- 4th order COMPACT
	272	CALL interp_4th_cpt( ptn(:,:,:,jn) , ztw ) ! zwt = COMPACT interpolation of T at w-point
[5770]	273	DO jk = 2, jpkm1
	274	DO jj = 2, jpjm1
	275	DO ji = fs_2, fs_jpim1
	276	zwz(ji,jj,jk) = ( pwn(ji,jj,jk) * ztw(ji,jj,jk) - zwz(ji,jj,jk) ) * wmask(ji,jj,jk)
	277	END DO
	278	END DO
	279	END DO
	280	!
	281	END SELECT
[6140]	282	IF( ln_linssh ) THEN ! top ocean value: high order = upstream ==>> zwz=0
[7753]	283	zwz(:,:,1) = 0._wp ! only ocean surface as interior zwz values have been w-masked
[6140]	284	ENDIF
[5770]	285	!
[10425]	286	CALL lbc_lnk_multi( 'traadv_fct', zwi, 'T', 1., zwx, 'U', -1. , zwy, 'V', -1., zwz, 'W', 1. )
[6140]	287	!
[5770]	288	! !== monotonicity algorithm ==!
	289	!
[2528]	290	CALL nonosc( ptb(:,:,:,jn), zwx, zwy, zwz, zwi, p2dt )
[6140]	291	!
[5770]	292	! !== final trend with corrected fluxes ==!
	293	!
[216]	294	DO jk = 1, jpkm1
	295	DO jj = 2, jpjm1
[2528]	296	DO ji = fs_2, fs_jpim1 ! vector opt.
[5770]	297	pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) - ( zwx(ji,jj,jk) - zwx(ji-1,jj ,jk ) &
	298	& + zwy(ji,jj,jk) - zwy(ji ,jj-1,jk ) &
	299	& + zwz(ji,jj,jk) - zwz(ji ,jj ,jk+1) ) &
[6140]	300	& * r1_e1e2t(ji,jj) / e3t_n(ji,jj,jk)
[216]	301	END DO
	302	END DO
	303	END DO
[5770]	304	!
[9019]	305	IF( l_trd .OR. l_hst ) THEN ! trend diagnostics // heat/salt transport
	306	ztrdx(:,:,:) = ztrdx(:,:,:) + zwx(:,:,:) ! <<< add anti-diffusive fluxes
	307	ztrdy(:,:,:) = ztrdy(:,:,:) + zwy(:,:,:) ! to upstream fluxes
	308	ztrdz(:,:,:) = ztrdz(:,:,:) + zwz(:,:,:) !
[5770]	309	!
[9019]	310	IF( l_trd ) THEN ! trend diagnostics
	311	CALL trd_tra( kt, cdtype, jn, jptra_xad, ztrdx, pun, ptn(:,:,:,jn) )
	312	CALL trd_tra( kt, cdtype, jn, jptra_yad, ztrdy, pvn, ptn(:,:,:,jn) )
	313	CALL trd_tra( kt, cdtype, jn, jptra_zad, ztrdz, pwn, ptn(:,:,:,jn) )
	314	ENDIF
	315	! ! heat/salt transport
	316	IF( l_hst ) CALL dia_ar5_hst( jn, 'adv', ztrdx(:,:,:), ztrdy(:,:,:) )
[5770]	317	!
[9019]	318	ENDIF
	319	IF( l_ptr ) THEN ! "Poleward" transports
	320	zptry(:,:,:) = zptry(:,:,:) + zwy(:,:,:) ! <<< add anti-diffusive fluxes
[7646]	321	CALL dia_ptr_hst( jn, 'adv', zptry(:,:,:) )
[2528]	322	ENDIF
[503]	323	!
[6140]	324	END DO ! end of tracer loop
[503]	325	!
[10024]	326	IF( l_trd .OR. l_hst ) THEN
	327	DEALLOCATE( ztrdx, ztrdy, ztrdz )
	328	ENDIF
	329	IF( l_ptr ) THEN
	330	DEALLOCATE( zptry )
	331	ENDIF
	332	!
[5770]	333	END SUBROUTINE tra_adv_fct
[3]	334
[5737]	335
[2528]	336	SUBROUTINE nonosc( pbef, paa, pbb, pcc, paft, p2dt )
[3]	337	!!---------------------------------------------------------------------
	338	!! * ROUTINE nonosc *
	339	!!
	340	!! ** Purpose : compute monotonic tracer fluxes from the upstream
	341	!! scheme and the before field by a nonoscillatory algorithm
	342	!!
	343	!! ** Method : ... ???
	344	!! warning : pbef and paft must be masked, but the boundaries
	345	!! conditions on the fluxes are not necessary zalezak (1979)
	346	!! drange (1995) multi-dimensional forward-in-time and upstream-
	347	!! in-space based differencing for fluid
	348	!!----------------------------------------------------------------------
[6140]	349	REAL(wp) , INTENT(in ) :: p2dt ! tracer time-step
[2528]	350	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(in ) :: pbef, paft ! before & after field
	351	REAL(wp), DIMENSION (jpi,jpj,jpk), INTENT(inout) :: paa, pbb, pcc ! monotonic fluxes in the 3 directions
[2715]	352	!
[4990]	353	INTEGER :: ji, jj, jk ! dummy loop indices
	354	INTEGER :: ikm1 ! local integer
[6140]	355	REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zrtrn ! local scalars
[2715]	356	REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - -
[13149]	357	! REAL(wp), DIMENSION(jpi,jpj,jpk) :: zbetup, zbetdo, zbup, zbdo
[3]	358	!!----------------------------------------------------------------------
[3294]	359	!
[2715]	360	zbig = 1.e+40_wp
	361	zrtrn = 1.e-15_wp
[7753]	362	zbetup(:,:,:) = 0._wp ; zbetdo(:,:,:) = 0._wp
[785]	363
[3]	364	! Search local extrema
	365	! --------------------
[785]	366	! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land
[4990]	367	zbup = MAX( pbef * tmask - zbig * ( 1._wp - tmask ), &
	368	& paft * tmask - zbig * ( 1._wp - tmask ) )
	369	zbdo = MIN( pbef * tmask + zbig * ( 1._wp - tmask ), &
	370	& paft * tmask + zbig * ( 1._wp - tmask ) )
[785]	371
[5120]	372	DO jk = 1, jpkm1
	373	ikm1 = MAX(jk-1,1)
	374	DO jj = 2, jpjm1
	375	DO ji = fs_2, fs_jpim1 ! vector opt.
	376
[785]	377	! search maximum in neighbourhood
	378	zup = MAX( zbup(ji ,jj ,jk ), &
	379	& zbup(ji-1,jj ,jk ), zbup(ji+1,jj ,jk ), &
	380	& zbup(ji ,jj-1,jk ), zbup(ji ,jj+1,jk ), &
	381	& zbup(ji ,jj ,ikm1), zbup(ji ,jj ,jk+1) )
[3]	382
[785]	383	! search minimum in neighbourhood
	384	zdo = MIN( zbdo(ji ,jj ,jk ), &
	385	& zbdo(ji-1,jj ,jk ), zbdo(ji+1,jj ,jk ), &
	386	& zbdo(ji ,jj-1,jk ), zbdo(ji ,jj+1,jk ), &
	387	& zbdo(ji ,jj ,ikm1), zbdo(ji ,jj ,jk+1) )
[3]	388
[785]	389	! positive part of the flux
[3]	390	zpos = MAX( 0., paa(ji-1,jj ,jk ) ) - MIN( 0., paa(ji ,jj ,jk ) ) &
	391	& + MAX( 0., pbb(ji ,jj-1,jk ) ) - MIN( 0., pbb(ji ,jj ,jk ) ) &
	392	& + MAX( 0., pcc(ji ,jj ,jk+1) ) - MIN( 0., pcc(ji ,jj ,jk ) )
[785]	393
	394	! negative part of the flux
[3]	395	zneg = MAX( 0., paa(ji ,jj ,jk ) ) - MIN( 0., paa(ji-1,jj ,jk ) ) &
	396	& + MAX( 0., pbb(ji ,jj ,jk ) ) - MIN( 0., pbb(ji ,jj-1,jk ) ) &
	397	& + MAX( 0., pcc(ji ,jj ,jk ) ) - MIN( 0., pcc(ji ,jj ,jk+1) )
[785]	398
[3]	399	! up & down beta terms
[6140]	400	zbt = e1e2t(ji,jj) * e3t_n(ji,jj,jk) / p2dt
[785]	401	zbetup(ji,jj,jk) = ( zup - paft(ji,jj,jk) ) / ( zpos + zrtrn ) * zbt
	402	zbetdo(ji,jj,jk) = ( paft(ji,jj,jk) - zdo ) / ( zneg + zrtrn ) * zbt
[3]	403	END DO
	404	END DO
	405	END DO
[10425]	406	CALL lbc_lnk_multi( 'traadv_fct', zbetup, 'T', 1. , zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign)
[3]	407
[237]	408	! 3. monotonic flux in the i & j direction (paa & pbb)
	409	! ----------------------------------------
[3]	410	DO jk = 1, jpkm1
	411	DO jj = 2, jpjm1
	412	DO ji = fs_2, fs_jpim1 ! vector opt.
[4990]	413	zau = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji+1,jj,jk) )
	414	zbu = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji+1,jj,jk) )
[785]	415	zcu = ( 0.5 + SIGN( 0.5 , paa(ji,jj,jk) ) )
[4990]	416	paa(ji,jj,jk) = paa(ji,jj,jk) * ( zcu * zau + ( 1._wp - zcu) * zbu )
[3]	417
[4990]	418	zav = MIN( 1._wp, zbetdo(ji,jj,jk), zbetup(ji,jj+1,jk) )
	419	zbv = MIN( 1._wp, zbetup(ji,jj,jk), zbetdo(ji,jj+1,jk) )
[785]	420	zcv = ( 0.5 + SIGN( 0.5 , pbb(ji,jj,jk) ) )
[4990]	421	pbb(ji,jj,jk) = pbb(ji,jj,jk) * ( zcv * zav + ( 1._wp - zcv) * zbv )
[3]	422
	423	! monotonic flux in the k direction, i.e. pcc
	424	! -------------------------------------------
[785]	425	za = MIN( 1., zbetdo(ji,jj,jk+1), zbetup(ji,jj,jk) )
	426	zb = MIN( 1., zbetup(ji,jj,jk+1), zbetdo(ji,jj,jk) )
	427	zc = ( 0.5 + SIGN( 0.5 , pcc(ji,jj,jk+1) ) )
[4990]	428	pcc(ji,jj,jk+1) = pcc(ji,jj,jk+1) * ( zc * za + ( 1._wp - zc) * zb )
[3]	429	END DO
	430	END DO
	431	END DO
[10425]	432	CALL lbc_lnk_multi( 'traadv_fct', paa, 'U', -1. , pbb, 'V', -1. ) ! lateral boundary condition (changed sign)
[503]	433	!
[3]	434	END SUBROUTINE nonosc
	435
[5770]	436
[7646]	437	SUBROUTINE interp_4th_cpt_org( pt_in, pt_out )
[5770]	438	!!----------------------------------------------------------------------
[7646]	439	!! * ROUTINE interp_4th_cpt_org *
[5770]	440	!!
	441	!! ** Purpose : Compute the interpolation of tracer at w-point
	442	!!
	443	!! ** Method : 4th order compact interpolation
	444	!!----------------------------------------------------------------------
	445	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! now tracer fields
	446	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! now tracer field interpolated at w-pts
	447	!
	448	INTEGER :: ji, jj, jk ! dummy loop integers
	449	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	450	!!----------------------------------------------------------------------
	451
	452	DO jk = 3, jpkm1 !== build the three diagonal matrix ==!
	453	DO jj = 1, jpj
	454	DO ji = 1, jpi
	455	zwd (ji,jj,jk) = 4._wp
	456	zwi (ji,jj,jk) = 1._wp
	457	zws (ji,jj,jk) = 1._wp
	458	zwrm(ji,jj,jk) = 3._wp * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	459	!
	460	IF( tmask(ji,jj,jk+1) == 0._wp) THEN ! Switch to second order centered at bottom
	461	zwd (ji,jj,jk) = 1._wp
	462	zwi (ji,jj,jk) = 0._wp
	463	zws (ji,jj,jk) = 0._wp
	464	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	465	ENDIF
	466	END DO
	467	END DO
	468	END DO
	469	!
[7646]	470	jk = 2 ! Switch to second order centered at top
	471	DO jj = 1, jpj
	472	DO ji = 1, jpi
[5770]	473	zwd (ji,jj,jk) = 1._wp
	474	zwi (ji,jj,jk) = 0._wp
	475	zws (ji,jj,jk) = 0._wp
	476	zwrm(ji,jj,jk) = 0.5 * ( pt_in(ji,jj,jk-1) + pt_in(ji,jj,jk) )
	477	END DO
	478	END DO
	479	!
	480	! !== tridiagonal solve ==!
	481	DO jj = 1, jpj ! first recurrence
	482	DO ji = 1, jpi
	483	zwt(ji,jj,2) = zwd(ji,jj,2)
	484	END DO
	485	END DO
	486	DO jk = 3, jpkm1
	487	DO jj = 1, jpj
	488	DO ji = 1, jpi
	489	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	490	END DO
	491	END DO
	492	END DO
	493	!
	494	DO jj = 1, jpj ! second recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	495	DO ji = 1, jpi
	496	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	497	END DO
	498	END DO
	499	DO jk = 3, jpkm1
	500	DO jj = 1, jpj
	501	DO ji = 1, jpi
	502	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	503	END DO
	504	END DO
	505	END DO
	506
	507	DO jj = 1, jpj ! third recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	508	DO ji = 1, jpi
	509	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	510	END DO
	511	END DO
	512	DO jk = jpk-2, 2, -1
	513	DO jj = 1, jpj
	514	DO ji = 1, jpi
	515	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	516	END DO
	517	END DO
	518	END DO
	519	!
[7646]	520	END SUBROUTINE interp_4th_cpt_org
	521
	522
	523	SUBROUTINE interp_4th_cpt( pt_in, pt_out )
	524	!!----------------------------------------------------------------------
	525	!! * ROUTINE interp_4th_cpt *
	526	!!
	527	!! ** Purpose : Compute the interpolation of tracer at w-point
	528	!!
	529	!! ** Method : 4th order compact interpolation
	530	!!----------------------------------------------------------------------
	531	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pt_in ! field at t-point
	532	REAL(wp),DIMENSION(jpi,jpj,jpk), INTENT( out) :: pt_out ! field interpolated at w-point
	533	!
	534	INTEGER :: ji, jj, jk ! dummy loop integers
	535	INTEGER :: ikt, ikb ! local integers
	536	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwd, zwi, zws, zwrm, zwt
	537	!!----------------------------------------------------------------------
	538	!
	539	! !== build the three diagonal matrix & the RHS ==!
	540	!
	541	DO jk = 3, jpkm1 ! interior (from jk=3 to jpk-1)
	542	DO jj = 2, jpjm1
	543	DO ji = fs_2, fs_jpim1
	544	zwd (ji,jj,jk) = 3._wp * wmask(ji,jj,jk) + 1._wp ! diagonal
	545	zwi (ji,jj,jk) = wmask(ji,jj,jk) ! lower diagonal
	546	zws (ji,jj,jk) = wmask(ji,jj,jk) ! upper diagonal
	547	zwrm(ji,jj,jk) = 3._wp * wmask(ji,jj,jk) & ! RHS
	548	& * ( pt_in(ji,jj,jk) + pt_in(ji,jj,jk-1) )
	549	END DO
	550	END DO
	551	END DO
	552	!
	553	!!gm
	554	! SELECT CASE( kbc ) !* boundary condition
	555	! CASE( np_NH ) ! Neumann homogeneous at top & bottom
	556	! CASE( np_CEN2 ) ! 2nd order centered at top & bottom
	557	! END SELECT
	558	!!gm
	559	!
[9901]	560	IF ( ln_isfcav ) THEN ! set level two values which may not be set in ISF case
	561	zwd(:,:,2) = 1._wp ; zwi(:,:,2) = 0._wp ; zws(:,:,2) = 0._wp ; zwrm(:,:,2) = 0._wp
	562	END IF
	563	!
[7646]	564	DO jj = 2, jpjm1 ! 2nd order centered at top & bottom
	565	DO ji = fs_2, fs_jpim1
	566	ikt = mikt(ji,jj) + 1 ! w-point below the 1st wet point
	567	ikb = mbkt(ji,jj) ! - above the last wet point
	568	!
	569	zwd (ji,jj,ikt) = 1._wp ! top
	570	zwi (ji,jj,ikt) = 0._wp
	571	zws (ji,jj,ikt) = 0._wp
[9901]	572	zwrm(ji,jj,ikt) = 0.5_wp * ( pt_in(ji,jj,ikt-1) + pt_in(ji,jj,ikt) )
[7646]	573	!
	574	zwd (ji,jj,ikb) = 1._wp ! bottom
	575	zwi (ji,jj,ikb) = 0._wp
	576	zws (ji,jj,ikb) = 0._wp
[9901]	577	zwrm(ji,jj,ikb) = 0.5_wp * ( pt_in(ji,jj,ikb-1) + pt_in(ji,jj,ikb) )
[7646]	578	END DO
	579	END DO
	580	!
	581	! !== tridiagonal solver ==!
	582	!
	583	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	584	DO ji = fs_2, fs_jpim1
	585	zwt(ji,jj,2) = zwd(ji,jj,2)
	586	END DO
	587	END DO
	588	DO jk = 3, jpkm1
	589	DO jj = 2, jpjm1
	590	DO ji = fs_2, fs_jpim1
	591	zwt(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	592	END DO
	593	END DO
	594	END DO
	595	!
	596	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	597	DO ji = fs_2, fs_jpim1
	598	pt_out(ji,jj,2) = zwrm(ji,jj,2)
	599	END DO
	600	END DO
	601	DO jk = 3, jpkm1
	602	DO jj = 2, jpjm1
	603	DO ji = fs_2, fs_jpim1
	604	pt_out(ji,jj,jk) = zwrm(ji,jj,jk) - zwi(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	605	END DO
	606	END DO
	607	END DO
	608
	609	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	610	DO ji = fs_2, fs_jpim1
	611	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	612	END DO
	613	END DO
	614	DO jk = jpk-2, 2, -1
	615	DO jj = 2, jpjm1
	616	DO ji = fs_2, fs_jpim1
	617	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - zws(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	618	END DO
	619	END DO
	620	END DO
	621	!
[5770]	622	END SUBROUTINE interp_4th_cpt
[7646]	623
	624
	625	SUBROUTINE tridia_solver( pD, pU, pL, pRHS, pt_out , klev )
	626	!!----------------------------------------------------------------------
	627	!! * ROUTINE tridia_solver *
	628	!!
	629	!! ** Purpose : solve a symmetric 3diagonal system
	630	!!
	631	!! ** Method : solve M.t_out = RHS(t) where M is a tri diagonal matrix ( jpk*jpk )
	632	!!
	633	!! ( D_1 U_1 0 0 0 )( t_1 ) ( RHS_1 )
	634	!! ( L_2 D_2 U_2 0 0 )( t_2 ) ( RHS_2 )
	635	!! ( 0 L_3 D_3 U_3 0 )( t_3 ) = ( RHS_3 )
	636	!! ( ... )( ... ) ( ... )
	637	!! ( 0 0 0 L_k D_k )( t_k ) ( RHS_k )
	638	!!
	639	!! M is decomposed in the product of an upper and lower triangular matrix.
	640	!! The tri-diagonals matrix is given as input 3D arrays: pD, pU, pL
	641	!! (i.e. the Diagonal, the Upper diagonal, and the Lower diagonal).
	642	!! The solution is pta.
	643	!! The 3d array zwt is used as a work space array.
	644	!!----------------------------------------------------------------------
	645	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pD, pU, PL ! 3-diagonal matrix
	646	REAL(wp),DIMENSION(:,:,:), INTENT(in ) :: pRHS ! Right-Hand-Side
	647	REAL(wp),DIMENSION(:,:,:), INTENT( out) :: pt_out !!gm field at level=F(klev)
	648	INTEGER , INTENT(in ) :: klev ! =1 pt_out at w-level
	649	! ! =0 pt at t-level
	650	INTEGER :: ji, jj, jk ! dummy loop integers
	651	INTEGER :: kstart ! local indices
	652	REAL(wp),DIMENSION(jpi,jpj,jpk) :: zwt ! 3D work array
	653	!!----------------------------------------------------------------------
	654	!
	655	kstart = 1 + klev
	656	!
	657	DO jj = 2, jpjm1 !* 1st recurrence: Tk = Dk - Ik Sk-1 / Tk-1
	658	DO ji = fs_2, fs_jpim1
	659	zwt(ji,jj,kstart) = pD(ji,jj,kstart)
	660	END DO
	661	END DO
	662	DO jk = kstart+1, jpkm1
	663	DO jj = 2, jpjm1
	664	DO ji = fs_2, fs_jpim1
	665	zwt(ji,jj,jk) = pD(ji,jj,jk) - pL(ji,jj,jk) * pU(ji,jj,jk-1) /zwt(ji,jj,jk-1)
	666	END DO
	667	END DO
	668	END DO
	669	!
	670	DO jj = 2, jpjm1 !* 2nd recurrence: Zk = Yk - Ik / Tk-1 Zk-1
	671	DO ji = fs_2, fs_jpim1
	672	pt_out(ji,jj,kstart) = pRHS(ji,jj,kstart)
	673	END DO
	674	END DO
	675	DO jk = kstart+1, jpkm1
	676	DO jj = 2, jpjm1
	677	DO ji = fs_2, fs_jpim1
	678	pt_out(ji,jj,jk) = pRHS(ji,jj,jk) - pL(ji,jj,jk) / zwt(ji,jj,jk-1) *pt_out(ji,jj,jk-1)
	679	END DO
	680	END DO
	681	END DO
	682
	683	DO jj = 2, jpjm1 !* 3d recurrence: Xk = (Zk - Sk Xk+1 ) / Tk
	684	DO ji = fs_2, fs_jpim1
	685	pt_out(ji,jj,jpkm1) = pt_out(ji,jj,jpkm1) / zwt(ji,jj,jpkm1)
	686	END DO
	687	END DO
	688	DO jk = jpk-2, kstart, -1
	689	DO jj = 2, jpjm1
	690	DO ji = fs_2, fs_jpim1
	691	pt_out(ji,jj,jk) = ( pt_out(ji,jj,jk) - pU(ji,jj,jk) * pt_out(ji,jj,jk+1) ) / zwt(ji,jj,jk)
	692	END DO
	693	END DO
	694	END DO
	695	!
	696	END SUBROUTINE tridia_solver
	697
[3]	698	!!======================================================================
[5770]	699	END MODULE traadv_fct

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source: NEMO/branches/UKMO/NEMO_4.0_mirror_SI3_GPU/src/OCE/TRA/traadv_fct.F90 @ 13149

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