[8586] | 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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[9604] | 7 | !! 4.0 ! 2018 (many people) SI3 [aka Sea Ice cube] |
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[8586] | 8 | !!---------------------------------------------------------------------- |
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[9570] | 9 | #if defined key_si3 |
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[8586] | 10 | !!---------------------------------------------------------------------- |
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[9570] | 11 | !! 'key_si3' SI3 sea-ice model |
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[8586] | 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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[10519] | 16 | !! nonosc_ice : compute monotonic tracer fluxes by a non-oscillatory algorithm |
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[8586] | 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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[10413] | 22 | USE icevar ! sea-ice: operations |
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[8586] | 23 | ! |
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| 24 | USE in_out_manager ! I/O manager |
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| 25 | USE lib_mpp ! MPP library |
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| 26 | USE lib_fortran ! fortran utilities (glob_sum + no signed zero) |
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| 27 | USE lbclnk ! lateral boundary conditions (or mpp links) |
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| 28 | |
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| 29 | IMPLICIT NONE |
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| 30 | PRIVATE |
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| 31 | |
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| 32 | PUBLIC ice_dyn_adv_umx ! called by icedyn_adv.F90 |
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| 33 | |
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| 34 | REAL(wp) :: z1_6 = 1._wp / 6._wp ! =1/6 |
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| 35 | REAL(wp) :: z1_120 = 1._wp / 120._wp ! =1/120 |
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[10413] | 36 | |
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[10519] | 37 | ! limiter: 1=nonosc_ice, 2=superbee, 3=h3(rachid) |
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[10446] | 38 | INTEGER :: kn_limiter = 1 |
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| 39 | |
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[10413] | 40 | ! if T interpolated at u/v points is negative, then interpolate T at u/v points using the upstream scheme |
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[10512] | 41 | ! clem: if set to true, the 2D test case "diagonal advection" does not work (I do not understand why) |
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| 42 | LOGICAL :: ll_neg = .FALSE. |
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[10413] | 43 | |
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| 44 | ! alternate directions for upstream |
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[10446] | 45 | LOGICAL :: ll_upsxy = .TRUE. |
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[10413] | 46 | |
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| 47 | ! alternate directions for high order |
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[10446] | 48 | LOGICAL :: ll_hoxy = .TRUE. |
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[10413] | 49 | |
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| 50 | ! prelimiter: use it to avoid overshoot in H |
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[10512] | 51 | ! clem: if set to true, the 2D test case "diagnoal advection" does not work (I do not understand why) |
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| 52 | LOGICAL :: ll_prelimiter_zalesak = .FALSE. ! from: Zalesak(1979) eq. 14 => better for 1D. Not well defined in 2D |
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[10413] | 53 | |
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| 54 | |
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[8586] | 55 | !! * Substitutions |
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| 56 | # include "vectopt_loop_substitute.h90" |
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| 57 | !!---------------------------------------------------------------------- |
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[9598] | 58 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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[10069] | 59 | !! $Id$ |
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[10413] | 60 | !! Software governed by the CeCILL licence (./LICENSE) |
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[8586] | 61 | !!---------------------------------------------------------------------- |
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| 62 | CONTAINS |
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| 63 | |
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[10413] | 64 | SUBROUTINE ice_dyn_adv_umx( kn_umx, kt, pu_ice, pv_ice, & |
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| 65 | & pato_i, pv_i, pv_s, psv_i, poa_i, pa_i, pa_ip, pv_ip, pe_s, pe_i ) |
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[8586] | 66 | !!---------------------------------------------------------------------- |
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| 67 | !! *** ROUTINE ice_dyn_adv_umx *** |
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| 68 | !! |
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| 69 | !! ** Purpose : Compute the now trend due to total advection of |
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| 70 | !! tracers and add it to the general trend of tracer equations |
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| 71 | !! using an "Ultimate-Macho" scheme |
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| 72 | !! |
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| 73 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
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| 74 | !!---------------------------------------------------------------------- |
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[10413] | 75 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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[8586] | 76 | INTEGER , INTENT(in ) :: kt ! time step |
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| 77 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pu_ice ! ice i-velocity |
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| 78 | REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pv_ice ! ice j-velocity |
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| 79 | REAL(wp), DIMENSION(:,:) , INTENT(inout) :: pato_i ! open water area |
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| 80 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_i ! ice volume |
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| 81 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_s ! snw volume |
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| 82 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: psv_i ! salt content |
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| 83 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: poa_i ! age content |
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| 84 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_i ! ice concentration |
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| 85 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pa_ip ! melt pond fraction |
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| 86 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pv_ip ! melt pond volume |
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| 87 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_s ! snw heat content |
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| 88 | REAL(wp), DIMENSION(:,:,:,:), INTENT(inout) :: pe_i ! ice heat content |
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| 89 | ! |
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| 90 | INTEGER :: ji, jj, jk, jl, jt ! dummy loop indices |
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[10413] | 91 | INTEGER :: icycle ! number of sub-timestep for the advection |
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| 92 | REAL(wp) :: zamsk ! 1 if advection of concentration, 0 if advection of other tracers |
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[10425] | 93 | REAL(wp) :: zdt |
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[10439] | 94 | REAL(wp), DIMENSION(1) :: zcflprv, zcflnow ! send zcflnow and receive zcflprv |
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| 95 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box |
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| 96 | REAL(wp), DIMENSION(jpi,jpj) :: zati1, zati2 |
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[10425] | 97 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zua_ho, zva_ho |
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| 98 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: z1_ai, z1_aip |
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| 99 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zhvar |
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[8586] | 100 | !!---------------------------------------------------------------------- |
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| 101 | ! |
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| 102 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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| 103 | ! |
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[10425] | 104 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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| 105 | ! When needed, the advection split is applied at the next time-step in order to avoid blocking global comm. |
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| 106 | ! ...this should not affect too much the stability... Was ok on the tests we did... |
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| 107 | zcflnow(1) = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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| 108 | zcflnow(1) = MAX( zcflnow(1), MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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| 109 | |
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| 110 | ! non-blocking global communication send zcflnow and receive zcflprv |
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| 111 | CALL mpp_delay_max( 'icedyn_adv_umx', 'cflice', zcflnow(:), zcflprv(:), kt == nitend - nn_fsbc + 1 ) |
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[8586] | 112 | |
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[10425] | 113 | IF( zcflprv(1) > .5 ) THEN ; icycle = 2 |
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| 114 | ELSE ; icycle = 1 |
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[8586] | 115 | ENDIF |
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[10413] | 116 | |
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| 117 | zdt = rdt_ice / REAL(icycle) |
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[8586] | 118 | |
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| 119 | ! --- transport --- ! |
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| 120 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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| 121 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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| 122 | |
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| 123 | ! --- define velocity for advection: u*grad(H) --- ! |
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| 124 | DO jj = 2, jpjm1 |
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| 125 | DO ji = fs_2, fs_jpim1 |
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| 126 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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| 127 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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| 128 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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| 129 | ENDIF |
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| 130 | |
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| 131 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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| 132 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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| 133 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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| 134 | ENDIF |
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| 135 | END DO |
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| 136 | END DO |
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| 137 | |
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| 138 | !---------------! |
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| 139 | !== advection ==! |
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| 140 | !---------------! |
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[10413] | 141 | DO jt = 1, icycle |
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| 142 | |
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[10439] | 143 | ! record at_i before advection (for open water) |
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| 144 | zati1(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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[10413] | 145 | |
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[10439] | 146 | ! inverse of A and Ap |
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[10425] | 147 | WHERE( pa_i(:,:,:) >= epsi20 ) ; z1_ai(:,:,:) = 1._wp / pa_i(:,:,:) |
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| 148 | ELSEWHERE ; z1_ai(:,:,:) = 0. |
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| 149 | END WHERE |
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| 150 | WHERE( pa_ip(:,:,:) >= epsi20 ) ; z1_aip(:,:,:) = 1._wp / pa_ip(:,:,:) |
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| 151 | ELSEWHERE ; z1_aip(:,:,:) = 0. |
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| 152 | END WHERE |
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| 153 | ! |
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[10439] | 154 | ! set u*a=u for advection of A only |
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[10425] | 155 | DO jl = 1, jpl |
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| 156 | zua_ho(:,:,jl) = zudy(:,:) |
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| 157 | zva_ho(:,:,jl) = zvdx(:,:) |
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| 158 | END DO |
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| 159 | |
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| 160 | zamsk = 1._wp |
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| 161 | 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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| 162 | zamsk = 0._wp |
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| 163 | ! |
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| 164 | zhvar(:,:,:) = pv_i(:,:,:) * z1_ai(:,:,:) |
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[10439] | 165 | 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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[10425] | 166 | ! |
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| 167 | zhvar(:,:,:) = pv_s(:,:,:) * z1_ai(:,:,:) |
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[10439] | 168 | 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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[10425] | 169 | ! |
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| 170 | zhvar(:,:,:) = psv_i(:,:,:) * z1_ai(:,:,:) |
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[10439] | 171 | 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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[10425] | 172 | ! |
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| 173 | zhvar(:,:,:) = poa_i(:,:,:) * z1_ai(:,:,:) |
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[10439] | 174 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, poa_i ) ! Age content |
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[10425] | 175 | ! |
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| 176 | DO jk = 1, nlay_i |
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| 177 | zhvar(:,:,:) = pe_i(:,:,jk,:) * z1_ai(:,:,:) |
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[10439] | 178 | 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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[10425] | 179 | END DO |
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| 180 | ! |
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| 181 | DO jk = 1, nlay_s |
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| 182 | zhvar(:,:,:) = pe_s(:,:,jk,:) * z1_ai(:,:,:) |
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[10439] | 183 | 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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[10425] | 184 | END DO |
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[10439] | 185 | ! |
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[10425] | 186 | IF ( ln_pnd_H12 ) THEN |
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[10439] | 187 | ! set u*a=u for advection of Ap only |
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[10425] | 188 | DO jl = 1, jpl |
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| 189 | zua_ho(:,:,jl) = zudy(:,:) |
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| 190 | zva_ho(:,:,jl) = zvdx(:,:) |
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[8586] | 191 | END DO |
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[10425] | 192 | |
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| 193 | zamsk = 1._wp |
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| 194 | 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 ) ! mp fraction |
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| 195 | zamsk = 0._wp |
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[10418] | 196 | ! |
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[10475] | 197 | zhvar(:,:,:) = pv_ip(:,:,:) * z1_aip(:,:,:) |
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[10439] | 198 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, zhvar, pv_ip ) ! mp volume |
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[10425] | 199 | ENDIF |
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[10418] | 200 | ! |
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[10439] | 201 | zati2(:,:) = SUM( pa_i(:,:,:), dim=3 ) |
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| 202 | DO jj = 2, jpjm1 |
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| 203 | DO ji = fs_2, fs_jpim1 |
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| 204 | pato_i(ji,jj) = pato_i(ji,jj) - ( zati2(ji,jj) - zati1(ji,jj) ) & ! Open water area |
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| 205 | & - ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) ) * r1_e1e2t(ji,jj) * zdt |
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[10413] | 206 | END DO |
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[10439] | 207 | END DO |
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| 208 | CALL lbc_lnk( 'icedyn_adv_umx', pato_i(:,:), 'T', 1. ) |
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[10418] | 209 | ! |
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[8586] | 210 | END DO |
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| 211 | ! |
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| 212 | END SUBROUTINE ice_dyn_adv_umx |
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[9929] | 213 | |
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[8586] | 214 | |
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[10413] | 215 | 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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[8586] | 216 | !!---------------------------------------------------------------------- |
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| 217 | !! *** ROUTINE adv_umx *** |
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| 218 | !! |
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| 219 | !! ** Purpose : Compute the now trend due to total advection of |
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[10446] | 220 | !! tracers and add it to the general trend of tracer equations |
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[8586] | 221 | !! |
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[10446] | 222 | !! ** Method : - calculate upstream fluxes and upstream solution for tracer H |
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| 223 | !! - calculate tracer H at u and v points (Ultimate) |
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| 224 | !! - calculate the high order fluxes using alterning directions (Macho?) |
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[10519] | 225 | !! - apply a limiter on the fluxes (nonosc_ice) |
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[10446] | 226 | !! - convert this tracer flux to a tracer content flux (uH -> uV) |
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| 227 | !! - calculate the high order solution for tracer content V |
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[8586] | 228 | !! |
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[10446] | 229 | !! ** Action : solve 2 equations => a) da/dt = -div(ua) |
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| 230 | !! b) dV/dt = -div(uV) using dH/dt = -u.grad(H) |
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[10519] | 231 | !! 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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[10446] | 232 | !! - then we convert this flux to a "volume" flux this way => uH*ua/u |
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| 233 | !! where ua is the flux from eq. a) |
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| 234 | !! - at last we estimate dV/dt = -div(uH*ua/u) |
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| 235 | !! |
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| 236 | !! ** 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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| 237 | !! - 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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| 238 | !! is to apply an upstream scheme when it occurs. A better solution would be to degrade the order of |
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| 239 | !! the scheme automatically by applying a mask of the ice cover inside Ultimate (not done). |
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| 240 | !! - Eventhough 1D tests give very good results (typically the one from Schar & Smolarkiewiecz), the 2D is less good. |
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| 241 | !! 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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| 242 | !! 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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| 243 | !! Therefore, after advection we limit the thickness to the largest value of the 9-points around (only if ice |
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| 244 | !! concentration is small). |
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| 245 | !! To-do: expand the prelimiter from zalesak to make it work in 2D |
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[8586] | 246 | !!---------------------------------------------------------------------- |
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[10439] | 247 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
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| 248 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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| 249 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
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| 250 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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| 251 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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| 252 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
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| 253 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
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| 254 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
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| 255 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: pt ! tracer field |
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| 256 | REAL(wp), DIMENSION(:,:,:) , INTENT(inout) :: ptc ! tracer content field |
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[10425] | 257 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
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[8586] | 258 | ! |
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[10425] | 259 | INTEGER :: ji, jj, jl ! dummy loop indices |
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[8586] | 260 | REAL(wp) :: ztra ! local scalar |
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[10446] | 261 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ho , zfv_ho , zpt |
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[10439] | 262 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zfu_ups, zfv_ups, zt_ups |
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[8586] | 263 | !!---------------------------------------------------------------------- |
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| 264 | ! |
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[10446] | 265 | ! Upstream (_ups) fluxes |
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| 266 | ! ----------------------- |
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| 267 | CALL upstream( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups ) |
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| 268 | |
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| 269 | ! High order (_ho) fluxes |
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| 270 | ! ----------------------- |
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| 271 | SELECT CASE( kn_umx ) |
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| 272 | ! |
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| 273 | CASE ( 20 ) !== centered second order ==! |
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| 274 | ! |
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[10475] | 275 | CALL cen2( pamsk, jt, kt, pdt, pt, pu, pv, zt_ups, zfu_ups, zfv_ups, zfu_ho, zfv_ho ) |
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[10446] | 276 | ! |
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| 277 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
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| 278 | ! |
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[10475] | 279 | 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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[10446] | 280 | ! |
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| 281 | END SELECT |
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[10439] | 282 | ! |
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[10446] | 283 | ! --ho --ho |
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| 284 | ! new fluxes = u*H * u*a / u |
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| 285 | ! ---------------------------- |
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[10475] | 286 | IF( pamsk == 0._wp ) THEN |
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[10446] | 287 | DO jl = 1, jpl |
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| 288 | DO jj = 1, jpjm1 |
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| 289 | DO ji = 1, fs_jpim1 |
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| 290 | IF( ABS( puc(ji,jj,jl) ) > 0._wp .AND. ABS( pu(ji,jj) ) > 0._wp ) THEN |
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| 291 | zfu_ho (ji,jj,jl) = zfu_ho (ji,jj,jl) * puc(ji,jj,jl) / pu(ji,jj) |
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| 292 | zfu_ups(ji,jj,jl) = zfu_ups(ji,jj,jl) * puc(ji,jj,jl) / pu(ji,jj) |
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| 293 | ELSE |
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| 294 | zfu_ho (ji,jj,jl) = 0._wp |
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| 295 | zfu_ups(ji,jj,jl) = 0._wp |
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| 296 | ENDIF |
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| 297 | ! |
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| 298 | IF( ABS( pvc(ji,jj,jl) ) > 0._wp .AND. ABS( pv(ji,jj) ) > 0._wp ) THEN |
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| 299 | zfv_ho (ji,jj,jl) = zfv_ho (ji,jj,jl) * pvc(ji,jj,jl) / pv(ji,jj) |
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| 300 | zfv_ups(ji,jj,jl) = zfv_ups(ji,jj,jl) * pvc(ji,jj,jl) / pv(ji,jj) |
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| 301 | ELSE |
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| 302 | zfv_ho (ji,jj,jl) = 0._wp |
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| 303 | zfv_ups(ji,jj,jl) = 0._wp |
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| 304 | ENDIF |
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| 305 | END DO |
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| 306 | END DO |
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| 307 | END DO |
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| 308 | ENDIF |
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| 309 | ! --ho |
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| 310 | ! in case of advection of A: output u*a |
---|
| 311 | ! ------------------------------------- |
---|
| 312 | IF( PRESENT( pua_ho ) ) THEN |
---|
| 313 | DO jl = 1, jpl |
---|
| 314 | DO jj = 1, jpjm1 |
---|
| 315 | DO ji = 1, fs_jpim1 |
---|
| 316 | pua_ho(ji,jj,jl) = zfu_ho(ji,jj,jl) |
---|
| 317 | pva_ho(ji,jj,jl) = zfv_ho(ji,jj,jl) |
---|
| 318 | END DO |
---|
| 319 | END DO |
---|
| 320 | END DO |
---|
| 321 | ENDIF |
---|
| 322 | ! |
---|
| 323 | ! final trend with corrected fluxes |
---|
| 324 | ! --------------------------------- |
---|
| 325 | DO jl = 1, jpl |
---|
| 326 | DO jj = 2, jpjm1 |
---|
| 327 | DO ji = fs_2, fs_jpim1 |
---|
| 328 | ztra = - ( zfu_ho(ji,jj,jl) - zfu_ho(ji-1,jj,jl) + zfv_ho(ji,jj,jl) - zfv_ho(ji,jj-1,jl) ) |
---|
| 329 | ! |
---|
| 330 | ptc(ji,jj,jl) = ( ptc(ji,jj,jl) + ztra * r1_e1e2t(ji,jj) * pdt ) * tmask(ji,jj,1) |
---|
| 331 | END DO |
---|
| 332 | END DO |
---|
| 333 | END DO |
---|
| 334 | CALL lbc_lnk( 'icedyn_adv_umx', ptc, 'T', 1. ) |
---|
| 335 | ! |
---|
| 336 | END SUBROUTINE adv_umx |
---|
| 337 | |
---|
| 338 | |
---|
| 339 | SUBROUTINE upstream( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups ) |
---|
| 340 | !!--------------------------------------------------------------------- |
---|
| 341 | !! *** ROUTINE upstream *** |
---|
| 342 | !! |
---|
| 343 | !! ** Purpose : compute the upstream fluxes and upstream guess of tracer |
---|
| 344 | !!---------------------------------------------------------------------- |
---|
| 345 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 346 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 347 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 348 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 349 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 350 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 351 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_ups ! upstream guess of tracer |
---|
| 352 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
| 353 | ! |
---|
| 354 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 355 | REAL(wp) :: ztra ! local scalar |
---|
| 356 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
| 357 | !!---------------------------------------------------------------------- |
---|
| 358 | |
---|
[10439] | 359 | IF( .NOT. ll_upsxy ) THEN !** no alternate directions **! |
---|
[10446] | 360 | ! |
---|
[10425] | 361 | DO jl = 1, jpl |
---|
| 362 | DO jj = 1, jpjm1 |
---|
| 363 | DO ji = 1, fs_jpim1 |
---|
[10446] | 364 | 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) |
---|
| 365 | 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) |
---|
[10425] | 366 | END DO |
---|
[10413] | 367 | END DO |
---|
| 368 | END DO |
---|
[10446] | 369 | ! |
---|
[10439] | 370 | ELSE !** alternate directions **! |
---|
[10413] | 371 | ! |
---|
| 372 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[10439] | 373 | ! |
---|
| 374 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 375 | DO jj = 1, jpjm1 |
---|
| 376 | DO ji = 1, fs_jpim1 |
---|
[10446] | 377 | 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) |
---|
[10425] | 378 | END DO |
---|
[10413] | 379 | END DO |
---|
| 380 | END DO |
---|
[10439] | 381 | ! |
---|
| 382 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 383 | DO jj = 2, jpjm1 |
---|
[10439] | 384 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 385 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj,jl) ) & |
---|
| 386 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 387 | ! |
---|
| 388 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 389 | END DO |
---|
[10413] | 390 | END DO |
---|
| 391 | END DO |
---|
[10425] | 392 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 393 | ! |
---|
[10439] | 394 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 395 | DO jj = 1, jpjm1 |
---|
| 396 | DO ji = 1, fs_jpim1 |
---|
[10446] | 397 | 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) |
---|
[10425] | 398 | END DO |
---|
[10413] | 399 | END DO |
---|
| 400 | END DO |
---|
[10439] | 401 | ! |
---|
[10413] | 402 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
[10439] | 403 | ! |
---|
| 404 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 405 | DO jj = 1, jpjm1 |
---|
| 406 | DO ji = 1, fs_jpim1 |
---|
[10446] | 407 | 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) |
---|
[10425] | 408 | END DO |
---|
[10413] | 409 | END DO |
---|
| 410 | END DO |
---|
[10439] | 411 | ! |
---|
| 412 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 413 | DO jj = 2, jpjm1 |
---|
[10439] | 414 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 415 | ztra = - ( pfv_ups(ji,jj,jl) - pfv_ups(ji,jj-1,jl) ) & |
---|
| 416 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 417 | ! |
---|
| 418 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 419 | END DO |
---|
| 420 | END DO |
---|
[10413] | 421 | END DO |
---|
[10425] | 422 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 423 | ! |
---|
[10439] | 424 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 425 | DO jj = 1, jpjm1 |
---|
| 426 | DO ji = 1, fs_jpim1 |
---|
[10446] | 427 | 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) |
---|
[10425] | 428 | END DO |
---|
[10413] | 429 | END DO |
---|
| 430 | END DO |
---|
| 431 | ! |
---|
| 432 | ENDIF |
---|
| 433 | |
---|
| 434 | ENDIF |
---|
[10439] | 435 | ! |
---|
| 436 | DO jl = 1, jpl !-- after tracer with upstream scheme |
---|
[10425] | 437 | DO jj = 2, jpjm1 |
---|
| 438 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 439 | ztra = - ( pfu_ups(ji,jj,jl) - pfu_ups(ji-1,jj ,jl) & |
---|
| 440 | & + pfv_ups(ji,jj,jl) - pfv_ups(ji ,jj-1,jl) ) & |
---|
| 441 | & + ( pu (ji,jj ) - pu (ji-1,jj ) & |
---|
| 442 | & + pv (ji,jj ) - pv (ji ,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 443 | ! |
---|
[10475] | 444 | pt_ups(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 445 | END DO |
---|
[10413] | 446 | END DO |
---|
[8586] | 447 | END DO |
---|
[10446] | 448 | CALL lbc_lnk( 'icedyn_adv_umx', pt_ups, 'T', 1. ) |
---|
[10413] | 449 | |
---|
[10446] | 450 | END SUBROUTINE upstream |
---|
[8586] | 451 | |
---|
[10446] | 452 | |
---|
[10475] | 453 | SUBROUTINE cen2( pamsk, jt, kt, pdt, pt, pu, pv, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 454 | !!--------------------------------------------------------------------- |
---|
[10446] | 455 | !! *** ROUTINE cen2 *** |
---|
[8586] | 456 | !! |
---|
[10446] | 457 | !! ** Purpose : compute the high order fluxes using a centered |
---|
| 458 | !! second order scheme |
---|
[8586] | 459 | !!---------------------------------------------------------------------- |
---|
[10439] | 460 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 461 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 462 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 463 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 464 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 465 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
[10446] | 466 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 467 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 468 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[8586] | 469 | ! |
---|
[10425] | 470 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 471 | REAL(wp) :: ztra ! local scalar |
---|
| 472 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zpt |
---|
[8586] | 473 | !!---------------------------------------------------------------------- |
---|
| 474 | ! |
---|
[10439] | 475 | IF( .NOT.ll_hoxy ) THEN !** no alternate directions **! |
---|
[8586] | 476 | ! |
---|
[10425] | 477 | DO jl = 1, jpl |
---|
| 478 | DO jj = 1, jpjm1 |
---|
| 479 | DO ji = 1, fs_jpim1 |
---|
[10475] | 480 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj ,jl) ) |
---|
| 481 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji ,jj+1,jl) ) |
---|
[10425] | 482 | END DO |
---|
[8586] | 483 | END DO |
---|
| 484 | END DO |
---|
[10475] | 485 | ! |
---|
[10413] | 486 | IF ( kn_limiter == 1 ) THEN |
---|
[10519] | 487 | CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10446] | 488 | ELSEIF( kn_limiter == 2 .OR. kn_limiter == 3 ) THEN |
---|
| 489 | CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 490 | CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 491 | ENDIF |
---|
[8586] | 492 | ! |
---|
[10439] | 493 | ELSE !** alternate directions **! |
---|
[8586] | 494 | ! |
---|
[10413] | 495 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
| 496 | ! |
---|
[10439] | 497 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 498 | DO jj = 1, jpjm1 |
---|
| 499 | DO ji = 1, fs_jpim1 |
---|
[10475] | 500 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( pt(ji,jj,jl) + pt(ji+1,jj,jl) ) |
---|
[10425] | 501 | END DO |
---|
[10413] | 502 | END DO |
---|
| 503 | END DO |
---|
[10446] | 504 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 505 | |
---|
[10439] | 506 | DO jl = 1, jpl !-- first guess of tracer from u-flux |
---|
[10425] | 507 | DO jj = 2, jpjm1 |
---|
[10439] | 508 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 509 | ztra = - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) & |
---|
| 510 | & + ( pu (ji,jj ) - pu (ji-1,jj ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 511 | ! |
---|
| 512 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 513 | END DO |
---|
[10413] | 514 | END DO |
---|
| 515 | END DO |
---|
[10446] | 516 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 517 | |
---|
[10439] | 518 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 519 | DO jj = 1, jpjm1 |
---|
| 520 | DO ji = 1, fs_jpim1 |
---|
[10475] | 521 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji,jj+1,jl) ) |
---|
[10425] | 522 | END DO |
---|
[10413] | 523 | END DO |
---|
| 524 | END DO |
---|
[10446] | 525 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 526 | |
---|
| 527 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 528 | ! |
---|
[10439] | 529 | DO jl = 1, jpl !-- flux in y-direction |
---|
[10425] | 530 | DO jj = 1, jpjm1 |
---|
| 531 | DO ji = 1, fs_jpim1 |
---|
[10475] | 532 | pfv_ho(ji,jj,jl) = 0.5_wp * pv(ji,jj) * ( pt(ji,jj,jl) + pt(ji,jj+1,jl) ) |
---|
[10425] | 533 | END DO |
---|
[10413] | 534 | END DO |
---|
| 535 | END DO |
---|
[10446] | 536 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 537 | ! |
---|
[10439] | 538 | DO jl = 1, jpl !-- first guess of tracer from v-flux |
---|
[10425] | 539 | DO jj = 2, jpjm1 |
---|
[10439] | 540 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 541 | ztra = - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) & |
---|
| 542 | & + ( pv (ji,jj ) - pv (ji,jj-1 ) ) * pt(ji,jj,jl) * (1.-pamsk) |
---|
| 543 | ! |
---|
| 544 | zpt(ji,jj,jl) = ( pt(ji,jj,jl) + ztra * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
[10425] | 545 | END DO |
---|
[10413] | 546 | END DO |
---|
| 547 | END DO |
---|
[10446] | 548 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 549 | ! |
---|
[10439] | 550 | DO jl = 1, jpl !-- flux in x-direction |
---|
[10425] | 551 | DO jj = 1, jpjm1 |
---|
| 552 | DO ji = 1, fs_jpim1 |
---|
[10475] | 553 | pfu_ho(ji,jj,jl) = 0.5_wp * pu(ji,jj) * ( zpt(ji,jj,jl) + zpt(ji+1,jj,jl) ) |
---|
[10425] | 554 | END DO |
---|
[10413] | 555 | END DO |
---|
| 556 | END DO |
---|
[10446] | 557 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 558 | |
---|
| 559 | ENDIF |
---|
[10519] | 560 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 561 | |
---|
| 562 | ENDIF |
---|
| 563 | |
---|
| 564 | END SUBROUTINE cen2 |
---|
| 565 | |
---|
| 566 | |
---|
[10475] | 567 | SUBROUTINE macho( pamsk, kn_umx, jt, kt, pdt, pt, pu, pv, pubox, pvbox, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[10413] | 568 | !!--------------------------------------------------------------------- |
---|
| 569 | !! *** ROUTINE macho *** |
---|
| 570 | !! |
---|
[10446] | 571 | !! ** Purpose : compute the high order fluxes using Ultimate-Macho scheme |
---|
[10413] | 572 | !! |
---|
[10446] | 573 | !! ** Method : ... |
---|
[10413] | 574 | !! |
---|
| 575 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 576 | !!---------------------------------------------------------------------- |
---|
[10439] | 577 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 578 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 579 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
| 580 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
| 581 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 582 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
| 583 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
| 584 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
[10446] | 585 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt_ups ! upstream guess of tracer |
---|
| 586 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
[10425] | 587 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
[10413] | 588 | ! |
---|
[10425] | 589 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10446] | 590 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zt_u, zt_v, zpt |
---|
[10413] | 591 | !!---------------------------------------------------------------------- |
---|
| 592 | ! |
---|
| 593 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
[8586] | 594 | ! |
---|
[10413] | 595 | ! !-- ultimate interpolation of pt at u-point --! |
---|
[10446] | 596 | CALL ultimate_x( kn_umx, pdt, pt, pu, zt_u, pfu_ho ) |
---|
[10413] | 597 | ! !-- limiter in x --! |
---|
[10446] | 598 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
| 599 | ! !-- advective form update in zpt --! |
---|
[10439] | 600 | DO jl = 1, jpl |
---|
| 601 | DO jj = 2, jpjm1 |
---|
| 602 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 603 | 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) & |
---|
| 604 | & + pt (ji,jj,jl) * ( pu (ji,jj ) - pu (ji-1,jj ) ) * r1_e1e2t(ji,jj) & |
---|
| 605 | & * pamsk & |
---|
| 606 | & ) * pdt ) * tmask(ji,jj,1) |
---|
[10413] | 607 | END DO |
---|
[8586] | 608 | END DO |
---|
[10439] | 609 | END DO |
---|
[10446] | 610 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[8586] | 611 | ! |
---|
[10413] | 612 | ! !-- ultimate interpolation of pt at v-point --! |
---|
| 613 | IF( ll_hoxy ) THEN |
---|
[10446] | 614 | CALL ultimate_y( kn_umx, pdt, zpt, pv, zt_v, pfv_ho ) |
---|
[10413] | 615 | ELSE |
---|
[10446] | 616 | CALL ultimate_y( kn_umx, pdt, pt , pv, zt_v, pfv_ho ) |
---|
[10413] | 617 | ENDIF |
---|
| 618 | ! !-- limiter in y --! |
---|
[10446] | 619 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 620 | ! |
---|
| 621 | ! |
---|
| 622 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
| 623 | ! |
---|
| 624 | ! !-- ultimate interpolation of pt at v-point --! |
---|
[10446] | 625 | CALL ultimate_y( kn_umx, pdt, pt, pv, zt_v, pfv_ho ) |
---|
[10413] | 626 | ! !-- limiter in y --! |
---|
[10446] | 627 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
| 628 | ! !-- advective form update in zpt --! |
---|
[10439] | 629 | DO jl = 1, jpl |
---|
| 630 | DO jj = 2, jpjm1 |
---|
| 631 | DO ji = fs_2, fs_jpim1 |
---|
[10446] | 632 | 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) & |
---|
| 633 | & + pt (ji,jj,jl) * ( pv (ji,jj ) - pv (ji,jj-1 ) ) * r1_e1e2t(ji,jj) & |
---|
| 634 | & * pamsk & |
---|
| 635 | & ) * pdt ) * tmask(ji,jj,1) |
---|
[10425] | 636 | END DO |
---|
[10413] | 637 | END DO |
---|
[10439] | 638 | END DO |
---|
[10446] | 639 | CALL lbc_lnk( 'icedyn_adv_umx', zpt, 'T', 1. ) |
---|
[10413] | 640 | ! |
---|
| 641 | ! !-- ultimate interpolation of pt at u-point --! |
---|
| 642 | IF( ll_hoxy ) THEN |
---|
[10446] | 643 | CALL ultimate_x( kn_umx, pdt, zpt, pu, zt_u, pfu_ho ) |
---|
[10413] | 644 | ELSE |
---|
[10446] | 645 | CALL ultimate_x( kn_umx, pdt, pt , pu, zt_u, pfu_ho ) |
---|
[10413] | 646 | ENDIF |
---|
| 647 | ! !-- limiter in x --! |
---|
[10446] | 648 | IF( kn_limiter == 2 .OR. kn_limiter == 3 ) CALL limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 649 | ! |
---|
| 650 | ENDIF |
---|
| 651 | |
---|
[10519] | 652 | IF( kn_limiter == 1 ) CALL nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 653 | ! |
---|
| 654 | END SUBROUTINE macho |
---|
| 655 | |
---|
| 656 | |
---|
[10439] | 657 | SUBROUTINE ultimate_x( kn_umx, pdt, pt, pu, pt_u, pfu_ho ) |
---|
[8586] | 658 | !!--------------------------------------------------------------------- |
---|
| 659 | !! *** ROUTINE ultimate_x *** |
---|
| 660 | !! |
---|
[10446] | 661 | !! ** Purpose : compute tracer at u-points |
---|
[8586] | 662 | !! |
---|
[10446] | 663 | !! ** Method : ... |
---|
[8586] | 664 | !! |
---|
| 665 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 666 | !!---------------------------------------------------------------------- |
---|
[10439] | 667 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 668 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 669 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pu ! ice i-velocity component |
---|
| 670 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 671 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_u ! tracer at u-point |
---|
| 672 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfu_ho ! high order flux |
---|
[8586] | 673 | ! |
---|
[10425] | 674 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10439] | 675 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
[10425] | 676 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztu1, ztu2, ztu3, ztu4 |
---|
[8586] | 677 | !!---------------------------------------------------------------------- |
---|
| 678 | ! |
---|
| 679 | ! !-- Laplacian in i-direction --! |
---|
[10425] | 680 | DO jl = 1, jpl |
---|
| 681 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
| 682 | DO ji = 1, fs_jpim1 |
---|
| 683 | ztu1(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 684 | END DO |
---|
| 685 | ! ! Second derivative (Laplacian) |
---|
| 686 | DO ji = fs_2, fs_jpim1 |
---|
| 687 | ztu2(ji,jj,jl) = ( ztu1(ji,jj,jl) - ztu1(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 688 | END DO |
---|
[8586] | 689 | END DO |
---|
| 690 | END DO |
---|
[10425] | 691 | CALL lbc_lnk( 'icedyn_adv_umx', ztu2, 'T', 1. ) |
---|
[8586] | 692 | ! |
---|
| 693 | ! !-- BiLaplacian in i-direction --! |
---|
[10425] | 694 | DO jl = 1, jpl |
---|
| 695 | DO jj = 2, jpjm1 ! Third derivative |
---|
| 696 | DO ji = 1, fs_jpim1 |
---|
| 697 | ztu3(ji,jj,jl) = ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
| 698 | END DO |
---|
| 699 | ! ! Fourth derivative |
---|
| 700 | DO ji = fs_2, fs_jpim1 |
---|
| 701 | ztu4(ji,jj,jl) = ( ztu3(ji,jj,jl) - ztu3(ji-1,jj,jl) ) * r1_e1t(ji,jj) |
---|
| 702 | END DO |
---|
[8586] | 703 | END DO |
---|
| 704 | END DO |
---|
[10425] | 705 | CALL lbc_lnk( 'icedyn_adv_umx', ztu4, 'T', 1. ) |
---|
[8586] | 706 | ! |
---|
| 707 | ! |
---|
[10413] | 708 | SELECT CASE (kn_umx ) |
---|
[8586] | 709 | ! |
---|
| 710 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
| 711 | ! |
---|
[10425] | 712 | DO jl = 1, jpl |
---|
| 713 | DO jj = 1, jpjm1 |
---|
| 714 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10475] | 715 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 716 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 717 | END DO |
---|
[8586] | 718 | END DO |
---|
| 719 | END DO |
---|
| 720 | ! |
---|
| 721 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
| 722 | ! |
---|
[10425] | 723 | DO jl = 1, jpl |
---|
| 724 | DO jj = 1, jpjm1 |
---|
| 725 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 726 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 727 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
[10475] | 728 | & - zcu * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 729 | END DO |
---|
[8586] | 730 | END DO |
---|
| 731 | END DO |
---|
| 732 | ! |
---|
| 733 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
| 734 | ! |
---|
[10425] | 735 | DO jl = 1, jpl |
---|
| 736 | DO jj = 1, jpjm1 |
---|
| 737 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 738 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 739 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 740 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10446] | 741 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
[10475] | 742 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 743 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
[10446] | 744 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 745 | END DO |
---|
[8586] | 746 | END DO |
---|
| 747 | END DO |
---|
| 748 | ! |
---|
| 749 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
| 750 | ! |
---|
[10425] | 751 | DO jl = 1, jpl |
---|
| 752 | DO jj = 1, jpjm1 |
---|
| 753 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 754 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 755 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 756 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10475] | 757 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 758 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 759 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 760 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) ) |
---|
[10425] | 761 | END DO |
---|
[8586] | 762 | END DO |
---|
| 763 | END DO |
---|
| 764 | ! |
---|
| 765 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
| 766 | ! |
---|
[10425] | 767 | DO jl = 1, jpl |
---|
| 768 | DO jj = 1, jpjm1 |
---|
| 769 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 770 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
| 771 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
[10439] | 772 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
[10425] | 773 | zdx4 = zdx2 * zdx2 |
---|
[10475] | 774 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj,jl) + pt (ji,jj,jl) & |
---|
| 775 | & - zcu * ( pt (ji+1,jj,jl) - pt (ji,jj,jl) ) ) & |
---|
| 776 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj,jl) + ztu2(ji,jj,jl) & |
---|
| 777 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj,jl) - ztu2(ji,jj,jl) ) ) & |
---|
[10446] | 778 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj,jl) + ztu4(ji,jj,jl) & |
---|
[10425] | 779 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj,jl) - ztu4(ji,jj,jl) ) ) ) |
---|
| 780 | END DO |
---|
[8586] | 781 | END DO |
---|
| 782 | END DO |
---|
| 783 | ! |
---|
| 784 | END SELECT |
---|
[10439] | 785 | ! |
---|
| 786 | ! if pt at u-point is negative then use the upstream value |
---|
| 787 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 788 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 789 | IF( ll_neg ) THEN |
---|
[10425] | 790 | DO jl = 1, jpl |
---|
| 791 | DO jj = 1, jpjm1 |
---|
| 792 | DO ji = 1, fs_jpim1 |
---|
| 793 | IF( pt_u(ji,jj,jl) < 0._wp ) THEN |
---|
[10475] | 794 | pt_u(ji,jj,jl) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj,jl) + pt(ji,jj,jl) & |
---|
| 795 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 796 | ENDIF |
---|
| 797 | END DO |
---|
[10413] | 798 | END DO |
---|
| 799 | END DO |
---|
| 800 | ENDIF |
---|
[10439] | 801 | ! !-- High order flux in i-direction --! |
---|
[10425] | 802 | DO jl = 1, jpl |
---|
| 803 | DO jj = 1, jpjm1 |
---|
| 804 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 805 | pfu_ho(ji,jj,jl) = pu(ji,jj) * pt_u(ji,jj,jl) |
---|
[10425] | 806 | END DO |
---|
[10413] | 807 | END DO |
---|
| 808 | END DO |
---|
[8586] | 809 | ! |
---|
| 810 | END SUBROUTINE ultimate_x |
---|
| 811 | |
---|
| 812 | |
---|
[10439] | 813 | SUBROUTINE ultimate_y( kn_umx, pdt, pt, pv, pt_v, pfv_ho ) |
---|
[8586] | 814 | !!--------------------------------------------------------------------- |
---|
| 815 | !! *** ROUTINE ultimate_y *** |
---|
| 816 | !! |
---|
[10446] | 817 | !! ** Purpose : compute tracer at v-points |
---|
[8586] | 818 | !! |
---|
[10446] | 819 | !! ** Method : ... |
---|
[8586] | 820 | !! |
---|
| 821 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
| 822 | !!---------------------------------------------------------------------- |
---|
[10439] | 823 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
| 824 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 825 | REAL(wp), DIMENSION(:,: ) , INTENT(in ) :: pv ! ice j-velocity component |
---|
| 826 | REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pt ! tracer fields |
---|
[10425] | 827 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pt_v ! tracer at v-point |
---|
| 828 | REAL(wp), DIMENSION(jpi,jpj,jpl), INTENT( out) :: pfv_ho ! high order flux |
---|
[8586] | 829 | ! |
---|
[10439] | 830 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[8586] | 831 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
[10425] | 832 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: ztv1, ztv2, ztv3, ztv4 |
---|
[8586] | 833 | !!---------------------------------------------------------------------- |
---|
| 834 | ! |
---|
| 835 | ! !-- Laplacian in j-direction --! |
---|
[10425] | 836 | DO jl = 1, jpl |
---|
| 837 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
| 838 | DO ji = fs_2, fs_jpim1 |
---|
| 839 | ztv1(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 840 | END DO |
---|
[8586] | 841 | END DO |
---|
[10425] | 842 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
| 843 | DO ji = fs_2, fs_jpim1 |
---|
| 844 | ztv2(ji,jj,jl) = ( ztv1(ji,jj,jl) - ztv1(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 845 | END DO |
---|
[8586] | 846 | END DO |
---|
| 847 | END DO |
---|
[10425] | 848 | CALL lbc_lnk( 'icedyn_adv_umx', ztv2, 'T', 1. ) |
---|
[8586] | 849 | ! |
---|
| 850 | ! !-- BiLaplacian in j-direction --! |
---|
[10425] | 851 | DO jl = 1, jpl |
---|
| 852 | DO jj = 1, jpjm1 ! First derivative |
---|
| 853 | DO ji = fs_2, fs_jpim1 |
---|
| 854 | ztv3(ji,jj,jl) = ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
| 855 | END DO |
---|
[8586] | 856 | END DO |
---|
[10425] | 857 | DO jj = 2, jpjm1 ! Second derivative |
---|
| 858 | DO ji = fs_2, fs_jpim1 |
---|
| 859 | ztv4(ji,jj,jl) = ( ztv3(ji,jj,jl) - ztv3(ji,jj-1,jl) ) * r1_e2t(ji,jj) |
---|
| 860 | END DO |
---|
[8586] | 861 | END DO |
---|
| 862 | END DO |
---|
[10425] | 863 | CALL lbc_lnk( 'icedyn_adv_umx', ztv4, 'T', 1. ) |
---|
[8586] | 864 | ! |
---|
| 865 | ! |
---|
[10413] | 866 | SELECT CASE (kn_umx ) |
---|
[10425] | 867 | ! |
---|
[8586] | 868 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
[10425] | 869 | DO jl = 1, jpl |
---|
| 870 | DO jj = 1, jpjm1 |
---|
| 871 | DO ji = 1, fs_jpim1 |
---|
[10475] | 872 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 873 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 874 | END DO |
---|
[8586] | 875 | END DO |
---|
| 876 | END DO |
---|
| 877 | ! |
---|
| 878 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
[10425] | 879 | DO jl = 1, jpl |
---|
| 880 | DO jj = 1, jpjm1 |
---|
| 881 | DO ji = 1, fs_jpim1 |
---|
| 882 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
[10475] | 883 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( pt(ji,jj+1,jl) + pt(ji,jj,jl) & |
---|
| 884 | & - zcv * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 885 | END DO |
---|
[8586] | 886 | END DO |
---|
| 887 | END DO |
---|
| 888 | ! |
---|
| 889 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
[10425] | 890 | DO jl = 1, jpl |
---|
| 891 | DO jj = 1, jpjm1 |
---|
| 892 | DO ji = 1, fs_jpim1 |
---|
| 893 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
| 894 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
[10439] | 895 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 896 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
| 897 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
[10446] | 898 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
[10425] | 899 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
| 900 | END DO |
---|
[8586] | 901 | END DO |
---|
| 902 | END DO |
---|
| 903 | ! |
---|
| 904 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
[10425] | 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) |
---|
[10439] | 910 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10475] | 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 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) ) |
---|
[10425] | 915 | END DO |
---|
[8586] | 916 | END DO |
---|
| 917 | END DO |
---|
| 918 | ! |
---|
| 919 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
[10425] | 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) |
---|
[10439] | 925 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
[10425] | 926 | zdy4 = zdy2 * zdy2 |
---|
[10446] | 927 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1,jl) + pt (ji,jj,jl) & |
---|
[10475] | 928 | & - zcv * ( pt (ji,jj+1,jl) - pt (ji,jj,jl) ) ) & |
---|
| 929 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1,jl) + ztv2(ji,jj,jl) & |
---|
| 930 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1,jl) - ztv2(ji,jj,jl) ) ) & |
---|
[10446] | 931 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1,jl) + ztv4(ji,jj,jl) & |
---|
[10425] | 932 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1,jl) - ztv4(ji,jj,jl) ) ) ) |
---|
| 933 | END DO |
---|
[8586] | 934 | END DO |
---|
| 935 | END DO |
---|
| 936 | ! |
---|
| 937 | END SELECT |
---|
[10439] | 938 | ! |
---|
| 939 | ! if pt at v-point is negative then use the upstream value |
---|
| 940 | ! this should not be necessary if a proper sea-ice mask is set in Ultimate |
---|
| 941 | ! to degrade the order of the scheme when necessary (for ex. at the ice edge) |
---|
[10413] | 942 | IF( ll_neg ) THEN |
---|
[10425] | 943 | DO jl = 1, jpl |
---|
| 944 | DO jj = 1, jpjm1 |
---|
| 945 | DO ji = 1, fs_jpim1 |
---|
| 946 | IF( pt_v(ji,jj,jl) < 0._wp ) THEN |
---|
[10475] | 947 | pt_v(ji,jj,jl) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1,jl) + pt(ji,jj,jl) ) & |
---|
| 948 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) ) |
---|
[10425] | 949 | ENDIF |
---|
| 950 | END DO |
---|
[10413] | 951 | END DO |
---|
| 952 | END DO |
---|
| 953 | ENDIF |
---|
[10439] | 954 | ! !-- High order flux in j-direction --! |
---|
[10425] | 955 | DO jl = 1, jpl |
---|
| 956 | DO jj = 1, jpjm1 |
---|
| 957 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 958 | pfv_ho(ji,jj,jl) = pv(ji,jj) * pt_v(ji,jj,jl) |
---|
[10425] | 959 | END DO |
---|
[10413] | 960 | END DO |
---|
| 961 | END DO |
---|
[8586] | 962 | ! |
---|
| 963 | END SUBROUTINE ultimate_y |
---|
[10413] | 964 | |
---|
| 965 | |
---|
[10519] | 966 | SUBROUTINE nonosc_ice( pamsk, pdt, pu, pv, pt, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
[8586] | 967 | !!--------------------------------------------------------------------- |
---|
[10519] | 968 | !! *** ROUTINE nonosc_ice *** |
---|
[8586] | 969 | !! |
---|
[10446] | 970 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
[10519] | 971 | !! scheme and the before field by a non-oscillatory algorithm |
---|
[8586] | 972 | !! |
---|
[10446] | 973 | !! ** Method : ... |
---|
[8586] | 974 | !!---------------------------------------------------------------------- |
---|
[10439] | 975 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
| 976 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
[10425] | 977 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 978 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice j-velocity => v*e1 |
---|
[10446] | 979 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt, pt_ups ! before field & upstream guess of after field |
---|
| 980 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups, pfu_ups ! upstream flux |
---|
[10425] | 981 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
[8586] | 982 | ! |
---|
[10425] | 983 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
[10475] | 984 | REAL(wp) :: zpos, zneg, zbig, zup, zdo, z1_dt ! local scalars |
---|
| 985 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zcoef, zzt ! - - |
---|
[10425] | 986 | REAL(wp), DIMENSION(jpi,jpj ) :: zbup, zbdo |
---|
[10439] | 987 | REAL(wp), DIMENSION(jpi,jpj,jpl) :: zbetup, zbetdo, zti_ups, ztj_ups |
---|
[8586] | 988 | !!---------------------------------------------------------------------- |
---|
| 989 | zbig = 1.e+40_wp |
---|
[10425] | 990 | |
---|
[10413] | 991 | ! antidiffusive flux : high order minus low order |
---|
| 992 | ! -------------------------------------------------- |
---|
[10425] | 993 | DO jl = 1, jpl |
---|
| 994 | DO jj = 1, jpjm1 |
---|
| 995 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
[10439] | 996 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 997 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
[10425] | 998 | END DO |
---|
| 999 | END DO |
---|
[8586] | 1000 | END DO |
---|
| 1001 | |
---|
[10413] | 1002 | ! extreme case where pfu_ho has to be zero |
---|
| 1003 | ! ---------------------------------------- |
---|
| 1004 | ! pfu_ho |
---|
| 1005 | ! * ---> |
---|
| 1006 | ! | | * | | |
---|
| 1007 | ! | | | * | |
---|
| 1008 | ! | | | | * |
---|
[10439] | 1009 | ! t_ups : i-1 i i+1 i+2 |
---|
[10413] | 1010 | IF( ll_prelimiter_zalesak ) THEN |
---|
| 1011 | |
---|
[10425] | 1012 | DO jl = 1, jpl |
---|
| 1013 | DO jj = 2, jpjm1 |
---|
| 1014 | DO ji = fs_2, fs_jpim1 |
---|
[10439] | 1015 | zti_ups(ji,jj,jl)= pt_ups(ji+1,jj ,jl) |
---|
| 1016 | ztj_ups(ji,jj,jl)= pt_ups(ji ,jj+1,jl) |
---|
[10425] | 1017 | END DO |
---|
[10413] | 1018 | END DO |
---|
| 1019 | END DO |
---|
[10439] | 1020 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zti_ups, 'T', 1., ztj_ups, 'T', 1. ) |
---|
[8586] | 1021 | |
---|
[10425] | 1022 | DO jl = 1, jpl |
---|
| 1023 | DO jj = 2, jpjm1 |
---|
| 1024 | DO ji = fs_2, fs_jpim1 |
---|
[10475] | 1025 | IF ( pfu_ho(ji,jj,jl) * ( pt_ups(ji+1,jj ,jl) - pt_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1026 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji ,jj+1,jl) - pt_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
[10425] | 1027 | ! |
---|
[10475] | 1028 | IF( pfu_ho(ji,jj,jl) * ( zti_ups(ji+1,jj ,jl) - zti_ups(ji,jj,jl) ) <= 0._wp .AND. & |
---|
| 1029 | & pfv_ho(ji,jj,jl) * ( ztj_ups(ji ,jj+1,jl) - ztj_ups(ji,jj,jl) ) <= 0._wp ) THEN |
---|
| 1030 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1031 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1032 | ENDIF |
---|
[10425] | 1033 | ! |
---|
[10475] | 1034 | IF( pfu_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji-1,jj ,jl) ) <= 0._wp .AND. & |
---|
| 1035 | & pfv_ho(ji,jj,jl) * ( pt_ups(ji,jj,jl) - pt_ups(ji ,jj-1,jl) ) <= 0._wp ) THEN |
---|
| 1036 | pfu_ho(ji,jj,jl)=0._wp |
---|
| 1037 | pfv_ho(ji,jj,jl)=0._wp |
---|
[10439] | 1038 | ENDIF |
---|
[10425] | 1039 | ! |
---|
| 1040 | ENDIF |
---|
| 1041 | END DO |
---|
[10413] | 1042 | END DO |
---|
| 1043 | END DO |
---|
[10425] | 1044 | CALL lbc_lnk_multi( 'icedyn_adv_umx', pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
[10413] | 1045 | |
---|
| 1046 | ENDIF |
---|
[10425] | 1047 | |
---|
[8586] | 1048 | ! Search local extrema |
---|
| 1049 | ! -------------------- |
---|
[10439] | 1050 | ! max/min of pt & pt_ups with large negative/positive value (-/+zbig) outside ice cover |
---|
[10425] | 1051 | z1_dt = 1._wp / pdt |
---|
| 1052 | DO jl = 1, jpl |
---|
| 1053 | |
---|
| 1054 | DO jj = 1, jpj |
---|
| 1055 | DO ji = 1, jpi |
---|
[10439] | 1056 | IF ( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1057 | zbup(ji,jj) = -zbig |
---|
| 1058 | zbdo(ji,jj) = zbig |
---|
[10439] | 1059 | ELSEIF( pt(ji,jj,jl) <= 0._wp .AND. pt_ups(ji,jj,jl) > 0._wp ) THEN |
---|
| 1060 | zbup(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1061 | zbdo(ji,jj) = pt_ups(ji,jj,jl) |
---|
| 1062 | ELSEIF( pt(ji,jj,jl) > 0._wp .AND. pt_ups(ji,jj,jl) <= 0._wp ) THEN |
---|
[10425] | 1063 | zbup(ji,jj) = pt(ji,jj,jl) |
---|
| 1064 | zbdo(ji,jj) = pt(ji,jj,jl) |
---|
| 1065 | ELSE |
---|
[10439] | 1066 | zbup(ji,jj) = MAX( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
| 1067 | zbdo(ji,jj) = MIN( pt(ji,jj,jl) , pt_ups(ji,jj,jl) ) |
---|
[10425] | 1068 | ENDIF |
---|
| 1069 | END DO |
---|
[10413] | 1070 | END DO |
---|
[8586] | 1071 | |
---|
[10425] | 1072 | DO jj = 2, jpjm1 |
---|
| 1073 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1074 | ! |
---|
[10475] | 1075 | 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 |
---|
| 1076 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj), zbdo(ji+1,jj), zbdo(ji,jj-1), zbdo(ji,jj+1) ) |
---|
[10425] | 1077 | ! |
---|
[10475] | 1078 | zpos = MAX( 0._wp, pfu_ho(ji-1,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji ,jj ,jl) ) & ! positive/negative part of the flux |
---|
| 1079 | & + MAX( 0._wp, pfv_ho(ji ,jj-1,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj ,jl) ) |
---|
| 1080 | zneg = MAX( 0._wp, pfu_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfu_ho(ji-1,jj ,jl) ) & |
---|
| 1081 | & + MAX( 0._wp, pfv_ho(ji ,jj ,jl) ) - MIN( 0._wp, pfv_ho(ji ,jj-1,jl) ) |
---|
[10425] | 1082 | ! |
---|
[10475] | 1083 | 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) ) & |
---|
[10439] | 1084 | & ) * ( 1. - pamsk ) |
---|
[10475] | 1085 | 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) ) & |
---|
[10439] | 1086 | & ) * ( 1. - pamsk ) |
---|
[10425] | 1087 | ! |
---|
| 1088 | ! ! up & down beta terms |
---|
[10475] | 1089 | IF( zpos > 0._wp ) THEN ; zbetup(ji,jj,jl) = MAX( 0._wp, zup - pt_ups(ji,jj,jl) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
| 1090 | ELSE ; zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1091 | ENDIF |
---|
| 1092 | ! |
---|
[10475] | 1093 | IF( zneg > 0._wp ) THEN ; zbetdo(ji,jj,jl) = MAX( 0._wp, pt_ups(ji,jj,jl) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
| 1094 | ELSE ; zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1095 | ENDIF |
---|
| 1096 | ! |
---|
| 1097 | ! if all the points are outside ice cover |
---|
[10475] | 1098 | IF( zup == -zbig ) zbetup(ji,jj,jl) = 0._wp ! zbig |
---|
| 1099 | IF( zdo == zbig ) zbetdo(ji,jj,jl) = 0._wp ! zbig |
---|
[10425] | 1100 | ! |
---|
| 1101 | END DO |
---|
[8586] | 1102 | END DO |
---|
| 1103 | END DO |
---|
[10425] | 1104 | CALL lbc_lnk_multi( 'icedyn_adv_umx', zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
[8586] | 1105 | |
---|
[10413] | 1106 | |
---|
| 1107 | ! monotonic flux in the y direction |
---|
| 1108 | ! --------------------------------- |
---|
[10425] | 1109 | DO jl = 1, jpl |
---|
| 1110 | DO jj = 1, jpjm1 |
---|
| 1111 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1112 | zau = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji+1,jj,jl) ) |
---|
| 1113 | zbu = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji+1,jj,jl) ) |
---|
[10475] | 1114 | zcu = 0.5_wp + SIGN( 0.5_wp , pfu_ho(ji,jj,jl) ) |
---|
[10425] | 1115 | ! |
---|
| 1116 | zcoef = ( zcu * zau + ( 1._wp - zcu ) * zbu ) |
---|
[10439] | 1117 | ! |
---|
| 1118 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) * zcoef + pfu_ups(ji,jj,jl) |
---|
| 1119 | ! |
---|
[10425] | 1120 | END DO |
---|
[8637] | 1121 | END DO |
---|
[10413] | 1122 | |
---|
[10425] | 1123 | DO jj = 1, jpjm1 |
---|
| 1124 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
| 1125 | zav = MIN( 1._wp , zbetdo(ji,jj,jl) , zbetup(ji,jj+1,jl) ) |
---|
| 1126 | zbv = MIN( 1._wp , zbetup(ji,jj,jl) , zbetdo(ji,jj+1,jl) ) |
---|
[10475] | 1127 | zcv = 0.5_wp + SIGN( 0.5_wp , pfv_ho(ji,jj,jl) ) |
---|
[10425] | 1128 | ! |
---|
| 1129 | zcoef = ( zcv * zav + ( 1._wp - zcv ) * zbv ) |
---|
[10439] | 1130 | ! |
---|
| 1131 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) * zcoef + pfv_ups(ji,jj,jl) |
---|
| 1132 | ! |
---|
[10425] | 1133 | END DO |
---|
[8586] | 1134 | END DO |
---|
[10413] | 1135 | |
---|
[10425] | 1136 | ! clem test |
---|
[10439] | 1137 | !! DO jj = 2, jpjm1 |
---|
| 1138 | !! DO ji = 2, fs_jpim1 ! vector opt. |
---|
| 1139 | !! zzt = ( pt(ji,jj,jl) - ( pfu_ho(ji,jj,jl) - pfu_ho(ji-1,jj,jl) ) * pdt * r1_e1e2t(ji,jj) & |
---|
| 1140 | !! & - ( pfv_ho(ji,jj,jl) - pfv_ho(ji,jj-1,jl) ) * pdt * r1_e1e2t(ji,jj) & |
---|
| 1141 | !! & + pt(ji,jj,jl) * pdt * ( pu(ji,jj) - pu(ji-1,jj) ) * r1_e1e2t(ji,jj) * (1.-pamsk) & |
---|
| 1142 | !! & + pt(ji,jj,jl) * pdt * ( pv(ji,jj) - pv(ji,jj-1) ) * r1_e1e2t(ji,jj) * (1.-pamsk) & |
---|
| 1143 | !! & ) * tmask(ji,jj,1) |
---|
| 1144 | !! IF( zzt < -epsi20 ) THEN |
---|
[10519] | 1145 | !! WRITE(numout,*) 'T<0 nonosc_ice',zzt |
---|
[10439] | 1146 | !! ENDIF |
---|
| 1147 | !! END DO |
---|
| 1148 | !! END DO |
---|
[10425] | 1149 | |
---|
[10413] | 1150 | END DO |
---|
[8586] | 1151 | ! |
---|
[10519] | 1152 | END SUBROUTINE nonosc_ice |
---|
[8586] | 1153 | |
---|
[10446] | 1154 | |
---|
| 1155 | SUBROUTINE limiter_x( pdt, pu, pt, pfu_ups, pfu_ho ) |
---|
[10413] | 1156 | !!--------------------------------------------------------------------- |
---|
| 1157 | !! *** ROUTINE limiter_x *** |
---|
| 1158 | !! |
---|
| 1159 | !! ** Purpose : compute flux limiter |
---|
| 1160 | !!---------------------------------------------------------------------- |
---|
[10446] | 1161 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1162 | REAL(wp), DIMENSION(:,: ), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
| 1163 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1164 | REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pfu_ups ! upstream flux |
---|
| 1165 | REAL(wp), DIMENSION(:,:,:), INTENT(inout) :: pfu_ho ! high order flux |
---|
[10413] | 1166 | ! |
---|
| 1167 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1168 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1169 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpx ! tracer slopes |
---|
[10413] | 1170 | !!---------------------------------------------------------------------- |
---|
| 1171 | ! |
---|
[10425] | 1172 | DO jl = 1, jpl |
---|
| 1173 | DO jj = 2, jpjm1 |
---|
| 1174 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1175 | zslpx(ji,jj,jl) = ( pt(ji+1,jj,jl) - pt(ji,jj,jl) ) * umask(ji,jj,1) |
---|
| 1176 | END DO |
---|
[10413] | 1177 | END DO |
---|
| 1178 | END DO |
---|
[10425] | 1179 | CALL lbc_lnk( 'icedyn_adv_umx', zslpx, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1180 | |
---|
[10425] | 1181 | DO jl = 1, jpl |
---|
| 1182 | DO jj = 2, jpjm1 |
---|
| 1183 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1184 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
| 1185 | |
---|
| 1186 | Rjm = zslpx(ji-1,jj,jl) |
---|
| 1187 | Rj = zslpx(ji ,jj,jl) |
---|
| 1188 | Rjp = zslpx(ji+1,jj,jl) |
---|
[10413] | 1189 | |
---|
[10446] | 1190 | IF( kn_limiter == 3 ) THEN |
---|
[10413] | 1191 | |
---|
[10425] | 1192 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1193 | ELSE ; Rr = Rjp |
---|
| 1194 | ENDIF |
---|
[10413] | 1195 | |
---|
[10425] | 1196 | zh3 = pfu_ho(ji,jj,jl) - pfu_ups(ji,jj,jl) |
---|
| 1197 | IF( Rj > 0. ) THEN |
---|
| 1198 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1199 | & MIN( 2. * Rr * 0.5 * ABS(pu(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1200 | ELSE |
---|
| 1201 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pu(ji,jj)), & |
---|
| 1202 | & MIN(-2. * Rr * 0.5 * ABS(pu(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pu(ji,jj)) ) ) ) ) |
---|
| 1203 | ENDIF |
---|
| 1204 | pfu_ho(ji,jj,jl) = pfu_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1205 | |
---|
[10446] | 1206 | ELSEIF( kn_limiter == 2 ) THEN |
---|
[10425] | 1207 | IF( Rj /= 0. ) THEN |
---|
| 1208 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1209 | ELSE ; Cr = Rjp / Rj |
---|
| 1210 | ENDIF |
---|
| 1211 | ELSE |
---|
| 1212 | Cr = 0. |
---|
[10413] | 1213 | ENDIF |
---|
[10425] | 1214 | |
---|
| 1215 | ! -- superbee -- |
---|
| 1216 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1217 | ! -- van albada 2 -- |
---|
| 1218 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1219 | ! -- sweby (with beta=1) -- |
---|
| 1220 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1221 | ! -- van Leer -- |
---|
| 1222 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1223 | ! -- ospre -- |
---|
| 1224 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1225 | ! -- koren -- |
---|
| 1226 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1227 | ! -- charm -- |
---|
| 1228 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1229 | !ELSE ; zpsi = 0. |
---|
[10413] | 1230 | !ENDIF |
---|
[10425] | 1231 | ! -- van albada 1 -- |
---|
| 1232 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1233 | ! -- smart -- |
---|
| 1234 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1235 | ! -- umist -- |
---|
| 1236 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1237 | |
---|
[10425] | 1238 | ! high order flux corrected by the limiter |
---|
| 1239 | pfu_ho(ji,jj,jl) = pfu_ho(ji,jj,jl) - ABS( pu(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
[10413] | 1240 | |
---|
[10425] | 1241 | ENDIF |
---|
| 1242 | END DO |
---|
[10413] | 1243 | END DO |
---|
| 1244 | END DO |
---|
[10425] | 1245 | CALL lbc_lnk( 'icedyn_adv_umx', pfu_ho, 'U', -1.) ! lateral boundary cond. |
---|
[10413] | 1246 | ! |
---|
| 1247 | END SUBROUTINE limiter_x |
---|
| 1248 | |
---|
[10446] | 1249 | |
---|
| 1250 | SUBROUTINE limiter_y( pdt, pv, pt, pfv_ups, pfv_ho ) |
---|
[10413] | 1251 | !!--------------------------------------------------------------------- |
---|
| 1252 | !! *** ROUTINE limiter_y *** |
---|
| 1253 | !! |
---|
| 1254 | !! ** Purpose : compute flux limiter |
---|
| 1255 | !!---------------------------------------------------------------------- |
---|
[10446] | 1256 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
| 1257 | REAL(wp), DIMENSION (:,: ), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
| 1258 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pt ! ice tracer |
---|
| 1259 | REAL(wp), DIMENSION (:,:,:), INTENT(in ) :: pfv_ups ! upstream flux |
---|
| 1260 | REAL(wp), DIMENSION (:,:,:), INTENT(inout) :: pfv_ho ! high order flux |
---|
[10413] | 1261 | ! |
---|
| 1262 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
[10425] | 1263 | INTEGER :: ji, jj, jl ! dummy loop indices |
---|
| 1264 | REAL(wp), DIMENSION (jpi,jpj,jpl) :: zslpy ! tracer slopes |
---|
[10413] | 1265 | !!---------------------------------------------------------------------- |
---|
| 1266 | ! |
---|
[10425] | 1267 | DO jl = 1, jpl |
---|
| 1268 | DO jj = 2, jpjm1 |
---|
| 1269 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1270 | zslpy(ji,jj,jl) = ( pt(ji,jj+1,jl) - pt(ji,jj,jl) ) * vmask(ji,jj,1) |
---|
| 1271 | END DO |
---|
[10413] | 1272 | END DO |
---|
| 1273 | END DO |
---|
[10425] | 1274 | CALL lbc_lnk( 'icedyn_adv_umx', zslpy, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1275 | |
---|
[10425] | 1276 | DO jl = 1, jpl |
---|
| 1277 | DO jj = 2, jpjm1 |
---|
| 1278 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 1279 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
[10413] | 1280 | |
---|
[10425] | 1281 | Rjm = zslpy(ji,jj-1,jl) |
---|
| 1282 | Rj = zslpy(ji,jj ,jl) |
---|
| 1283 | Rjp = zslpy(ji,jj+1,jl) |
---|
[10413] | 1284 | |
---|
[10446] | 1285 | IF( kn_limiter == 3 ) THEN |
---|
[10413] | 1286 | |
---|
[10425] | 1287 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
| 1288 | ELSE ; Rr = Rjp |
---|
| 1289 | ENDIF |
---|
[10413] | 1290 | |
---|
[10425] | 1291 | zh3 = pfv_ho(ji,jj,jl) - pfv_ups(ji,jj,jl) |
---|
| 1292 | IF( Rj > 0. ) THEN |
---|
| 1293 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1294 | & MIN( 2. * Rr * 0.5 * ABS(pv(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1295 | ELSE |
---|
| 1296 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pv(ji,jj)), & |
---|
| 1297 | & MIN(-2. * Rr * 0.5 * ABS(pv(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pv(ji,jj)) ) ) ) ) |
---|
| 1298 | ENDIF |
---|
| 1299 | pfv_ho(ji,jj,jl) = pfv_ups(ji,jj,jl) + zlimiter |
---|
[10413] | 1300 | |
---|
[10446] | 1301 | ELSEIF( kn_limiter == 2 ) THEN |
---|
[10413] | 1302 | |
---|
[10425] | 1303 | IF( Rj /= 0. ) THEN |
---|
| 1304 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
| 1305 | ELSE ; Cr = Rjp / Rj |
---|
| 1306 | ENDIF |
---|
| 1307 | ELSE |
---|
| 1308 | Cr = 0. |
---|
| 1309 | ENDIF |
---|
[10413] | 1310 | |
---|
[10425] | 1311 | ! -- superbee -- |
---|
| 1312 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
| 1313 | ! -- van albada 2 -- |
---|
| 1314 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
| 1315 | ! -- sweby (with beta=1) -- |
---|
| 1316 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
| 1317 | ! -- van Leer -- |
---|
| 1318 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
| 1319 | ! -- ospre -- |
---|
| 1320 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
| 1321 | ! -- koren -- |
---|
| 1322 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
| 1323 | ! -- charm -- |
---|
| 1324 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
| 1325 | !ELSE ; zpsi = 0. |
---|
| 1326 | !ENDIF |
---|
| 1327 | ! -- van albada 1 -- |
---|
| 1328 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
| 1329 | ! -- smart -- |
---|
| 1330 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
| 1331 | ! -- umist -- |
---|
| 1332 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
[10413] | 1333 | |
---|
[10425] | 1334 | ! high order flux corrected by the limiter |
---|
| 1335 | pfv_ho(ji,jj,jl) = pfv_ho(ji,jj,jl) - ABS( pv(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
| 1336 | |
---|
| 1337 | ENDIF |
---|
| 1338 | END DO |
---|
[10413] | 1339 | END DO |
---|
| 1340 | END DO |
---|
[10425] | 1341 | CALL lbc_lnk( 'icedyn_adv_umx', pfv_ho, 'V', -1.) ! lateral boundary cond. |
---|
[10413] | 1342 | ! |
---|
| 1343 | END SUBROUTINE limiter_y |
---|
| 1344 | |
---|
[8586] | 1345 | #else |
---|
| 1346 | !!---------------------------------------------------------------------- |
---|
[9570] | 1347 | !! Default option Dummy module NO SI3 sea-ice model |
---|
[8586] | 1348 | !!---------------------------------------------------------------------- |
---|
| 1349 | #endif |
---|
| 1350 | |
---|
| 1351 | !!====================================================================== |
---|
| 1352 | END MODULE icedyn_adv_umx |
---|