| 1 | MODULE icedyn_adv_umx |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE icedyn_adv_umx *** |
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| 4 | !! sea-ice : advection using the ULTIMATE-MACHO scheme |
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| 5 | !!============================================================================== |
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| 6 | !! History : 3.6 ! 2014-11 (C. Rousset, G. Madec) Original code |
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| 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | #if defined key_si3 |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! 'key_si3' SI3 sea-ice model |
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| 12 | !!---------------------------------------------------------------------- |
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| 13 | !! ice_dyn_adv_umx : update the tracer trend with the 3D advection trends using a TVD scheme |
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| 14 | !! ultimate_x(_y) : compute a tracer value at velocity points using ULTIMATE scheme at various orders |
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| 15 | !! macho : ??? |
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| 16 | !! nonosc_ice : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | USE phycst ! physical constant |
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| 19 | USE dom_oce ! ocean domain |
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| 20 | USE sbc_oce , ONLY : nn_fsbc ! update frequency of surface boundary condition |
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| 21 | USE ice ! sea-ice variables |
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| 22 | USE icevar ! sea-ice: operations |
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| 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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| 25 | USE iom ! I/O manager library |
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| 26 | USE lib_mpp ! MPP library |
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| 27 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 28 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 29 | |
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| 30 | IMPLICIT NONE |
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| 31 | PRIVATE |
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| 32 | |
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| 33 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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| 34 | |
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| 35 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 36 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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| 37 | |
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| 38 | ! limiter: 1=nonosc_ice, 2=superbee, 3=h3(rachid) |
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| 39 | INTEGER :: kn_limiter = 1 |
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| 40 | |
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| 41 | ! if T interpolated at u/v points is negative, then interpolate T at u/v points using the upstream scheme |
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| 42 | ! clem: if set to true, the 2D test case "diagonal advection" does not work (I do not understand why) |
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| 43 | ! but in realistic cases, it avoids having very negative ice temperature (-50) at low ice concentration |
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| 44 | LOGICAL :: ll_neg = .TRUE. |
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| 45 | |
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| 46 | ! alternate directions for upstream |
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| 47 | LOGICAL :: ll_upsxy = .TRUE. |
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| 48 | |
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| 49 | ! alternate directions for high order |
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| 50 | LOGICAL :: ll_hoxy = .TRUE. |
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| 51 | |
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| 52 | ! prelimiter: use it to avoid overshoot in H |
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| 53 | ! clem: if set to true, the 2D test case "diagnoal advection" does not work (I do not understand why) |
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| 54 | LOGICAL :: ll_prelimiter_zalesak = .FALSE. ! from: Zalesak(1979) eq. 14 => better for 1D. Not well defined in 2D |
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| 55 | |
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| 56 | |
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| 57 | !! * Substitutions |
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| 58 | # include "vectopt_loop_substitute.h90" |
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| 59 | !!---------------------------------------------------------------------- |
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| 60 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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| 61 | !! $Id$ |
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| 62 | !! Software governed by the CeCILL licence (./LICENSE) |
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| 63 | !!---------------------------------------------------------------------- |
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| 64 | CONTAINS |
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| 65 | |
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| 66 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, & |
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| 67 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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| 68 | !!---------------------------------------------------------------------- |
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| 69 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 70 | !! |
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| 71 | !! ** Purpose : Compute the now trend due to total advection of |
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| 72 | !! tracers and add it to the general trend of tracer equations |
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| 73 | !! using an "Ultimate-Macho" scheme |
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| 74 | !! |
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| 75 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 76 | !!---------------------------------------------------------------------- |
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| 77 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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| 78 | INTEGER , INTENT(in ) :: kt ! time step |
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| 79 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 80 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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| 81 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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| 87 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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| 88 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 89 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 90 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 91 | ! |
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| 92 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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| 93 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 94 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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| 95 | REAL(wp) :: zdt |
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| 96 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! send zcflnow and receive zcflprv |
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| 97 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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| 98 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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| 99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho |
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| 100 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai, z1_aip |
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| 101 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhvar |
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| 102 | !!---------------------------------------------------------------------- |
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| 103 | ! |
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| 104 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 105 | ! |
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| 106 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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| 107 | ! When needed, the advection split is applied at the next time-step in order to avoid blocking global comm. |
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| 108 | ! ...this should not affect too much the stability... Was ok on the tests we did... |
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| 109 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 110 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 111 | |
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| 112 | ! non-blocking global communication send zcflnow and receive zcflprv |
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| 113 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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| 114 | |
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| 115 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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| 116 | ELSE ; icycle = 1 |
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| 117 | ENDIF |
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| 118 | |
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| 119 | zdt = rdt_ice / REAL(icycle) |
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| 120 | |
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| 121 | ! --- transport --- ! |
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| 122 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 123 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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| 124 | |
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| 125 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 126 | DO jj = 2, jpjm1 |
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| 127 | DO ji = fs_2, fs_jpim1 |
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| 128 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 129 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 130 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 131 | ENDIF |
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| 132 | |
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| 133 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 134 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 135 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 136 | ENDIF |
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| 137 | END DO |
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| 138 | END DO |
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| 139 | |
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| 140 | !---------------! |
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| 141 | !== advection ==! |
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| 142 | !---------------! |
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| 143 | DO jt = 1, icycle |
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| 144 | |
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| 145 | ! record at_i before advection (for open water) |
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| 146 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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| 147 | |
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| 148 | ! inverse of A and Ap |
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| 149 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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| 150 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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| 151 | END WHERE |
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| 152 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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| 153 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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| 154 | END WHERE |
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| 155 | ! |
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| 156 | ! set u*a=u for advection of A only |
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| 157 | DO jl = 1, jpl |
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| 158 | zua_ho(:,:,jl) = zudy(:,:) |
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| 159 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 160 | END DO |
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| 161 | |
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| 162 | zamsk = 1._wp |
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| 163 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, pa_i, pa_i, zua_ho, zva_ho ) !-- Ice area |
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| 164 | zamsk = 0._wp |
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| 165 | ! |
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| 166 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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| 167 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pv_i ) !-- Ice volume |
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| 168 | ! |
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| 169 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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| 170 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pv_s ) !-- Snw volume |
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| 171 | ! |
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| 172 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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| 173 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, psv_i ) !-- Salt content |
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| 174 | ! |
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| 175 | DO jk = 1, nlay_i |
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| 176 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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| 177 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pe_i(:,:,jk,:) ) !-- Ice heat content |
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| 178 | END DO |
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| 179 | ! |
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| 180 | DO jk = 1, nlay_s |
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| 181 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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| 182 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pe_s(:,:,jk,:) ) !-- Snw heat content |
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| 183 | END DO |
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| 184 | ! |
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| 185 | IF( iom_use('iceage') .OR. iom_use('iceage_cat') ) THEN !-- Ice Age |
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| 186 | ! clem: in theory we should use the formulation below to advect the ice age, but the code is unable to deal with |
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| 187 | ! fields that do not depend on volume (here oa_i depends on concentration). It creates abnormal ages that |
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| 188 | ! spread into the domain. Therefore we cheat and consider that ice age should be advected as ice concentration |
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| 189 | !!zhvar(:,:,:) = poa_i(:,:,:) * z1_ai(:,:,:) |
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| 190 | !!CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, poa_i ) |
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| 191 | ! set u*a=u for advection of ice age |
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| 192 | DO jl = 1, jpl |
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| 193 | zua_ho(:,:,jl) = zudy(:,:) |
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| 194 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 195 | END DO |
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| 196 | zamsk = 1._wp |
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| 197 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, poa_i, poa_i ) |
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| 198 | zamsk = 0._wp |
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| 199 | ENDIF |
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| 200 | ! |
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| 201 | IF ( ln_pnd_H12 ) THEN !-- melt ponds |
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| 202 | ! set u*a=u for advection of Ap only |
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| 203 | DO jl = 1, jpl |
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| 204 | zua_ho(:,:,jl) = zudy(:,:) |
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| 205 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 206 | END DO |
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| 207 | ! |
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| 208 | zamsk = 1._wp |
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| 209 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, pa_ip, pa_ip, zua_ho, zva_ho ) ! fraction |
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| 210 | zamsk = 0._wp |
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| 211 | ! |
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| 212 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
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| 213 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pv_ip ) ! volume |
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| 214 | ENDIF |
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| 215 | ! |
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| 216 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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| 217 | DO jj = 2, jpjm1 |
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| 218 | DO ji = fs_2, fs_jpim1 |
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| 219 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & !-- Open water area |
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| 220 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
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| 221 | END DO |
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| 222 | END DO |
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| 223 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i(:,:), 'T', 1. ) |
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| 224 | ! |
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| 225 | END DO |
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| 226 | ! |
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| 227 | END SUBROUTINE ice_dyn_adv_umx |
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| 228 | |
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| 229 | |
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| 230 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, pt, ptc, pua_ho, pva_ho ) |
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| 231 | !!---------------------------------------------------------------------- |
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| 232 | !! *** ROUTINE adv_umx *** |
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| 233 | !! |
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| 234 | !! ** Purpose : Compute the now trend due to total advection of |
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| 235 | !! tracers and add it to the general trend of tracer equations |
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| 236 | !! |
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| 237 | !! ** Method : - calculate upstream fluxes and upstream solution for tracer H |
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| 238 | !! - calculate tracer H at u and v points (Ultimate) |
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| 239 | !! - calculate the high order fluxes using alterning directions (Macho?) |
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| 240 | !! - apply a limiter on the fluxes (nonosc_ice) |
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| 241 | !! - convert this tracer flux to a tracer content flux (uH -> uV) |
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| 242 | !! - calculate the high order solution for tracer content V |
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| 243 | !! |
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| 244 | !! ** Action : solve 2 equations => a) da/dt = -div(ua) |
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| 245 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
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| 246 | !! in eq. b), - fluxes uH are evaluated (with UMx) and limited (with nonosc_ice). This step is necessary to get a good H. |
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| 247 | !! - then we convert this flux to a "volume" flux this way => uH*ua/u |
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| 248 | !! where ua is the flux from eq. a) |
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| 249 | !! - at last we estimate dV/dt = -div(uH*ua/u) |
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| 250 | !! |
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| 251 | !! ** Note : - this method can lead to small negative V (since we only limit H) => corrected in icedyn_adv.F90 conserving mass etc. |
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| 252 | !! - negative tracers at u-v points can also occur from the Ultimate scheme (usually at the ice edge) and the solution for now |
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| 253 | !! is to apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
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| 254 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
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| 255 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
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| 256 | !! Large values of H can appear for very small ice concentration, and when it does it messes the things up since we |
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| 257 | !! work on H (and not V). It probably comes from the prelimiter of zalesak which is coded for 1D and not 2D. |
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| 258 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
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| 259 | !! concentration is small). |
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| 260 | !! To-do: expand the prelimiter from zalesak to make it work in 2D |
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| 261 | !!---------------------------------------------------------------------- |
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| 262 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
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| 263 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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| 264 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
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| 265 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 266 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 267 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
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| 268 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
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| 269 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
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| 270 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
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| 271 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
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| 272 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
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| 273 | ! |
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| 274 | INTEGER :: ji, jj, jl ! dummy loop indices |
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| 275 | REAL(wp) :: ztra ! local scalar |
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| 276 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
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| 277 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
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| 278 | !!---------------------------------------------------------------------- |
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| 279 | ! |
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| 280 | ! Upstream (_ups) fluxes |
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| 281 | ! ----------------------- |
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| 282 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
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| 283 | |
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| 284 | ! High order (_ho) fluxes |
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| 285 | ! ----------------------- |
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| 286 | SELECT CASE( kn_umx ) |
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| 287 | ! |
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| 288 | CASE ( 20 ) !== centered second order ==! |
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| 289 | ! |
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| 290 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
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| 291 | ! |
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| 292 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
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| 293 | ! |
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| 294 | CALL macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
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| 295 | ! |
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| 296 | END SELECT |
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| 297 | ! |
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| 298 | ! --ho --ho |
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| 299 | ! new fluxes = u*H * u*a / u |
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| 300 | ! ---------------------------- |
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| 301 | IF( pamsk == 0._wp ) THEN |
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| 302 | DO jl = 1, jpl |
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| 303 | DO jj = 1, jpjm1 |
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| 304 | DO ji = 1, fs_jpim1 |
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| 305 | IF( ABS( puc(ji,jj,jl) ) > 0._wp .AND. ABS( pu(ji,jj) ) > 0._wp ) THEN |
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| 306 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc(ji,jj,jl) / pu(ji,jj) |
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| 307 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * puc(ji,jj,jl) / pu(ji,jj) |
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| 308 | ELSE |
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| 309 | zfu_ho (ji,jj,jl) = 0._wp |
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| 310 | zfu_ups(ji,jj,jl) = 0._wp |
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| 311 | ENDIF |
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| 312 | ! |
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| 313 | IF( ABS( pvc(ji,jj,jl) ) > 0._wp .AND. ABS( pv(ji,jj) ) > 0._wp ) THEN |
|---|
| 314 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc(ji,jj,jl) / pv(ji,jj) |
|---|
| 315 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pvc(ji,jj,jl) / pv(ji,jj) |
|---|
| 316 | ELSE |
|---|
| 317 | zfv_ho (ji,jj,jl) = 0._wp |
|---|
| 318 | zfv_ups(ji,jj,jl) = 0._wp |
|---|
| 319 | ENDIF |
|---|
| 320 | END DO |
|---|
| 321 | END DO |
|---|
| 322 | END DO |
|---|
| 323 | ENDIF |
|---|
| 324 | ! --ho |
|---|
| 325 | ! in case of advection of A: output u*a |
|---|
| 326 | ! ------------------------------------- |
|---|
| 327 | IF( PRESENT( pua_ho ) ) THEN |
|---|
| 328 | DO jl = 1, jpl |
|---|
| 329 | DO jj = 1, jpjm1 |
|---|
| 330 | DO ji = 1, fs_jpim1 |
|---|
| 331 | pua_ho(ji,jj,jl) = zfu_ho(ji,jj,jl) |
|---|
| 332 | pva_ho(ji,jj,jl) = zfv_ho(ji,jj,jl) |
|---|
| 333 | END DO |
|---|
| 334 | END DO |
|---|
| 335 | END DO |
|---|
| 336 | ENDIF |
|---|
| 337 | ! |
|---|
| 338 | ! final trend with corrected fluxes |
|---|
| 339 | ! --------------------------------- |
|---|
| 340 | DO jl = 1, jpl |
|---|
| 341 | DO jj = 2, jpjm1 |
|---|
| 342 | DO ji = fs_2, fs_jpim1 |
|---|
| 343 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
|---|
| 344 | ! |
|---|
| 345 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
|---|
| 346 | END DO |
|---|
| 347 | END DO |
|---|
| 348 | END DO |
|---|
| 349 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. ) |
|---|
| 350 | ! |
|---|
| 351 | END SUBROUTINE adv_umx |
|---|
| 352 | |
|---|
| 353 | |
|---|
| 354 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
|---|
| 355 | !!--------------------------------------------------------------------- |
|---|
| 356 | !! *** ROUTINE upstream *** |
|---|
| 357 | !! |
|---|
| 358 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
|---|
| 359 | !!---------------------------------------------------------------------- |
|---|
| 360 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
|---|
| 361 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
|---|
| 362 | INTEGER , INTENT(in ) :: kt ! number of iteration |
|---|
| 363 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 364 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
|---|
| 365 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
|---|
| 366 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
|---|
| 367 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
|---|
| 368 | ! |
|---|
| 369 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 370 | REAL(wp) :: ztra ! local scalar |
|---|
| 371 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
|---|
| 372 | !!---------------------------------------------------------------------- |
|---|
| 373 | |
|---|
| 374 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
|---|
| 375 | ! |
|---|
| 376 | DO jl = 1, jpl |
|---|
| 377 | DO jj = 1, jpjm1 |
|---|
| 378 | DO ji = 1, fs_jpim1 |
|---|
| 379 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
|---|
| 380 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
|---|
| 381 | END DO |
|---|
| 382 | END DO |
|---|
| 383 | END DO |
|---|
| 384 | ! |
|---|
| 385 | ELSE !** alternate directions **! |
|---|
| 386 | ! |
|---|
| 387 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
|---|
| 388 | ! |
|---|
| 389 | DO jl = 1, jpl !-- flux in x-direction |
|---|
| 390 | DO jj = 1, jpjm1 |
|---|
| 391 | DO ji = 1, fs_jpim1 |
|---|
| 392 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * pt(ji+1,jj,jl) |
|---|
| 393 | END DO |
|---|
| 394 | END DO |
|---|
| 395 | END DO |
|---|
| 396 | ! |
|---|
| 397 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
|---|
| 398 | DO jj = 2, jpjm1 |
|---|
| 399 | DO ji = fs_2, fs_jpim1 |
|---|
| 400 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
|---|
| 401 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
|---|
| 402 | ! |
|---|
| 403 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 404 | END DO |
|---|
| 405 | END DO |
|---|
| 406 | END DO |
|---|
| 407 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 408 | ! |
|---|
| 409 | DO jl = 1, jpl !-- flux in y-direction |
|---|
| 410 | DO jj = 1, jpjm1 |
|---|
| 411 | DO ji = 1, fs_jpim1 |
|---|
| 412 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * zpt(ji,jj+1,jl) |
|---|
| 413 | END DO |
|---|
| 414 | END DO |
|---|
| 415 | END DO |
|---|
| 416 | ! |
|---|
| 417 | ELSE !== even ice time step: adv_y then adv_x ==! |
|---|
| 418 | ! |
|---|
| 419 | DO jl = 1, jpl !-- flux in y-direction |
|---|
| 420 | DO jj = 1, jpjm1 |
|---|
| 421 | DO ji = 1, fs_jpim1 |
|---|
| 422 | pfv_ups(ji,jj,jl) = MAX( pv(ji,jj), 0._wp ) * pt(ji,jj,jl) + MIN( pv(ji,jj), 0._wp ) * pt(ji,jj+1,jl) |
|---|
| 423 | END DO |
|---|
| 424 | END DO |
|---|
| 425 | END DO |
|---|
| 426 | ! |
|---|
| 427 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
|---|
| 428 | DO jj = 2, jpjm1 |
|---|
| 429 | DO ji = fs_2, fs_jpim1 |
|---|
| 430 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
|---|
| 431 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
|---|
| 432 | ! |
|---|
| 433 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 434 | END DO |
|---|
| 435 | END DO |
|---|
| 436 | END DO |
|---|
| 437 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 438 | ! |
|---|
| 439 | DO jl = 1, jpl !-- flux in x-direction |
|---|
| 440 | DO jj = 1, jpjm1 |
|---|
| 441 | DO ji = 1, fs_jpim1 |
|---|
| 442 | pfu_ups(ji,jj,jl) = MAX( pu(ji,jj), 0._wp ) * zpt(ji,jj,jl) + MIN( pu(ji,jj), 0._wp ) * zpt(ji+1,jj,jl) |
|---|
| 443 | END DO |
|---|
| 444 | END DO |
|---|
| 445 | END DO |
|---|
| 446 | ! |
|---|
| 447 | ENDIF |
|---|
| 448 | |
|---|
| 449 | ENDIF |
|---|
| 450 | ! |
|---|
| 451 | DO jl = 1, jpl !-- after tracer with upstream scheme |
|---|
| 452 | DO jj = 2, jpjm1 |
|---|
| 453 | DO ji = fs_2, fs_jpim1 |
|---|
| 454 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
|---|
| 455 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
|---|
| 456 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
|---|
| 457 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
|---|
| 458 | ! |
|---|
| 459 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 460 | END DO |
|---|
| 461 | END DO |
|---|
| 462 | END DO |
|---|
| 463 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. ) |
|---|
| 464 | |
|---|
| 465 | END SUBROUTINE upstream |
|---|
| 466 | |
|---|
| 467 | |
|---|
| 468 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 469 | !!--------------------------------------------------------------------- |
|---|
| 470 | !! *** ROUTINE cen2 *** |
|---|
| 471 | !! |
|---|
| 472 | !! ** Purpose : compute the high order fluxes using a centered |
|---|
| 473 | !! second order scheme |
|---|
| 474 | !!---------------------------------------------------------------------- |
|---|
| 475 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
|---|
| 476 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
|---|
| 477 | INTEGER , INTENT(in ) :: kt ! number of iteration |
|---|
| 478 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 479 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
|---|
| 480 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
|---|
| 481 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
|---|
| 482 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
|---|
| 483 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
|---|
| 484 | ! |
|---|
| 485 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 486 | REAL(wp) :: ztra ! local scalar |
|---|
| 487 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
|---|
| 488 | !!---------------------------------------------------------------------- |
|---|
| 489 | ! |
|---|
| 490 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
|---|
| 491 | ! |
|---|
| 492 | DO jl = 1, jpl |
|---|
| 493 | DO jj = 1, jpjm1 |
|---|
| 494 | DO ji = 1, fs_jpim1 |
|---|
| 495 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
|---|
| 496 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
|---|
| 497 | END DO |
|---|
| 498 | END DO |
|---|
| 499 | END DO |
|---|
| 500 | ! |
|---|
| 501 | IF ( kn_limiter == 1 ) THEN |
|---|
| 502 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 503 | ELSEIF( kn_limiter == 2 .OR. kn_limiter == 3 ) THEN |
|---|
| 504 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 505 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 506 | ENDIF |
|---|
| 507 | ! |
|---|
| 508 | ELSE !** alternate directions **! |
|---|
| 509 | ! |
|---|
| 510 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
|---|
| 511 | ! |
|---|
| 512 | DO jl = 1, jpl !-- flux in x-direction |
|---|
| 513 | DO jj = 1, jpjm1 |
|---|
| 514 | DO ji = 1, fs_jpim1 |
|---|
| 515 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
|---|
| 516 | END DO |
|---|
| 517 | END DO |
|---|
| 518 | END DO |
|---|
| 519 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 520 | |
|---|
| 521 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
|---|
| 522 | DO jj = 2, jpjm1 |
|---|
| 523 | DO ji = fs_2, fs_jpim1 |
|---|
| 524 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
|---|
| 525 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
|---|
| 526 | ! |
|---|
| 527 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 528 | END DO |
|---|
| 529 | END DO |
|---|
| 530 | END DO |
|---|
| 531 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 532 | |
|---|
| 533 | DO jl = 1, jpl !-- flux in y-direction |
|---|
| 534 | DO jj = 1, jpjm1 |
|---|
| 535 | DO ji = 1, fs_jpim1 |
|---|
| 536 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
|---|
| 537 | END DO |
|---|
| 538 | END DO |
|---|
| 539 | END DO |
|---|
| 540 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 541 | |
|---|
| 542 | ELSE !== even ice time step: adv_y then adv_x ==! |
|---|
| 543 | ! |
|---|
| 544 | DO jl = 1, jpl !-- flux in y-direction |
|---|
| 545 | DO jj = 1, jpjm1 |
|---|
| 546 | DO ji = 1, fs_jpim1 |
|---|
| 547 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
|---|
| 548 | END DO |
|---|
| 549 | END DO |
|---|
| 550 | END DO |
|---|
| 551 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 552 | ! |
|---|
| 553 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
|---|
| 554 | DO jj = 2, jpjm1 |
|---|
| 555 | DO ji = fs_2, fs_jpim1 |
|---|
| 556 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
|---|
| 557 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
|---|
| 558 | ! |
|---|
| 559 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
|---|
| 560 | END DO |
|---|
| 561 | END DO |
|---|
| 562 | END DO |
|---|
| 563 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 564 | ! |
|---|
| 565 | DO jl = 1, jpl !-- flux in x-direction |
|---|
| 566 | DO jj = 1, jpjm1 |
|---|
| 567 | DO ji = 1, fs_jpim1 |
|---|
| 568 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
|---|
| 569 | END DO |
|---|
| 570 | END DO |
|---|
| 571 | END DO |
|---|
| 572 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 573 | |
|---|
| 574 | ENDIF |
|---|
| 575 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 576 | |
|---|
| 577 | ENDIF |
|---|
| 578 | |
|---|
| 579 | END SUBROUTINE cen2 |
|---|
| 580 | |
|---|
| 581 | |
|---|
| 582 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 583 | !!--------------------------------------------------------------------- |
|---|
| 584 | !! *** ROUTINE macho *** |
|---|
| 585 | !! |
|---|
| 586 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
|---|
| 587 | !! |
|---|
| 588 | !! ** Method : ... |
|---|
| 589 | !! |
|---|
| 590 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
|---|
| 591 | !!---------------------------------------------------------------------- |
|---|
| 592 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
|---|
| 593 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
|---|
| 594 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
|---|
| 595 | INTEGER , INTENT(in ) :: kt ! number of iteration |
|---|
| 596 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 597 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
|---|
| 598 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
|---|
| 599 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
|---|
| 600 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
|---|
| 601 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
|---|
| 602 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
|---|
| 603 | ! |
|---|
| 604 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 605 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
|---|
| 606 | !!---------------------------------------------------------------------- |
|---|
| 607 | ! |
|---|
| 608 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
|---|
| 609 | ! |
|---|
| 610 | ! !-- ultimate interpolation of pt at u-point --! |
|---|
| 611 | CALL ultimate_x( kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
|---|
| 612 | ! !-- limiter in x --! |
|---|
| 613 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 614 | ! !-- advective form update in zpt --! |
|---|
| 615 | DO jl = 1, jpl |
|---|
| 616 | DO jj = 2, jpjm1 |
|---|
| 617 | DO ji = fs_2, fs_jpim1 |
|---|
| 618 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pubox(ji,jj ) * ( zt_u(ji,jj,jl) - zt_u(ji-1,jj,jl) ) * r1_e1t (ji,jj) & |
|---|
| 619 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
|---|
| 620 | & * pamsk & |
|---|
| 621 | & ) * pdt ) * tmask(ji,jj,1) |
|---|
| 622 | END DO |
|---|
| 623 | END DO |
|---|
| 624 | END DO |
|---|
| 625 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 626 | ! |
|---|
| 627 | ! !-- ultimate interpolation of pt at v-point --! |
|---|
| 628 | IF( ll_hoxy ) THEN |
|---|
| 629 | CALL ultimate_y( kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
|---|
| 630 | ELSE |
|---|
| 631 | CALL ultimate_y( kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
|---|
| 632 | ENDIF |
|---|
| 633 | ! !-- limiter in y --! |
|---|
| 634 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 635 | ! |
|---|
| 636 | ! |
|---|
| 637 | ELSE !== even ice time step: adv_y then adv_x ==! |
|---|
| 638 | ! |
|---|
| 639 | ! !-- ultimate interpolation of pt at v-point --! |
|---|
| 640 | CALL ultimate_y( kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
|---|
| 641 | ! !-- limiter in y --! |
|---|
| 642 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 643 | ! !-- advective form update in zpt --! |
|---|
| 644 | DO jl = 1, jpl |
|---|
| 645 | DO jj = 2, jpjm1 |
|---|
| 646 | DO ji = fs_2, fs_jpim1 |
|---|
| 647 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) - ( pvbox(ji,jj ) * ( zt_v(ji,jj,jl) - zt_v(ji,jj-1,jl) ) * r1_e2t (ji,jj) & |
|---|
| 648 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
|---|
| 649 | & * pamsk & |
|---|
| 650 | & ) * pdt ) * tmask(ji,jj,1) |
|---|
| 651 | END DO |
|---|
| 652 | END DO |
|---|
| 653 | END DO |
|---|
| 654 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
|---|
| 655 | ! |
|---|
| 656 | ! !-- ultimate interpolation of pt at u-point --! |
|---|
| 657 | IF( ll_hoxy ) THEN |
|---|
| 658 | CALL ultimate_x( kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
|---|
| 659 | ELSE |
|---|
| 660 | CALL ultimate_x( kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
|---|
| 661 | ENDIF |
|---|
| 662 | ! !-- limiter in x --! |
|---|
| 663 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 664 | ! |
|---|
| 665 | ENDIF |
|---|
| 666 | |
|---|
| 667 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 668 | ! |
|---|
| 669 | END SUBROUTINE macho |
|---|
| 670 | |
|---|
| 671 | |
|---|
| 672 | SUBROUTINE ultimate_x( kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
|---|
| 673 | !!--------------------------------------------------------------------- |
|---|
| 674 | !! *** ROUTINE ultimate_x *** |
|---|
| 675 | !! |
|---|
| 676 | !! ** Purpose : compute tracer at u-points |
|---|
| 677 | !! |
|---|
| 678 | !! ** Method : ... |
|---|
| 679 | !! |
|---|
| 680 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
|---|
| 681 | !!---------------------------------------------------------------------- |
|---|
| 682 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
|---|
| 683 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 684 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
|---|
| 685 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
|---|
| 686 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
|---|
| 687 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
|---|
| 688 | ! |
|---|
| 689 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 690 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
|---|
| 691 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
|---|
| 692 | !!---------------------------------------------------------------------- |
|---|
| 693 | ! |
|---|
| 694 | ! !-- Laplacian in i-direction --! |
|---|
| 695 | DO jl = 1, jpl |
|---|
| 696 | DO jj = 2, jpjm1 ! First derivative (gradient) |
|---|
| 697 | DO ji = 1, fs_jpim1 |
|---|
| 698 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
|---|
| 699 | END DO |
|---|
| 700 | ! ! Second derivative (Laplacian) |
|---|
| 701 | DO ji = fs_2, fs_jpim1 |
|---|
| 702 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
|---|
| 703 | END DO |
|---|
| 704 | END DO |
|---|
| 705 | END DO |
|---|
| 706 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. ) |
|---|
| 707 | ! |
|---|
| 708 | ! !-- BiLaplacian in i-direction --! |
|---|
| 709 | DO jl = 1, jpl |
|---|
| 710 | DO jj = 2, jpjm1 ! Third derivative |
|---|
| 711 | DO ji = 1, fs_jpim1 |
|---|
| 712 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
|---|
| 713 | END DO |
|---|
| 714 | ! ! Fourth derivative |
|---|
| 715 | DO ji = fs_2, fs_jpim1 |
|---|
| 716 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
|---|
| 717 | END DO |
|---|
| 718 | END DO |
|---|
| 719 | END DO |
|---|
| 720 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. ) |
|---|
| 721 | ! |
|---|
| 722 | ! |
|---|
| 723 | SELECT CASE (kn_umx ) |
|---|
| 724 | ! |
|---|
| 725 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
|---|
| 726 | ! |
|---|
| 727 | DO jl = 1, jpl |
|---|
| 728 | DO jj = 1, jpjm1 |
|---|
| 729 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 730 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
|---|
| 731 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
|---|
| 732 | END DO |
|---|
| 733 | END DO |
|---|
| 734 | END DO |
|---|
| 735 | ! |
|---|
| 736 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
|---|
| 737 | ! |
|---|
| 738 | DO jl = 1, jpl |
|---|
| 739 | DO jj = 1, jpjm1 |
|---|
| 740 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 741 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
|---|
| 742 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
|---|
| 743 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
|---|
| 744 | END DO |
|---|
| 745 | END DO |
|---|
| 746 | END DO |
|---|
| 747 | ! |
|---|
| 748 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
|---|
| 749 | ! |
|---|
| 750 | DO jl = 1, jpl |
|---|
| 751 | DO jj = 1, jpjm1 |
|---|
| 752 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 753 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
|---|
| 754 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
|---|
| 755 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
|---|
| 756 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
|---|
| 757 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 758 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
|---|
| 759 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
|---|
| 760 | END DO |
|---|
| 761 | END DO |
|---|
| 762 | END DO |
|---|
| 763 | ! |
|---|
| 764 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
|---|
| 765 | ! |
|---|
| 766 | DO jl = 1, jpl |
|---|
| 767 | DO jj = 1, jpjm1 |
|---|
| 768 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 769 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
|---|
| 770 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
|---|
| 771 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
|---|
| 772 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
|---|
| 773 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 774 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
|---|
| 775 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
|---|
| 776 | END DO |
|---|
| 777 | END DO |
|---|
| 778 | END DO |
|---|
| 779 | ! |
|---|
| 780 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
|---|
| 781 | ! |
|---|
| 782 | DO jl = 1, jpl |
|---|
| 783 | DO jj = 1, jpjm1 |
|---|
| 784 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 785 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
|---|
| 786 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
|---|
| 787 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
|---|
| 788 | zdx4 = zdx2 * zdx2 |
|---|
| 789 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
|---|
| 790 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 791 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
|---|
| 792 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
|---|
| 793 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
|---|
| 794 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
|---|
| 795 | END DO |
|---|
| 796 | END DO |
|---|
| 797 | END DO |
|---|
| 798 | ! |
|---|
| 799 | END SELECT |
|---|
| 800 | ! |
|---|
| 801 | ! if pt at u-point is negative then use the upstream value |
|---|
| 802 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
|---|
| 803 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
|---|
| 804 | IF( ll_neg ) THEN |
|---|
| 805 | DO jl = 1, jpl |
|---|
| 806 | DO jj = 1, jpjm1 |
|---|
| 807 | DO ji = 1, fs_jpim1 |
|---|
| 808 | IF( pt_u(ji,jj,jl) < 0._wp ) THEN |
|---|
| 809 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
|---|
| 810 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
|---|
| 811 | ENDIF |
|---|
| 812 | END DO |
|---|
| 813 | END DO |
|---|
| 814 | END DO |
|---|
| 815 | ENDIF |
|---|
| 816 | ! !-- High order flux in i-direction --! |
|---|
| 817 | DO jl = 1, jpl |
|---|
| 818 | DO jj = 1, jpjm1 |
|---|
| 819 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 820 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
|---|
| 821 | END DO |
|---|
| 822 | END DO |
|---|
| 823 | END DO |
|---|
| 824 | ! |
|---|
| 825 | END SUBROUTINE ultimate_x |
|---|
| 826 | |
|---|
| 827 | |
|---|
| 828 | SUBROUTINE ultimate_y( kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
|---|
| 829 | !!--------------------------------------------------------------------- |
|---|
| 830 | !! *** ROUTINE ultimate_y *** |
|---|
| 831 | !! |
|---|
| 832 | !! ** Purpose : compute tracer at v-points |
|---|
| 833 | !! |
|---|
| 834 | !! ** Method : ... |
|---|
| 835 | !! |
|---|
| 836 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
|---|
| 837 | !!---------------------------------------------------------------------- |
|---|
| 838 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
|---|
| 839 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 840 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
|---|
| 841 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
|---|
| 842 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
|---|
| 843 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
|---|
| 844 | ! |
|---|
| 845 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 846 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
|---|
| 847 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
|---|
| 848 | !!---------------------------------------------------------------------- |
|---|
| 849 | ! |
|---|
| 850 | ! !-- Laplacian in j-direction --! |
|---|
| 851 | DO jl = 1, jpl |
|---|
| 852 | DO jj = 1, jpjm1 ! First derivative (gradient) |
|---|
| 853 | DO ji = fs_2, fs_jpim1 |
|---|
| 854 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 855 | END DO |
|---|
| 856 | END DO |
|---|
| 857 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
|---|
| 858 | DO ji = fs_2, fs_jpim1 |
|---|
| 859 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
|---|
| 860 | END DO |
|---|
| 861 | END DO |
|---|
| 862 | END DO |
|---|
| 863 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. ) |
|---|
| 864 | ! |
|---|
| 865 | ! !-- BiLaplacian in j-direction --! |
|---|
| 866 | DO jl = 1, jpl |
|---|
| 867 | DO jj = 1, jpjm1 ! First derivative |
|---|
| 868 | DO ji = fs_2, fs_jpim1 |
|---|
| 869 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
|---|
| 870 | END DO |
|---|
| 871 | END DO |
|---|
| 872 | DO jj = 2, jpjm1 ! Second derivative |
|---|
| 873 | DO ji = fs_2, fs_jpim1 |
|---|
| 874 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
|---|
| 875 | END DO |
|---|
| 876 | END DO |
|---|
| 877 | END DO |
|---|
| 878 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. ) |
|---|
| 879 | ! |
|---|
| 880 | ! |
|---|
| 881 | SELECT CASE (kn_umx ) |
|---|
| 882 | ! |
|---|
| 883 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
|---|
| 884 | DO jl = 1, jpl |
|---|
| 885 | DO jj = 1, jpjm1 |
|---|
| 886 | DO ji = 1, fs_jpim1 |
|---|
| 887 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
|---|
| 888 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
|---|
| 889 | END DO |
|---|
| 890 | END DO |
|---|
| 891 | END DO |
|---|
| 892 | ! |
|---|
| 893 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
|---|
| 894 | DO jl = 1, jpl |
|---|
| 895 | DO jj = 1, jpjm1 |
|---|
| 896 | DO ji = 1, fs_jpim1 |
|---|
| 897 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
|---|
| 898 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
|---|
| 899 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
|---|
| 900 | END DO |
|---|
| 901 | END DO |
|---|
| 902 | END DO |
|---|
| 903 | ! |
|---|
| 904 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
|---|
| 905 | DO jl = 1, jpl |
|---|
| 906 | DO jj = 1, jpjm1 |
|---|
| 907 | DO ji = 1, fs_jpim1 |
|---|
| 908 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
|---|
| 909 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
|---|
| 910 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
|---|
| 911 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
|---|
| 912 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 913 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
|---|
| 914 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
|---|
| 915 | END DO |
|---|
| 916 | END DO |
|---|
| 917 | END DO |
|---|
| 918 | ! |
|---|
| 919 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
|---|
| 920 | DO jl = 1, jpl |
|---|
| 921 | DO jj = 1, jpjm1 |
|---|
| 922 | DO ji = 1, fs_jpim1 |
|---|
| 923 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
|---|
| 924 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
|---|
| 925 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
|---|
| 926 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
|---|
| 927 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 928 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
|---|
| 929 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
|---|
| 930 | END DO |
|---|
| 931 | END DO |
|---|
| 932 | END DO |
|---|
| 933 | ! |
|---|
| 934 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
|---|
| 935 | DO jl = 1, jpl |
|---|
| 936 | DO jj = 1, jpjm1 |
|---|
| 937 | DO ji = 1, fs_jpim1 |
|---|
| 938 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
|---|
| 939 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
|---|
| 940 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
|---|
| 941 | zdy4 = zdy2 * zdy2 |
|---|
| 942 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
|---|
| 943 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
|---|
| 944 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
|---|
| 945 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
|---|
| 946 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
|---|
| 947 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
|---|
| 948 | END DO |
|---|
| 949 | END DO |
|---|
| 950 | END DO |
|---|
| 951 | ! |
|---|
| 952 | END SELECT |
|---|
| 953 | ! |
|---|
| 954 | ! if pt at v-point is negative then use the upstream value |
|---|
| 955 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
|---|
| 956 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
|---|
| 957 | IF( ll_neg ) THEN |
|---|
| 958 | DO jl = 1, jpl |
|---|
| 959 | DO jj = 1, jpjm1 |
|---|
| 960 | DO ji = 1, fs_jpim1 |
|---|
| 961 | IF( pt_v(ji,jj,jl) < 0._wp ) THEN |
|---|
| 962 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
|---|
| 963 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
|---|
| 964 | ENDIF |
|---|
| 965 | END DO |
|---|
| 966 | END DO |
|---|
| 967 | END DO |
|---|
| 968 | ENDIF |
|---|
| 969 | ! !-- High order flux in j-direction --! |
|---|
| 970 | DO jl = 1, jpl |
|---|
| 971 | DO jj = 1, jpjm1 |
|---|
| 972 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 973 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
|---|
| 974 | END DO |
|---|
| 975 | END DO |
|---|
| 976 | END DO |
|---|
| 977 | ! |
|---|
| 978 | END SUBROUTINE ultimate_y |
|---|
| 979 | |
|---|
| 980 | |
|---|
| 981 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
|---|
| 982 | !!--------------------------------------------------------------------- |
|---|
| 983 | !! *** ROUTINE nonosc_ice *** |
|---|
| 984 | !! |
|---|
| 985 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
|---|
| 986 | !! scheme and the before field by a non-oscillatory algorithm |
|---|
| 987 | !! |
|---|
| 988 | !! ** Method : ... |
|---|
| 989 | !!---------------------------------------------------------------------- |
|---|
| 990 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
|---|
| 991 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 992 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
|---|
| 993 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
|---|
| 994 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
|---|
| 995 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
|---|
| 996 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
|---|
| 997 | ! |
|---|
| 998 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 999 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
|---|
| 1000 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
|---|
| 1001 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
|---|
| 1002 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
|---|
| 1003 | !!---------------------------------------------------------------------- |
|---|
| 1004 | zbig = 1.e+40_wp |
|---|
| 1005 | |
|---|
| 1006 | ! antidiffusive flux : high order minus low order |
|---|
| 1007 | ! -------------------------------------------------- |
|---|
| 1008 | DO jl = 1, jpl |
|---|
| 1009 | DO jj = 1, jpjm1 |
|---|
| 1010 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 1011 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
|---|
| 1012 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
|---|
| 1013 | END DO |
|---|
| 1014 | END DO |
|---|
| 1015 | END DO |
|---|
| 1016 | |
|---|
| 1017 | ! extreme case where pfu_ho has to be zero |
|---|
| 1018 | ! ---------------------------------------- |
|---|
| 1019 | ! pfu_ho |
|---|
| 1020 | ! * ---> |
|---|
| 1021 | ! | | * | | |
|---|
| 1022 | ! | | | * | |
|---|
| 1023 | ! | | | | * |
|---|
| 1024 | ! t_ups : i-1 i i+1 i+2 |
|---|
| 1025 | IF( ll_prelimiter_zalesak ) THEN |
|---|
| 1026 | |
|---|
| 1027 | DO jl = 1, jpl |
|---|
| 1028 | DO jj = 2, jpjm1 |
|---|
| 1029 | DO ji = fs_2, fs_jpim1 |
|---|
| 1030 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
|---|
| 1031 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
|---|
| 1032 | END DO |
|---|
| 1033 | END DO |
|---|
| 1034 | END DO |
|---|
| 1035 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. ) |
|---|
| 1036 | |
|---|
| 1037 | DO jl = 1, jpl |
|---|
| 1038 | DO jj = 2, jpjm1 |
|---|
| 1039 | DO ji = fs_2, fs_jpim1 |
|---|
| 1040 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
|---|
| 1041 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
|---|
| 1042 | ! |
|---|
| 1043 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
|---|
| 1044 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
|---|
| 1045 | pfu_ho(ji,jj,jl)=0._wp |
|---|
| 1046 | pfv_ho(ji,jj,jl)=0._wp |
|---|
| 1047 | ENDIF |
|---|
| 1048 | ! |
|---|
| 1049 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
|---|
| 1050 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
|---|
| 1051 | pfu_ho(ji,jj,jl)=0._wp |
|---|
| 1052 | pfv_ho(ji,jj,jl)=0._wp |
|---|
| 1053 | ENDIF |
|---|
| 1054 | ! |
|---|
| 1055 | ENDIF |
|---|
| 1056 | END DO |
|---|
| 1057 | END DO |
|---|
| 1058 | END DO |
|---|
| 1059 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
|---|
| 1060 | |
|---|
| 1061 | ENDIF |
|---|
| 1062 | |
|---|
| 1063 | ! Search local extrema |
|---|
| 1064 | ! -------------------- |
|---|
| 1065 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
|---|
| 1066 | z1_dt = 1._wp / pdt |
|---|
| 1067 | DO jl = 1, jpl |
|---|
| 1068 | |
|---|
| 1069 | DO jj = 1, jpj |
|---|
| 1070 | DO ji = 1, jpi |
|---|
| 1071 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
|---|
| 1072 | zbup(ji,jj) = -zbig |
|---|
| 1073 | zbdo(ji,jj) = zbig |
|---|
| 1074 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
|---|
| 1075 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
|---|
| 1076 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
|---|
| 1077 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
|---|
| 1078 | zbup(ji,jj) = pt(ji,jj,jl) |
|---|
| 1079 | zbdo(ji,jj) = pt(ji,jj,jl) |
|---|
| 1080 | ELSE |
|---|
| 1081 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
|---|
| 1082 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
|---|
| 1083 | ENDIF |
|---|
| 1084 | END DO |
|---|
| 1085 | END DO |
|---|
| 1086 | |
|---|
| 1087 | DO jj = 2, jpjm1 |
|---|
| 1088 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 1089 | ! |
|---|
| 1090 | zup = MAX( zbup(ji,jj), zbup(ji-1,jj), zbup(ji+1,jj), zbup(ji,jj-1), zbup(ji,jj+1) ) ! search max/min in neighbourhood |
|---|
| 1091 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
|---|
| 1092 | ! |
|---|
| 1093 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
|---|
| 1094 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
|---|
| 1095 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
|---|
| 1096 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
|---|
| 1097 | ! |
|---|
| 1098 | zpos = zpos - (pt(ji,jj,jl) * MIN( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MIN( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
|---|
| 1099 | & ) * ( 1. - pamsk ) |
|---|
| 1100 | zneg = zneg + (pt(ji,jj,jl) * MAX( 0., pu(ji,jj) - pu(ji-1,jj) ) + pt(ji,jj,jl) * MAX( 0., pv(ji,jj) - pv(ji,jj-1) ) & |
|---|
| 1101 | & ) * ( 1. - pamsk ) |
|---|
| 1102 | ! |
|---|
| 1103 | ! ! up & down beta terms |
|---|
| 1104 | IF( zpos > 0._wp ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
|---|
| 1105 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
|---|
| 1106 | ENDIF |
|---|
| 1107 | ! |
|---|
| 1108 | IF( zneg > 0._wp ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
|---|
| 1109 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
|---|
| 1110 | ENDIF |
|---|
| 1111 | ! |
|---|
| 1112 | ! if all the points are outside ice cover |
|---|
| 1113 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
|---|
| 1114 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
|---|
| 1115 | ! |
|---|
| 1116 | END DO |
|---|
| 1117 | END DO |
|---|
| 1118 | END DO |
|---|
| 1119 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
|---|
| 1120 | |
|---|
| 1121 | |
|---|
| 1122 | ! monotonic flux in the y direction |
|---|
| 1123 | ! --------------------------------- |
|---|
| 1124 | DO jl = 1, jpl |
|---|
| 1125 | DO jj = 1, jpjm1 |
|---|
| 1126 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 1127 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
|---|
| 1128 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
|---|
| 1129 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
|---|
| 1130 | ! |
|---|
| 1131 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
|---|
| 1132 | ! |
|---|
| 1133 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
|---|
| 1134 | ! |
|---|
| 1135 | END DO |
|---|
| 1136 | END DO |
|---|
| 1137 | |
|---|
| 1138 | DO jj = 1, jpjm1 |
|---|
| 1139 | DO ji = 1, fs_jpim1 ! vector opt. |
|---|
| 1140 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
|---|
| 1141 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
|---|
| 1142 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
|---|
| 1143 | ! |
|---|
| 1144 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
|---|
| 1145 | ! |
|---|
| 1146 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
|---|
| 1147 | ! |
|---|
| 1148 | END DO |
|---|
| 1149 | END DO |
|---|
| 1150 | |
|---|
| 1151 | ! clem test |
|---|
| 1152 | !! DO jj = 2, jpjm1 |
|---|
| 1153 | !! DO ji = 2, fs_jpim1 ! vector opt. |
|---|
| 1154 | !! zzt = ( pt(ji,jj,jl) - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) * pdt * r1_e1e2t(ji,jj) & |
|---|
| 1155 | !! & - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) * pdt * r1_e1e2t(ji,jj) & |
|---|
| 1156 | !! & + pt(ji,jj,jl) * pdt * ( pu(ji,jj) - pu(ji-1,jj) ) * r1_e1e2t(ji,jj) * (1.-pamsk) & |
|---|
| 1157 | !! & + pt(ji,jj,jl) * pdt * ( pv(ji,jj) - pv(ji,jj-1) ) * r1_e1e2t(ji,jj) * (1.-pamsk) & |
|---|
| 1158 | !! & ) * tmask(ji,jj,1) |
|---|
| 1159 | !! IF( zzt < -epsi20 ) THEN |
|---|
| 1160 | !! WRITE(numout,*) 'T<0 nonosc_ice',zzt |
|---|
| 1161 | !! ENDIF |
|---|
| 1162 | !! END DO |
|---|
| 1163 | !! END DO |
|---|
| 1164 | |
|---|
| 1165 | END DO |
|---|
| 1166 | ! |
|---|
| 1167 | END SUBROUTINE nonosc_ice |
|---|
| 1168 | |
|---|
| 1169 | |
|---|
| 1170 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
|---|
| 1171 | !!--------------------------------------------------------------------- |
|---|
| 1172 | !! *** ROUTINE limiter_x *** |
|---|
| 1173 | !! |
|---|
| 1174 | !! ** Purpose : compute flux limiter |
|---|
| 1175 | !!---------------------------------------------------------------------- |
|---|
| 1176 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 1177 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
|---|
| 1178 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
|---|
| 1179 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
|---|
| 1180 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
|---|
| 1181 | ! |
|---|
| 1182 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
|---|
| 1183 | INTEGER :: ji, jj, jl ! dummy loop indices |
|---|
| 1184 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
|---|
| 1185 | !!---------------------------------------------------------------------- |
|---|
| 1186 | ! |
|---|
| 1187 | DO jl = 1, jpl |
|---|
| 1188 | DO jj = 2, jpjm1 |
|---|
| 1189 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 1190 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
|---|
| 1191 | END DO |
|---|
| 1192 | END DO |
|---|
| 1193 | END DO |
|---|
| 1194 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond. |
|---|
| 1195 | |
|---|
| 1196 | DO jl = 1, jpl |
|---|
| 1197 | DO jj = 2, jpjm1 |
|---|
| 1198 | DO ji = fs_2, fs_jpim1 ! vector opt. |
|---|
| 1199 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
|---|
| 1200 | |
|---|
| 1201 | Rjm = zslpx(ji-1,jj,jl) |
|---|
| 1202 | Rj = zslpx(ji ,jj,jl) |
|---|
| 1203 | Rjp = zslpx(ji+1,jj,jl) |
|---|
| 1204 | |
|---|
| 1205 | IF( kn_limiter == 3 ) THEN |
|---|
| 1206 | |
|---|
| 1207 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
|---|
| 1208 | ELSE ; Rr = Rjp |
|---|
| 1209 | ENDIF |
|---|
| 1210 | |
|---|
| 1211 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
|---|
| 1212 | IF( Rj > 0. ) THEN |
|---|
| 1213 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
|---|
| 1214 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
|---|
| 1215 | ELSE |
|---|
| 1216 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
|---|
| 1217 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
|---|
| 1218 | ENDIF |
|---|
| 1219 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
|---|
| 1220 | |
|---|
| 1221 | ELSEIF( kn_limiter == 2 ) THEN |
|---|
| 1222 | IF( Rj /= 0. ) THEN |
|---|
| 1223 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
|---|
| 1224 | ELSE ; Cr = Rjp / Rj |
|---|
| 1225 | ENDIF |
|---|
| 1226 | ELSE |
|---|
| 1227 | Cr = 0. |
|---|
| 1228 | ENDIF |
|---|
| 1229 | |
|---|
| 1230 | ! -- superbee -- |
|---|
| 1231 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
|---|
| 1232 | ! -- van albada 2 -- |
|---|
| 1233 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
|---|
| 1234 | ! -- sweby (with beta=1) -- |
|---|
| 1235 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
|---|
| 1236 | ! -- van Leer -- |
|---|
| 1237 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
|---|
| 1238 | ! -- ospre -- |
|---|
| 1239 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
|---|
| 1240 | ! -- koren -- |
|---|
| 1241 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
|---|
| 1242 | ! -- charm -- |
|---|
| 1243 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
|---|
| 1244 | !ELSE ; zpsi = 0. |
|---|
| 1245 | !ENDIF |
|---|
| 1246 | ! -- van albada 1 -- |
|---|
| 1247 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
|---|
| 1248 | ! -- smart -- |
|---|
| 1249 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
|---|
| 1250 | ! -- umist -- |
|---|
| 1251 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
|---|
| 1252 | |
|---|
| 1253 | ! high order flux corrected by the limiter |
|---|
| 1254 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
|---|
| 1255 | |
|---|
| 1256 | ENDIF |
|---|
| 1257 | END DO |
|---|
| 1258 | END DO |
|---|
| 1259 | END DO |
|---|
| 1260 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond. |
|---|
| 1261 | ! |
|---|
| 1262 | END SUBROUTINE limiter_x |
|---|
| 1263 | |
|---|
| 1264 | |
|---|
| 1265 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
|---|
| 1266 | !!--------------------------------------------------------------------- |
|---|
| 1267 | !! *** ROUTINE limiter_y *** |
|---|
| 1268 | !! |
|---|
| 1269 | !! ** Purpose : compute flux limiter |
|---|
| 1270 | !!---------------------------------------------------------------------- |
|---|
| 1271 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
|---|
| 1272 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
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| 1273 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
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| 1274 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
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| 1275 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
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| 1276 | ! |
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| 1277 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
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| 1278 | INTEGER :: ji, jj, jl ! dummy loop indices |
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| 1279 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
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| 1280 | !!---------------------------------------------------------------------- |
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| 1281 | ! |
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| 1282 | DO jl = 1, jpl |
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| 1283 | DO jj = 2, jpjm1 |
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| 1284 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 1285 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
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| 1286 | END DO |
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| 1287 | END DO |
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| 1288 | END DO |
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| 1289 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond. |
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| 1290 | |
|---|
| 1291 | DO jl = 1, jpl |
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| 1292 | DO jj = 2, jpjm1 |
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| 1293 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 1294 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
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| 1295 | |
|---|
| 1296 | Rjm = zslpy(ji,jj-1,jl) |
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| 1297 | Rj = zslpy(ji,jj ,jl) |
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| 1298 | Rjp = zslpy(ji,jj+1,jl) |
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| 1299 | |
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| 1300 | IF( kn_limiter == 3 ) THEN |
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| 1301 | |
|---|
| 1302 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
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| 1303 | ELSE ; Rr = Rjp |
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| 1304 | ENDIF |
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| 1305 | |
|---|
| 1306 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
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| 1307 | IF( Rj > 0. ) THEN |
|---|
| 1308 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
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| 1309 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
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| 1310 | ELSE |
|---|
| 1311 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
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| 1312 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
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| 1313 | ENDIF |
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| 1314 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
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| 1315 | |
|---|
| 1316 | ELSEIF( kn_limiter == 2 ) THEN |
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| 1317 | |
|---|
| 1318 | IF( Rj /= 0. ) THEN |
|---|
| 1319 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
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| 1320 | ELSE ; Cr = Rjp / Rj |
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| 1321 | ENDIF |
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| 1322 | ELSE |
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| 1323 | Cr = 0. |
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| 1324 | ENDIF |
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| 1325 | |
|---|
| 1326 | ! -- superbee -- |
|---|
| 1327 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
|---|
| 1328 | ! -- van albada 2 -- |
|---|
| 1329 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
|---|
| 1330 | ! -- sweby (with beta=1) -- |
|---|
| 1331 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
|---|
| 1332 | ! -- van Leer -- |
|---|
| 1333 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
|---|
| 1334 | ! -- ospre -- |
|---|
| 1335 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
|---|
| 1336 | ! -- koren -- |
|---|
| 1337 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
|---|
| 1338 | ! -- charm -- |
|---|
| 1339 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
|---|
| 1340 | !ELSE ; zpsi = 0. |
|---|
| 1341 | !ENDIF |
|---|
| 1342 | ! -- van albada 1 -- |
|---|
| 1343 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
|---|
| 1344 | ! -- smart -- |
|---|
| 1345 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
|---|
| 1346 | ! -- umist -- |
|---|
| 1347 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
|---|
| 1348 | |
|---|
| 1349 | ! high order flux corrected by the limiter |
|---|
| 1350 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
|---|
| 1351 | |
|---|
| 1352 | ENDIF |
|---|
| 1353 | END DO |
|---|
| 1354 | END DO |
|---|
| 1355 | END DO |
|---|
| 1356 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond. |
|---|
| 1357 | ! |
|---|
| 1358 | END SUBROUTINE limiter_y |
|---|
| 1359 | |
|---|
| 1360 | #else |
|---|
| 1361 | !!---------------------------------------------------------------------- |
|---|
| 1362 | !! Default option Dummy module NO SI3 sea-ice model |
|---|
| 1363 | !!---------------------------------------------------------------------- |
|---|
| 1364 | #endif |
|---|
| 1365 | |
|---|
| 1366 | !!====================================================================== |
|---|
| 1367 | END MODULE icedyn_adv_umx |
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