[6515] | 1 | MODULE limadv_umx |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE limadv_umx *** |
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| 4 | !! LIM sea-ice model : sea-ice advection using the ULTIMATE-MACHO scheme |
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| 5 | !!============================================================================== |
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| 6 | !! History : 3.5 ! 2014-11 (C. Rousset, G. Madec) Original code |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! lim_adv_umx : update the tracer trend with the 3D advection trends using a TVD scheme |
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| 11 | !! ultimate : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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| 12 | !! macho : |
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| 13 | !! nonosc_2d : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | USE phycst ! physical constant |
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| 16 | USE dom_oce ! ocean domain |
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| 17 | USE sbc_oce ! ocean surface boundary condition |
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| 18 | USE ice ! ice variables |
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| 19 | ! |
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| 20 | USE in_out_manager ! I/O manager |
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| 21 | USE lbclnk ! lateral boundary conditions -- MPP exchanges |
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| 22 | USE lib_mpp ! MPP library |
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| 23 | USE wrk_nemo ! work arrays |
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| 24 | USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined) |
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| 25 | USE timing ! Timing |
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| 26 | |
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| 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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| 30 | PUBLIC lim_adv_umx ! routine called by limtrp.F90 |
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| 31 | |
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| 32 | INTEGER :: nn_ult_order = 4 ! order of the ULTIMATE scheme |
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| 33 | |
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| 34 | REAL(wp) :: r1_6 = 1._wp / 6._wp ! =1/6 |
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| 35 | |
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| 36 | !! * Substitutions |
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| 37 | # include "vectopt_loop_substitute.h90" |
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| 38 | !!---------------------------------------------------------------------- |
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| 39 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 40 | !! $Id: limadv_umx.F90 4499 2014-02-18 15:14:31Z timgraham $ |
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| 41 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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| 42 | !!---------------------------------------------------------------------- |
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| 43 | CONTAINS |
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| 44 | |
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| 45 | SUBROUTINE lim_adv_umx( lcon, kt, pdt, pu, pv, puc, pvc, pt, ptc, pfu, pfv ) |
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| 46 | !!---------------------------------------------------------------------- |
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| 47 | !! *** ROUTINE lim_adv_umx *** |
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| 48 | !! |
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| 49 | !! ** Purpose : Compute the now trend due to total advection of |
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| 50 | !! tracers and add it to the general trend of tracer equations |
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| 51 | !! |
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| 52 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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| 53 | !! corrected flux (monotonic correction) |
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| 54 | !! note: - this advection scheme needs a leap-frog time scheme |
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| 55 | !! |
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| 56 | !! ** Action : - pt the after advective tracer |
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| 57 | !!---------------------------------------------------------------------- |
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| 58 | LOGICAL , INTENT(in ) :: lcon ! "continuity" equations for a and H |
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| 59 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 60 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 61 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
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| 62 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity components (for a or H) |
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| 63 | ! 2 ice transport components (for tracers q) |
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| 64 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer field |
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| 65 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ptc ! tracer content field |
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| 66 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pfu, pfv ! advective fluxes at u- and v-points |
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| 67 | ! |
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| 68 | INTEGER :: ji, jj ! dummy loop indices |
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| 69 | REAL(wp) :: ztra ! local scalar |
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| 70 | REAL(wp) :: zfp_ui, zfp_vj ! - - |
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| 71 | REAL(wp) :: zfm_ui, zfm_vj ! - - |
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| 72 | REAL(wp), POINTER, DIMENSION(:,:) :: zt_ups, zfu_ups, zfv_ups, ztrd, zfu_ho, zfv_ho, zt_u, zt_v |
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| 73 | !!---------------------------------------------------------------------- |
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| 74 | ! |
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| 75 | IF( nn_timing == 1 ) CALL timing_start('lim_adv_umx') |
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| 76 | ! |
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| 77 | CALL wrk_alloc( jpi,jpj, zt_ups, zfu_ups, zfv_ups, ztrd, zfu_ho, zfv_ho, zt_u, zt_v ) |
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| 78 | ! |
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| 79 | ! |
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| 80 | !clem zt_ups(:,:) = 0._wp |
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| 81 | ! |
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| 82 | ! upstream advection with initial mass fluxes & intermediate update |
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| 83 | ! -------------------------------------------------------------------- |
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| 84 | DO jj = 1, jpjm1 ! upstream tracer flux in the i and j direction |
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| 85 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 86 | zfp_ui = puc(ji,jj) + ABS( puc(ji,jj) ) |
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| 87 | zfm_ui = puc(ji,jj) - ABS( puc(ji,jj) ) |
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| 88 | zfp_vj = pvc(ji,jj) + ABS( pvc(ji,jj) ) |
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| 89 | zfm_vj = pvc(ji,jj) - ABS( pvc(ji,jj) ) |
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| 90 | zfu_ups(ji,jj) = 0.5_wp * ( zfp_ui * pt(ji,jj) + zfm_ui * pt(ji+1,jj ) ) |
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| 91 | zfv_ups(ji,jj) = 0.5_wp * ( zfp_vj * pt(ji,jj) + zfm_vj * pt(ji ,jj+1) ) |
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| 92 | END DO |
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| 93 | END DO |
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| 94 | |
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| 95 | DO jj = 2, jpjm1 ! total intermediate advective trends |
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| 96 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 97 | ztra = - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj ) & |
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| 98 | & + zfv_ups(ji,jj) - zfv_ups(ji ,jj-1) ) * r1_e12t(ji,jj) |
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| 99 | ! |
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| 100 | ztrd(ji,jj) = ztra ! upstream trend [ -div(uh) or -div(uhT) ] |
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| 101 | zt_ups (ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) ! guess after content field with monotonic scheme |
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| 102 | END DO |
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| 103 | END DO |
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| 104 | CALL lbc_lnk( zt_ups, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
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| 105 | |
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| 106 | ! High order (_ho) fluxes |
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| 107 | ! ----------------------- |
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| 108 | SELECT CASE( nn_ult_order ) |
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| 109 | CASE ( 20 ) ! centered second order |
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| 110 | DO jj = 2, jpjm1 |
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| 111 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 112 | zfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( pt(ji,jj) + pt(ji+1,jj) ) |
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| 113 | zfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( pt(ji,jj) + pt(ji,jj+1) ) |
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| 114 | END DO |
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| 115 | END DO |
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| 116 | ! |
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| 117 | CASE ( 1 , 4 ) ! 1st to 4th order ULTIMATE-MACHO scheme |
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| 118 | CALL macho( lcon, kt, nn_ult_order, pdt, pt, pu, pv, zt_u, zt_v ) |
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| 119 | !! CALL macho( lcon, kt, nn_ult_order, pdt, ptc, pu, pv, zt_u, zt_v ) |
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| 120 | ! |
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| 121 | DO jj = 2, jpjm1 |
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| 122 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 123 | zfu_ho(ji,jj) = puc(ji,jj) * zt_u(ji,jj) |
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| 124 | zfv_ho(ji,jj) = pvc(ji,jj) * zt_v(ji,jj) |
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| 125 | END DO |
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| 126 | END DO |
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| 127 | ! |
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| 128 | END SELECT |
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| 129 | |
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| 130 | ! antidiffusive flux : high order minus low order |
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| 131 | ! -------------------------------------------------- |
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| 132 | DO jj = 2, jpjm1 |
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| 133 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 134 | zfu_ho(ji,jj) = zfu_ho(ji,jj) - zfu_ups(ji,jj) |
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| 135 | zfv_ho(ji,jj) = zfv_ho(ji,jj) - zfv_ups(ji,jj) |
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| 136 | END DO |
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| 137 | END DO |
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| 138 | CALL lbc_lnk_multi( zfu_ho, 'U', -1., zfv_ho, 'V', -1. ) ! Lateral bondary conditions |
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| 139 | |
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| 140 | ! monotonicity algorithm |
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| 141 | ! ------------------------- |
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| 142 | CALL nonosc_2d( ptc, zfu_ho, zfv_ho, zt_ups, pdt ) |
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| 143 | |
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| 144 | ! final trend with corrected fluxes |
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| 145 | ! ------------------------------------ |
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| 146 | DO jj = 2, jpjm1 |
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| 147 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 148 | ztra = ztrd(ji,jj) - ( zfu_ho(ji,jj) - zfu_ho(ji-1,jj ) & |
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| 149 | & + zfv_ho(ji,jj) - zfv_ho(ji ,jj-1) ) * r1_e12t(ji,jj) |
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| 150 | ptc(ji,jj) = ptc(ji,jj) + pdt * ztra |
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| 151 | END DO |
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| 152 | END DO |
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| 153 | CALL lbc_lnk( ptc(:,:) , 'T', 1. ) |
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| 154 | ! |
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| 155 | IF( PRESENT( pfu ) ) THEN |
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| 156 | DO jj = 2, jpjm1 |
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| 157 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 158 | pfu(ji,jj) = zfu_ups(ji,jj) + zfu_ho(ji,jj) |
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| 159 | pfv(ji,jj) = zfv_ups(ji,jj) + zfv_ho(ji,jj) |
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| 160 | END DO |
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| 161 | END DO |
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| 162 | CALL lbc_lnk_multi( pfu, 'U', -1., pfv, 'V', -1. ) ! Lateral bondary conditions |
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| 163 | ENDIF |
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| 164 | ! |
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| 165 | CALL wrk_dealloc( jpi,jpj, zt_ups, zfu_ups, zfv_ups, ztrd, zfu_ho, zfv_ho, zt_u, zt_v ) |
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| 166 | ! |
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| 167 | IF( nn_timing == 1 ) CALL timing_stop('lim_adv_umx') |
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| 168 | ! |
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| 169 | END SUBROUTINE lim_adv_umx |
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| 170 | |
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| 171 | |
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| 172 | SUBROUTINE macho( lcon, kt, k_order, pdt, pt, pu, pv, pt_u, pt_v ) |
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| 173 | !!--------------------------------------------------------------------- |
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| 174 | !! *** ROUTINE ultimate_x *** |
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| 175 | !! |
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| 176 | !! ** Purpose : compute |
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| 177 | !! |
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| 178 | !! ** Method : ... ??? |
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| 179 | !! TIM = transient interpolation Modeling |
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| 180 | !! |
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| 181 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 182 | !!---------------------------------------------------------------------- |
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| 183 | LOGICAL , INTENT(in ) :: lcon ! "continuity" equations for a and ah |
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| 184 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 185 | INTEGER , INTENT(in ) :: k_order ! order of the ULTIMATE scheme |
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| 186 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 187 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
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| 188 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
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| 189 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u, pt_v ! tracer at u- and v-points |
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| 190 | ! |
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| 191 | INTEGER :: ji, jj ! dummy loop indices |
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| 192 | REAL(wp) :: zc_box ! - - |
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| 193 | REAL(wp), POINTER, DIMENSION(:,:) :: zzt |
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| 194 | !!---------------------------------------------------------------------- |
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| 195 | ! |
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| 196 | IF( nn_timing == 1 ) CALL timing_start('macho') |
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| 197 | ! |
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| 198 | CALL wrk_alloc( jpi,jpj, zzt ) |
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| 199 | ! |
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| 200 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == 0 ) THEN !== odd ice time step: adv_x then adv_y ==! |
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| 201 | ! |
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| 202 | ! !-- ultimate interpolation of pt at u-point --! |
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| 203 | CALL ultimate_x( lcon, k_order, pdt, pt, pu, pt_u ) |
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| 204 | ! |
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| 205 | ! !-- advective form update in zzt --! |
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| 206 | DO jj = 1, jpj |
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| 207 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 208 | ! |
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| 209 | IF( pu(ji,jj) * pu(ji-1,jj) <= 0._wp ) THEN ; zc_box = 0._wp |
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| 210 | ELSEIF( pu(ji ,jj) > 0._wp ) THEN ; zc_box = pu(ji-1,jj) |
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| 211 | ELSE ; zc_box = pu(ji ,jj) |
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| 212 | ENDIF |
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| 213 | ! |
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| 214 | zzt(ji,jj) = pt(ji,jj) - zc_box * pdt * ( pt_u(ji,jj) - pt_u(ji-1,jj) ) * r1_e12t(ji,jj) |
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| 215 | IF( lcon == .TRUE. ) THEN ! clem => for a.div(u) ?? |
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| 216 | zzt(ji,jj) = zzt(ji,jj) - pt(ji,jj) * pdt * ( pu(ji,jj) - pu(ji-1,jj) ) * r1_e12t(ji,jj) |
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| 217 | END IF |
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| 218 | END DO |
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| 219 | END DO |
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| 220 | ! |
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| 221 | ! !-- ultimate interpolation of pt at v-point --! |
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| 222 | CALL ultimate_y( lcon, k_order, pdt, zzt, pv, pt_v ) |
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| 223 | ! |
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| 224 | ELSE !== even ice time step: adv_y then adv_x ==! |
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| 225 | ! |
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| 226 | ! !-- ultimate interpolation of pt at v-point --! |
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| 227 | CALL ultimate_y( lcon, k_order, pdt, pt, pv, pt_v ) |
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| 228 | ! |
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| 229 | ! !-- advective form update in zzt --! |
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| 230 | DO jj = 2, jpjm1 |
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| 231 | DO ji = 1, jpi |
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| 232 | ! |
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| 233 | IF( pv(ji,jj) * pv(ji,jj-1) <= 0._wp ) THEN ; zc_box = 0._wp |
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| 234 | ELSEIF( pv(ji,jj ) > 0._wp ) THEN ; zc_box = pv(ji,jj-1) |
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| 235 | ELSE ; zc_box = pv(ji,jj ) |
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| 236 | ENDIF |
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| 237 | ! |
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| 238 | zzt(ji,jj) = pt(ji,jj) - zc_box * pdt * ( pt_v(ji,jj) - pt_v(ji,jj-1) ) * r1_e12t(ji,jj) |
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| 239 | IF( lcon == .TRUE. ) THEN ! clem => for a.div(u) ?? |
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| 240 | zzt(ji,jj) = zzt(ji,jj) - pt(ji,jj) * pdt * ( pv(ji,jj) - pv(ji,jj-1) ) * r1_e12t(ji,jj) |
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| 241 | END IF |
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| 242 | END DO |
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| 243 | END DO |
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| 244 | ! |
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| 245 | ! !-- ultimate interpolation of pt at u-point --! |
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| 246 | CALL ultimate_x( lcon, k_order, pdt, zzt, pu, pt_u ) |
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| 247 | ! |
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| 248 | ENDIF |
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| 249 | ! |
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| 250 | CALL wrk_dealloc( jpi,jpj, zzt ) |
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| 251 | ! |
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| 252 | IF( nn_timing == 1 ) CALL timing_stop('macho') |
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| 253 | ! |
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| 254 | END SUBROUTINE macho |
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| 255 | |
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| 256 | |
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| 257 | SUBROUTINE ultimate_x( lcon, k_order, pdt, pt, pu, pt_u ) |
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| 258 | !!--------------------------------------------------------------------- |
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| 259 | !! *** ROUTINE ultimate_x *** |
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| 260 | !! |
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| 261 | !! ** Purpose : compute |
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| 262 | !! |
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| 263 | !! ** Method : ... ??? |
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| 264 | !! TIM = transient interpolation Modeling |
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| 265 | !! |
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| 266 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 267 | !!---------------------------------------------------------------------- |
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| 268 | LOGICAL , INTENT(in ) :: lcon ! "continuity" equations for a and ah |
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| 269 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
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| 270 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 271 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu ! ice i-velocity component |
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| 272 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
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| 273 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u ! tracer at u-point |
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| 274 | ! |
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| 275 | INTEGER :: ji, jj ! dummy loop indices |
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| 276 | REAL(wp) :: zcu, zdx2 ! - - |
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| 277 | REAL(wp), POINTER, DIMENSION(:,:) :: ztu, zltu |
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| 278 | !!---------------------------------------------------------------------- |
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| 279 | ! |
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| 280 | IF( nn_timing == 1 ) CALL timing_start('ultimate_x') |
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| 281 | ! |
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| 282 | CALL wrk_alloc( jpi,jpj, ztu, zltu ) |
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| 283 | ! |
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| 284 | SELECT CASE (k_order ) |
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| 285 | ! |
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| 286 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
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| 287 | ! |
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| 288 | DO jj = 1, jpj |
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| 289 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 290 | pt_u(ji,jj) = 0.5_wp * ( ( pt(ji+1,jj) + pt(ji,jj) ) & |
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| 291 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj) - pt(ji,jj) ) ) * umask(ji,jj,1) |
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| 292 | END DO |
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| 293 | END DO |
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| 294 | ! |
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| 295 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
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| 296 | DO jj = 1, jpj |
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| 297 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 298 | pt_u(ji,jj) = 0.5_wp * ( ( pt(ji+1,jj) + pt(ji,jj) ) & |
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| 299 | !! & - pdt * pu(ji,jj) * ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e1u(ji,jj) ) * umask(ji,jj,1) |
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| 300 | & - pdt * pu(ji,jj) * ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e12u(ji,jj) ) * umask(ji,jj,1) |
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| 301 | END DO |
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| 302 | END DO |
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| 303 | CALL lbc_lnk( pt_u(:,:) , 'U', 1. ) |
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| 304 | ! |
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| 305 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
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| 306 | ! |
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| 307 | ! !-- Laplacian in i- and in j-directions --! |
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| 308 | DO jj = 2, jpjm1 ! First derivative (gradient) |
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| 309 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 310 | ztu(ji,jj) = ( pt(ji+1,jj ) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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| 311 | END DO |
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| 312 | ! ! Second derivative (divergence) |
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| 313 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 314 | zltu(ji,jj) = ( ztu(ji,jj) - ztu(ji-1,jj) ) * r1_e1t(ji,jj) |
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| 315 | END DO |
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| 316 | END DO |
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| 317 | CALL lbc_lnk( zltu, 'T', 1. ) ! Lateral boundary cond. (unchanged sign) |
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| 318 | ! |
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| 319 | DO jj = 1, jpj |
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| 320 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 321 | !! zcu = pu(ji,jj) * pdt * r1_e1u(ji,jj) |
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| 322 | zcu = pu(ji,jj) * pdt * r1_e12u(ji,jj) |
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| 323 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
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| 324 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
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| 325 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
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| 326 | & - r1_6 * zdx2 * ( 1._wp - zcu*zcu ) * ( zltu(ji+1,jj) + zltu(ji,jj) & |
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| 327 | & - SIGN( 1._wp, zcu ) * ( zltu(ji+1,jj) - zltu(ji,jj) ) ) ) |
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| 328 | END DO |
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| 329 | END DO |
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| 330 | ! |
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| 331 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
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| 332 | ! |
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| 333 | ! !-- Laplacian in i- and in j-directions --! |
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| 334 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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| 335 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 336 | ztu(ji,jj) = ( pt(ji+1,jj ) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
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| 337 | END DO |
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| 338 | ! ! Second derivative (divergence) |
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| 339 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 340 | zltu(ji,jj) = ( ztu(ji,jj) - ztu(ji-1,jj) ) * r1_e1t(ji,jj) |
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| 341 | END DO |
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| 342 | END DO |
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| 343 | CALL lbc_lnk( zltu, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 344 | ! |
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| 345 | DO jj = 1, jpj |
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| 346 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 347 | !! zcu = pu(ji,jj) * pdt * r1_e1u(ji,jj) |
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| 348 | zcu = pu(ji,jj) * pdt * r1_e12u(ji,jj) |
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| 349 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
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| 350 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
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| 351 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
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| 352 | & - r1_6 * zdx2 * ( 1._wp - zcu*zcu ) * ( zltu(ji+1,jj) + zltu(ji,jj) & |
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| 353 | & - 0.5_wp * zcu * ( zltu(ji+1,jj) - zltu(ji,jj) ) ) ) |
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| 354 | END DO |
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| 355 | END DO |
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| 356 | ! |
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| 357 | END SELECT |
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| 358 | ! |
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| 359 | CALL wrk_dealloc( jpi,jpj, ztu, zltu ) |
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| 360 | ! |
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| 361 | IF( nn_timing == 1 ) CALL timing_stop('ultimate_x') |
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| 362 | ! |
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| 363 | END SUBROUTINE ultimate_x |
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| 364 | |
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| 365 | |
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| 366 | SUBROUTINE ultimate_y( lcon, k_order, pdt, pt, pv, pt_v ) |
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| 367 | !!--------------------------------------------------------------------- |
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| 368 | !! *** ROUTINE ultimate_y *** |
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| 369 | !! |
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| 370 | !! ** Purpose : compute |
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| 371 | !! |
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| 372 | !! ** Method : ... ??? |
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| 373 | !! TIM = transient interpolation Modeling |
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| 374 | !! |
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| 375 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 376 | !!---------------------------------------------------------------------- |
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| 377 | LOGICAL , INTENT(in ) :: lcon ! "continuity" equations for a and ah |
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| 378 | INTEGER , INTENT(in ) :: k_order ! ocean time-step index |
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| 379 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 380 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pv ! ice j-velocity component |
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| 381 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
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| 382 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_v ! tracer at v-point |
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| 383 | ! |
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| 384 | INTEGER :: ji, jj ! dummy loop indices |
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| 385 | REAL(wp) :: zcv, zdy2 ! - - |
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| 386 | REAL(wp), POINTER, DIMENSION(:,:) :: ztv, zltv |
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| 387 | !!---------------------------------------------------------------------- |
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| 388 | ! |
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| 389 | IF( nn_timing == 1 ) CALL timing_start('ultimate_y') |
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| 390 | ! |
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| 391 | CALL wrk_alloc( jpi,jpj, ztv, zltv ) |
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| 392 | ! |
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| 393 | SELECT CASE (k_order ) |
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| 394 | ! |
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| 395 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
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| 396 | ! |
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| 397 | DO jj = 1, jpjm1 |
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| 398 | DO ji = 1, jpi |
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| 399 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
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| 400 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
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| 401 | END DO |
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| 402 | END DO |
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| 403 | ! |
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| 404 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
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| 405 | DO jj = 1, jpjm1 |
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| 406 | DO ji = 1, jpi |
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| 407 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
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| 408 | !! & - pdt * pv(ji,jj) * ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) ) |
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| 409 | & - pdt * pv(ji,jj) * ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e12v(ji,jj) ) |
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| 410 | END DO |
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| 411 | END DO |
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| 412 | CALL lbc_lnk( pt_v(:,:) , 'V', 1. ) |
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| 413 | ! |
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| 414 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
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| 415 | ! |
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| 416 | ! !-- Laplacian in i- and in j-directions --! |
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| 417 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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| 418 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 419 | ztv(ji,jj) = ( pt(ji ,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
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| 420 | END DO |
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| 421 | END DO |
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| 422 | DO jj = 2, jpjm1 ! Second derivative (divergence) |
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| 423 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 424 | zltv(ji,jj) = ( ztv(ji,jj) - ztv(ji,jj-1) ) * r1_e2t(ji,jj) |
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| 425 | END DO |
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| 426 | END DO |
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| 427 | CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sign) |
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| 428 | ! |
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| 429 | DO jj = 1, jpjm1 |
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| 430 | DO ji = 1, jpi |
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| 431 | !! zcv = pv(ji,jj) * pdt * r1_e2v(ji,jj) |
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| 432 | zcv = pv(ji,jj) * pdt * r1_e12v(ji,jj) |
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| 433 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
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| 434 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
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| 435 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
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| 436 | & - r1_6 * zdy2 * ( 1._wp - zcv*zcv ) * ( zltv(ji,jj+1) + zltv(ji,jj) & |
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| 437 | & - SIGN( 1._wp, zcv ) * ( zltv(ji,jj+1) - zltv(ji,jj) ) ) ) |
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| 438 | END DO |
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| 439 | END DO |
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| 440 | ! |
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| 441 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
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| 442 | ! |
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| 443 | ! !-- Laplacian in i- and in j-directions --! |
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| 444 | DO jj = 1, jpjm1 ! First derivative (gradient) |
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| 445 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 446 | ztv(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
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| 447 | END DO |
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| 448 | END DO |
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| 449 | DO jj = 2, jpjm1 ! Second derivative (divergence) |
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| 450 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 451 | zltv(ji,jj) = ( ztv(ji,jj) - ztv(ji,jj-1) ) * r1_e2t(ji,jj) |
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| 452 | END DO |
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| 453 | END DO |
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| 454 | CALL lbc_lnk( zltv, 'T', 1. ) ! Lateral boundary cond. (unchanged sgn) |
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| 455 | ! |
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| 456 | DO jj = 1, jpjm1 |
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| 457 | DO ji = 1, jpi |
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| 458 | !! zcv = pv(ji,jj) * pdt * r1_e2v(ji,jj) |
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| 459 | zcv = pv(ji,jj) * pdt * r1_e12v(ji,jj) |
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| 460 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
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| 461 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
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| 462 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
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| 463 | & - r1_6 * zdy2 * ( 1._wp - zcv*zcv ) * ( zltv(ji,jj+1) + zltv(ji,jj) & |
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| 464 | & - 0.5_wp * zcv * ( zltv(ji,jj+1) - zltv(ji,jj) ) ) ) |
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| 465 | END DO |
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| 466 | END DO |
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| 467 | ! |
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| 468 | END SELECT |
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| 469 | ! |
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| 470 | CALL wrk_dealloc( jpi,jpj, ztv, zltv ) |
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| 471 | ! |
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| 472 | IF( nn_timing == 1 ) CALL timing_stop('ultimate_y') |
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| 473 | ! |
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| 474 | END SUBROUTINE ultimate_y |
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| 475 | |
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| 476 | |
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| 477 | SUBROUTINE nonosc_2d( pbef, paa, pbb, paft, pdt ) |
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| 478 | !!--------------------------------------------------------------------- |
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| 479 | !! *** ROUTINE nonosc *** |
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| 480 | !! |
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| 481 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
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| 482 | !! scheme and the before field by a nonoscillatory algorithm |
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| 483 | !! |
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| 484 | !! ** Method : ... ??? |
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| 485 | !! warning : pbef and paft must be masked, but the boundaries |
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| 486 | !! conditions on the fluxes are not necessary zalezak (1979) |
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| 487 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
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| 488 | !! in-space based differencing for fluid |
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| 489 | !!---------------------------------------------------------------------- |
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| 490 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 491 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pbef, paft ! before & after field |
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| 492 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: paa, pbb ! monotonic fluxes in the 2 directions |
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| 493 | ! |
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| 494 | INTEGER :: ji, jj ! dummy loop indices |
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| 495 | INTEGER :: ikm1 ! local integer |
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| 496 | REAL(wp) :: zpos, zneg, zbt, za, zb, zc, zbig, zsml, z1_dt ! local scalars |
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| 497 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo ! - - |
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| 498 | REAL(wp), POINTER, DIMENSION(:,:) :: zbetup, zbetdo, zbup, zbdo, zmsk, zdiv |
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| 499 | !!---------------------------------------------------------------------- |
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| 500 | ! |
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| 501 | IF( nn_timing == 1 ) CALL timing_start('nonosc_2d') |
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| 502 | ! |
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| 503 | CALL wrk_alloc( jpi,jpj, zbetup, zbetdo, zbup, zbdo, zmsk, zdiv ) |
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| 504 | ! |
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| 505 | zbig = 1.e+40_wp |
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| 506 | zsml = 1.e-15_wp |
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| 507 | |
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| 508 | ! clem test |
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| 509 | DO jj = 2, jpjm1 |
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| 510 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 511 | zdiv(ji,jj) = - ( paa(ji,jj) - paa(ji-1,jj ) & |
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| 512 | & + pbb(ji,jj) - pbb(ji ,jj-1) ) |
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| 513 | END DO |
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| 514 | END DO |
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| 515 | CALL lbc_lnk( zdiv, 'T', 1. ) ! Lateral boundary conditions (unchanged sign) |
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| 516 | |
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| 517 | ! Determine ice masks for before and after tracers |
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| 518 | WHERE( pbef(:,:) == 0._wp .AND. paft(:,:) == 0._wp .AND. zdiv(:,:) == 0._wp ) ; zmsk(:,:) = 0._wp |
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| 519 | ELSEWHERE ; zmsk(:,:) = 1._wp * tmask(:,:,1) |
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| 520 | END WHERE |
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| 521 | |
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| 522 | ! Search local extrema |
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| 523 | ! -------------------- |
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| 524 | ! max/min of pbef & paft with large negative/positive value (-/+zbig) inside land |
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| 525 | ! zbup(:,:) = MAX( pbef(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ), & |
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| 526 | ! & paft(:,:) * tmask(:,:,1) - zbig * ( 1.e0 - tmask(:,:,1) ) ) |
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| 527 | ! zbdo(:,:) = MIN( pbef(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ), & |
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| 528 | ! & paft(:,:) * tmask(:,:,1) + zbig * ( 1.e0 - tmask(:,:,1) ) ) |
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| 529 | zbup(:,:) = MAX( pbef(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ), & |
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| 530 | & paft(:,:) * zmsk(:,:) - zbig * ( 1.e0 - zmsk(:,:) ) ) |
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| 531 | zbdo(:,:) = MIN( pbef(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ), & |
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| 532 | & paft(:,:) * zmsk(:,:) + zbig * ( 1.e0 - zmsk(:,:) ) ) |
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| 533 | |
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| 534 | z1_dt = 1._wp / pdt |
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| 535 | DO jj = 2, jpjm1 |
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| 536 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 537 | ! |
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| 538 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj ), zbup(ji+1,jj ), & ! search max/min in neighbourhood |
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| 539 | & zbup(ji ,jj-1), zbup(ji ,jj+1) ) |
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| 540 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj ), zbdo(ji+1,jj ), & |
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| 541 | & zbdo(ji ,jj-1), zbdo(ji ,jj+1) ) |
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| 542 | ! |
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| 543 | zpos = MAX( 0., paa(ji-1,jj ) ) - MIN( 0., paa(ji ,jj ) ) & ! positive/negative part of the flux |
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| 544 | & + MAX( 0., pbb(ji ,jj-1) ) - MIN( 0., pbb(ji ,jj ) ) |
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| 545 | zneg = MAX( 0., paa(ji ,jj ) ) - MIN( 0., paa(ji-1,jj ) ) & |
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| 546 | & + MAX( 0., pbb(ji ,jj ) ) - MIN( 0., pbb(ji ,jj-1) ) |
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| 547 | ! |
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| 548 | zbt = e12t(ji,jj) * z1_dt ! up & down beta terms |
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| 549 | zbetup(ji,jj) = ( zup - paft(ji,jj) ) / ( zpos + zsml ) * zbt |
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| 550 | zbetdo(ji,jj) = ( paft(ji,jj) - zdo ) / ( zneg + zsml ) * zbt |
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| 551 | END DO |
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| 552 | END DO |
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| 553 | CALL lbc_lnk_multi( zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
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| 554 | |
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| 555 | ! monotonic flux in the i & j direction (paa & pbb) |
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| 556 | ! ------------------------------------- |
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| 557 | DO jj = 2, jpjm1 |
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| 558 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 559 | zau = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji+1,jj) ) |
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| 560 | zbu = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji+1,jj) ) |
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| 561 | zcu = 0.5 + SIGN( 0.5 , paa(ji,jj) ) |
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| 562 | ! |
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| 563 | zav = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji,jj+1) ) |
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| 564 | zbv = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji,jj+1) ) |
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| 565 | zcv = 0.5 + SIGN( 0.5 , pbb(ji,jj) ) |
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| 566 | ! |
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| 567 | paa(ji,jj) = paa(ji,jj) * ( zcu * zau + ( 1._wp - zcu) * zbu ) |
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| 568 | pbb(ji,jj) = pbb(ji,jj) * ( zcv * zav + ( 1._wp - zcv) * zbv ) |
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| 569 | ! |
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| 570 | END DO |
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| 571 | END DO |
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| 572 | CALL lbc_lnk_multi( paa, 'U', -1., pbb, 'V', -1. ) ! lateral boundary condition (changed sign) |
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| 573 | ! |
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| 574 | CALL wrk_dealloc( jpi,jpj, zbetup, zbetdo, zbup, zbdo, zmsk, zdiv ) |
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| 575 | ! |
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| 576 | IF( nn_timing == 1 ) CALL timing_stop('nonosc_2d') |
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| 577 | ! |
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| 578 | END SUBROUTINE nonosc_2d |
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| 579 | |
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| 580 | !!====================================================================== |
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| 581 | END MODULE limadv_umx |
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