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 : 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 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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36 | |
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37 | REAL(wp), DIMENSION(:,:), ALLOCATABLE :: z1_a, z1_a_ups, zua_ups, zva_ups |
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38 | |
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39 | ! alternate directions for upstream |
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40 | ! clem: it gives results for Lipscomb test that are the same as "ll_upsxy=false" |
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41 | ! clem: needs to be set to true in 2D when using prelimiter (otherwise "wavy solutions" are created) |
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42 | LOGICAL :: ll_upsxy = .TRUE. |
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43 | |
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44 | ! prelimiter |
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45 | ! clem: use it to avoid overshoot in H |
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46 | LOGICAL :: ll_prelimiter = .TRUE. |
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47 | LOGICAL :: ll_prelimiter_zalesak = .TRUE. ! from: Zalesak(1979) eq. 14 => better than Devore especially in 2D |
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48 | LOGICAL :: ll_prelimiter_devore = .FALSE. ! from: Devore eq. 11 |
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49 | |
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50 | ! iterate on the limiter (only nonosc) |
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51 | ! clem: useless |
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52 | LOGICAL :: ll_limiter_it2 = .FALSE. |
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53 | |
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54 | |
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55 | !! * Substitutions |
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56 | # include "vectopt_loop_substitute.h90" |
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57 | !!---------------------------------------------------------------------- |
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58 | !! NEMO/ICE 4.0 , NEMO Consortium (2018) |
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59 | !! $Id: icedyn_adv_umx.F90 4499 2014-02-18 15:14:31Z timgraham $ |
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60 | !! Software governed by the CeCILL licence (./LICENSE) |
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61 | !!---------------------------------------------------------------------- |
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62 | CONTAINS |
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63 | |
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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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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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75 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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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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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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93 | REAL(wp) :: zcfl , zdt |
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94 | REAL(wp) :: zeps = 0.0_wp ! shift in concentration to avoid division by 0 |
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95 | ! ! must be >= 0.01 and the best seems to be 0.1 |
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96 | REAL(wp), DIMENSION(jpi,jpj) :: zudy, zvdx, zcu_box, zcv_box, zua_ho, zva_ho, za_ups |
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97 | REAL(wp), DIMENSION(jpi,jpj) :: zh_i, zh_s, zs_i, zo_i, ze_i, ze_s, zh_ip |
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98 | !!---------------------------------------------------------------------- |
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99 | ! |
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100 | IF( kt == nit000 .AND. lwp ) WRITE(numout,*) '-- ice_dyn_adv_umx: Ultimate-Macho advection scheme' |
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101 | ! |
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102 | ! --- If ice drift field is too fast, use an appropriate time step for advection (CFL test for stability) --- ! |
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103 | zcfl = MAXVAL( ABS( pu_ice(:,:) ) * rdt_ice * r1_e1u(:,:) ) |
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104 | zcfl = MAX( zcfl, MAXVAL( ABS( pv_ice(:,:) ) * rdt_ice * r1_e2v(:,:) ) ) |
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105 | IF( lk_mpp ) CALL mpp_max( zcfl ) |
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106 | |
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107 | IF( zcfl > 0.5 ) THEN ; icycle = 2 |
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108 | ELSE ; icycle = 1 |
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109 | ENDIF |
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110 | |
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111 | zdt = rdt_ice / REAL(icycle) |
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112 | |
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113 | ! --- transport --- ! |
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114 | zudy(:,:) = pu_ice(:,:) * e2u(:,:) |
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115 | zvdx(:,:) = pv_ice(:,:) * e1v(:,:) |
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116 | |
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117 | ! --- define velocity for advection: u*grad(H) --- ! |
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118 | DO jj = 2, jpjm1 |
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119 | DO ji = fs_2, fs_jpim1 |
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120 | IF ( pu_ice(ji,jj) * pu_ice(ji-1,jj) <= 0._wp ) THEN ; zcu_box(ji,jj) = 0._wp |
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121 | ELSEIF( pu_ice(ji,jj) > 0._wp ) THEN ; zcu_box(ji,jj) = pu_ice(ji-1,jj) |
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122 | ELSE ; zcu_box(ji,jj) = pu_ice(ji ,jj) |
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123 | ENDIF |
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124 | |
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125 | IF ( pv_ice(ji,jj) * pv_ice(ji,jj-1) <= 0._wp ) THEN ; zcv_box(ji,jj) = 0._wp |
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126 | ELSEIF( pv_ice(ji,jj) > 0._wp ) THEN ; zcv_box(ji,jj) = pv_ice(ji,jj-1) |
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127 | ELSE ; zcv_box(ji,jj) = pv_ice(ji,jj ) |
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128 | ENDIF |
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129 | END DO |
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130 | END DO |
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131 | |
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132 | IF(.NOT. ALLOCATED(z1_a) ) ALLOCATE(z1_a (jpi,jpj)) |
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133 | IF(.NOT. ALLOCATED(z1_a_ups)) ALLOCATE(z1_a_ups(jpi,jpj)) |
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134 | IF(.NOT. ALLOCATED(zua_ups) ) ALLOCATE(zua_ups (jpi,jpj)) |
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135 | IF(.NOT. ALLOCATED(zva_ups) ) ALLOCATE(zva_ups (jpi,jpj)) |
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136 | !---------------! |
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137 | !== advection ==! |
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138 | !---------------! |
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139 | DO jt = 1, icycle |
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140 | |
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141 | zamsk = 1._wp ; zua_ups(:,:) = zudy(:,:) ; zva_ups(:,:) = zvdx(:,:) |
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142 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pato_i(:,:), pato_i(:,:), zua_ups, zva_ups, za_ups, zua_ho, zva_ho ) ! Open water area |
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143 | |
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144 | DO jl = 1, jpl |
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145 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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146 | pa_i(:,:,jl) = pa_i(:,:,jl) + zeps * tmask(:,:,1) |
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147 | ! |
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148 | WHERE( pa_i(:,:,jl) > epsi20 ) ; z1_a(:,:) = 1._wp / pa_i(:,:,jl) |
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149 | ELSEWHERE ; z1_a(:,:) = 0. |
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150 | END WHERE |
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151 | ! |
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152 | zamsk = 1._wp ; zua_ups(:,:) = zudy(:,:) ; zva_ups(:,:) = zvdx(:,:) |
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153 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pa_i(:,:,jl), pa_i(:,:,jl), zua_ups, zva_ups, za_ups, zua_ho, zva_ho ) ! Ice area |
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154 | |
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155 | ! 1/A_ups |
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156 | WHERE( za_ups(:,:) > epsi20 ) ; z1_a_ups(:,:) = 1._wp / za_ups(:,:) |
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157 | ELSEWHERE ; z1_a_ups(:,:) = 0. |
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158 | END WHERE |
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159 | |
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160 | !!zua_ho = zudy ; zva_ho = zvdx |
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161 | !!CALL adv_umx( kn_umx, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, pv_i(:,:,jl), pv_i(:,:,jl) ) |
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162 | zamsk = 0._wp ; zh_i(:,:) = pv_i (:,:,jl) * z1_a(:,:) |
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163 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, zh_i(:,:), pv_i (:,:,jl), zua_ups, zva_ups ) ! Ice volume |
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164 | zamsk = 0._wp ; zh_s(:,:) = pv_s (:,:,jl) * z1_a(:,:) |
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165 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, zh_s(:,:), pv_s (:,:,jl), zua_ups, zva_ups ) ! Snw volume |
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166 | zamsk = 0._wp ; zs_i(:,:) = psv_i(:,:,jl) * z1_a(:,:) |
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167 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, zs_i(:,:), psv_i(:,:,jl), zua_ups, zva_ups ) ! Salt content |
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168 | zamsk = 0._wp ; zo_i(:,:) = poa_i(:,:,jl) * z1_a(:,:) |
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169 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, zo_i(:,:), poa_i(:,:,jl), zua_ups, zva_ups ) ! Age content |
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170 | DO jk = 1, nlay_i |
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171 | zamsk = 0._wp ; ze_i(:,:) = pe_i(:,:,jk,jl) * z1_a(:,:) |
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172 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, ze_i(:,:), pe_i(:,:,jk,jl), zua_ups, zva_ups ) ! Ice heat content |
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173 | END DO |
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174 | DO jk = 1, nlay_s |
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175 | zamsk = 0._wp ; ze_s(:,:) = pe_s(:,:,jk,jl) * z1_a(:,:) |
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176 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho, zva_ho, zcu_box, zcv_box, ze_s(:,:), pe_s(:,:,jk,jl), zua_ups, zva_ups ) ! Snw heat content |
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177 | END DO |
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178 | ! |
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179 | IF ( ln_pnd_H12 ) THEN ! melt ponds (must be the last ones to be advected because of z1_a...) |
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180 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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181 | pa_ip(:,:,jl) = pa_ip(:,:,jl) + zeps * tmask(:,:,1) |
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182 | ! |
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183 | WHERE( pa_ip(:,:,jl) > epsi20 ) ; z1_a(:,:) = 1._wp / pa_ip(:,:,jl) |
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184 | ELSEWHERE ; z1_a(:,:) = 0. |
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185 | END WHERE |
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186 | ! |
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187 | zamsk = 1._wp ; zua_ups(:,:) = zudy(:,:) ; zva_ups(:,:) = zvdx(:,:) |
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188 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zudy, zvdx, zcu_box, zcv_box, pa_ip(:,:,jl), pa_ip(:,:,jl), zua_ups, zva_ups, za_ups, zua_ho, zva_ho ) ! mp fraction |
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189 | |
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190 | ! 1/A_ups |
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191 | WHERE( za_ups(:,:) > epsi20 ) ; z1_a_ups(:,:) = 1._wp / za_ups(:,:) |
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192 | ELSEWHERE ; z1_a_ups(:,:) = 0. |
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193 | END WHERE |
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194 | |
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195 | zamsk = 0._wp ; zh_ip(:,:) = pv_ip(:,:,jl) * z1_a(:,:) |
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196 | CALL adv_umx( zamsk, kn_umx, jt, kt, zdt, zudy, zvdx, zua_ho , zva_ho , zcu_box, zcv_box, zh_ip(:,:), pv_ip(:,:,jl), zua_ups, zva_ups ) ! mp volume |
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197 | ENDIF |
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198 | ! |
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199 | ! to avoid a problem with the limiter nonosc when A gets close to 0 |
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200 | DO jj = 2, jpjm1 |
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201 | DO ji = fs_2, fs_jpim1 |
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202 | !pa_i(ji,jj,jl) = ( pa_i(ji,jj,jl) - zeps ) * tmask(ji,jj,1) |
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203 | pa_i(ji,jj,jl) = ( pa_i(ji,jj,jl) - zeps & |
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204 | & + zeps * ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) )*r1_e1e2t(ji,jj)*zdt & |
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205 | & ) * tmask(ji,jj,1) |
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206 | IF ( ln_pnd_H12 ) THEN ! melt ponds |
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207 | pa_ip(ji,jj,jl) = ( pa_ip(ji,jj,jl) - zeps & |
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208 | & + zeps * ( zudy(ji,jj) - zudy(ji-1,jj) + zvdx(ji,jj) - zvdx(ji,jj-1) )*r1_e1e2t(ji,jj)*zdt & |
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209 | & ) * tmask(ji,jj,1) |
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210 | ENDIF |
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211 | END DO |
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212 | END DO |
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213 | CALL lbc_lnk_multi( pa_i(:,:,jl), 'T', 1., pa_ip(:,:,jl), 'T', 1. ) |
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214 | ! |
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215 | END DO |
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216 | |
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217 | END DO |
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218 | ! |
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219 | END SUBROUTINE ice_dyn_adv_umx |
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220 | |
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221 | |
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222 | SUBROUTINE adv_umx( pamsk, kn_umx, jt, kt, pdt, pu, pv, puc, pvc, pubox, pvbox, pt, ptc, pua_ups, pva_ups, pa_ups, pua_ho, pva_ho ) |
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223 | !!---------------------------------------------------------------------- |
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224 | !! *** ROUTINE adv_umx *** |
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225 | !! |
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226 | !! ** Purpose : Compute the now trend due to total advection of |
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227 | !! tracers and add it to the general trend of tracer equations |
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228 | !! |
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229 | !! ** Method : TVD scheme, i.e. 2nd order centered scheme with |
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230 | !! corrected flux (monotonic correction) |
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231 | !! note: - this advection scheme needs a leap-frog time scheme |
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232 | !! |
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233 | !! ** Action : - pt the after advective tracer |
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234 | !!---------------------------------------------------------------------- |
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235 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
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236 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
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237 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
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238 | INTEGER , INTENT(in ) :: kt ! number of iteration |
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239 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
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240 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu , pv ! 2 ice velocity components => u*e2 |
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241 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc , pvc ! 2 ice velocity components => u*e2 or u*a*e2u |
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242 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
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243 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer field |
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244 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: ptc ! tracer content field |
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245 | REAL(wp), DIMENSION(jpi,jpj), INTENT(inout) :: pua_ups, pva_ups ! upstream u*a fluxes or u |
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246 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pa_ups ! concentration advected upstream |
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247 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out), OPTIONAL :: pua_ho, pva_ho ! high order u*a fluxes |
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248 | ! |
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249 | INTEGER :: ji, jj ! dummy loop indices |
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250 | REAL(wp) :: ztra ! local scalar |
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251 | INTEGER :: kn_limiter = 1 ! 1=nonosc ; 2=superbee ; 3=h3(rachid) |
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252 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ho , zfv_ho , zt_u, zt_v, zpt |
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253 | REAL(wp), DIMENSION(jpi,jpj) :: zfu_ups, zfv_ups, zt_ups ! only for nonosc |
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254 | !!---------------------------------------------------------------------- |
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255 | ! |
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256 | ! upstream (_ups) advection with initial mass fluxes |
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257 | ! --------------------------------------------------- |
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258 | IF( .NOT. ll_upsxy ) THEN |
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259 | |
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260 | ! fluxes |
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261 | DO jj = 1, jpjm1 |
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262 | DO ji = 1, fs_jpim1 |
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263 | zfu_ups(ji,jj) = MAX( pua_ups(ji,jj), 0._wp ) * pt(ji,jj) + MIN( pua_ups(ji,jj), 0._wp ) * pt(ji+1,jj) |
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264 | zfv_ups(ji,jj) = MAX( pva_ups(ji,jj), 0._wp ) * pt(ji,jj) + MIN( pva_ups(ji,jj), 0._wp ) * pt(ji,jj+1) |
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265 | END DO |
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266 | END DO |
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267 | |
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268 | ELSE |
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269 | ! 1 if advection of A |
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270 | ! z1_a_ups already defined IF advection of other tracers |
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271 | IF( pamsk == 1. ) z1_a_ups(:,:) = 1._wp |
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272 | ! |
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273 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
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274 | ! flux in x-direction |
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275 | DO jj = 1, jpjm1 |
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276 | DO ji = 1, fs_jpim1 |
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277 | zfu_ups(ji,jj) = MAX( pua_ups(ji,jj), 0._wp ) * pt(ji,jj) + MIN( pua_ups(ji,jj), 0._wp ) * pt(ji+1,jj) |
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278 | END DO |
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279 | END DO |
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280 | ! first guess of tracer content from u-flux |
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281 | DO jj = 2, jpjm1 |
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282 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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283 | zpt(ji,jj) = ( ptc(ji,jj) - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj) ) * pdt * r1_e1e2t(ji,jj) ) & |
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284 | & * tmask(ji,jj,1) * z1_a_ups(ji,jj) |
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285 | END DO |
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286 | END DO |
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287 | CALL lbc_lnk( zpt, 'T', 1. ) |
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288 | ! |
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289 | ! flux in y-direction |
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290 | DO jj = 1, jpjm1 |
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291 | DO ji = 1, fs_jpim1 |
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292 | zfv_ups(ji,jj) = MAX( pva_ups(ji,jj), 0._wp ) * zpt(ji,jj) + MIN( pva_ups(ji,jj), 0._wp ) * zpt(ji,jj+1) |
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293 | END DO |
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294 | END DO |
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295 | ! |
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296 | ELSE !== even ice time step: adv_y then adv_x ==! |
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297 | ! flux in y-direction |
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298 | DO jj = 1, jpjm1 |
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299 | DO ji = 1, fs_jpim1 |
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300 | zfv_ups(ji,jj) = MAX( pva_ups(ji,jj), 0._wp ) * pt(ji,jj) + MIN( pva_ups(ji,jj), 0._wp ) * pt(ji,jj+1) |
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301 | END DO |
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302 | END DO |
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303 | ! first guess of tracer content from v-flux |
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304 | DO jj = 2, jpjm1 |
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305 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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306 | zpt(ji,jj) = ( ptc(ji,jj) - ( zfv_ups(ji,jj) - zfv_ups(ji,jj-1) ) * pdt * r1_e1e2t(ji,jj) ) & |
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307 | & * tmask(ji,jj,1) * z1_a_ups(ji,jj) |
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308 | END DO |
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309 | END DO |
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310 | CALL lbc_lnk( zpt, 'T', 1. ) |
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311 | ! |
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312 | ! flux in x-direction |
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313 | DO jj = 1, jpjm1 |
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314 | DO ji = 1, fs_jpim1 |
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315 | zfu_ups(ji,jj) = MAX( pua_ups(ji,jj), 0._wp ) * zpt(ji,jj) + MIN( pua_ups(ji,jj), 0._wp ) * zpt(ji+1,jj) |
---|
316 | END DO |
---|
317 | END DO |
---|
318 | ! |
---|
319 | ENDIF |
---|
320 | |
---|
321 | ENDIF |
---|
322 | ! guess after content field with upstream scheme |
---|
323 | DO jj = 2, jpjm1 |
---|
324 | DO ji = fs_2, fs_jpim1 |
---|
325 | ztra = - ( zfu_ups(ji,jj) - zfu_ups(ji-1,jj ) & |
---|
326 | & + zfv_ups(ji,jj) - zfv_ups(ji ,jj-1) ) * r1_e1e2t(ji,jj) |
---|
327 | zt_ups(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
---|
328 | END DO |
---|
329 | END DO |
---|
330 | CALL lbc_lnk( zt_ups, 'T', 1. ) |
---|
331 | |
---|
332 | ! High order (_ho) fluxes |
---|
333 | ! ----------------------- |
---|
334 | SELECT CASE( kn_umx ) |
---|
335 | ! |
---|
336 | CASE ( 20 ) !== centered second order ==! |
---|
337 | ! |
---|
338 | CALL cen2( kn_limiter, jt, kt, pdt, pt, pu, pv, puc, pvc, ptc, zfu_ho, zfv_ho, & |
---|
339 | & zt_ups, zfu_ups, zfv_ups ) |
---|
340 | ! |
---|
341 | CASE ( 1:5 ) !== 1st to 5th order ULTIMATE-MACHO scheme ==! |
---|
342 | ! |
---|
343 | CALL macho( pamsk, kn_limiter, kn_umx, jt, kt, pdt, pt, pu, pv, puc, pvc, pubox, pvbox, ptc, zt_u, zt_v, zfu_ho, zfv_ho, & |
---|
344 | & zt_ups, zfu_ups, zfv_ups ) |
---|
345 | ! |
---|
346 | END SELECT |
---|
347 | |
---|
348 | ! output upstream trend of concentration and high order fluxes |
---|
349 | ! ------------------------------------------------------------ |
---|
350 | IF( pamsk == 1. ) THEN |
---|
351 | ! upstream trend of concentration |
---|
352 | pa_ups(:,:) = zt_ups(:,:) |
---|
353 | ! upstream and high order u*a |
---|
354 | DO jj = 1, jpjm1 |
---|
355 | DO ji = 1, fs_jpim1 |
---|
356 | pua_ups(ji,jj) = zfu_ups(ji,jj) |
---|
357 | pva_ups(ji,jj) = zfv_ups(ji,jj) |
---|
358 | pua_ho (ji,jj) = zfu_ho (ji,jj) |
---|
359 | pva_ho (ji,jj) = zfv_ho (ji,jj) |
---|
360 | END DO |
---|
361 | END DO |
---|
362 | !!CALL lbc_lnk( pua_ho, 'U', -1. ) ! clem: not needed I think |
---|
363 | !!CALL lbc_lnk( pva_ho, 'V', -1. ) |
---|
364 | ENDIF |
---|
365 | |
---|
366 | ! final trend with corrected fluxes |
---|
367 | ! ------------------------------------ |
---|
368 | DO jj = 2, jpjm1 |
---|
369 | DO ji = fs_2, fs_jpim1 |
---|
370 | ztra = ( - ( zfu_ho(ji,jj) - zfu_ho(ji-1,jj) + zfv_ho(ji,jj) - zfv_ho(ji,jj-1) ) & ! Div(uaH) or Div(ua) |
---|
371 | & ) * r1_e1e2t(ji,jj) |
---|
372 | ptc(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
---|
373 | END DO |
---|
374 | END DO |
---|
375 | CALL lbc_lnk( ptc, 'T', 1. ) |
---|
376 | ! |
---|
377 | END SUBROUTINE adv_umx |
---|
378 | |
---|
379 | SUBROUTINE cen2( kn_limiter, jt, kt, pdt, pt, pu, pv, puc, pvc, ptc, pfu_ho, pfv_ho, & |
---|
380 | & pt_ups, pfu_ups, pfv_ups ) |
---|
381 | !!--------------------------------------------------------------------- |
---|
382 | !! *** ROUTINE macho *** |
---|
383 | !! |
---|
384 | !! ** Purpose : compute |
---|
385 | !! |
---|
386 | !! ** Method : ... ??? |
---|
387 | !! TIM = transient interpolation Modeling |
---|
388 | !! |
---|
389 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
390 | !!---------------------------------------------------------------------- |
---|
391 | INTEGER , INTENT(in ) :: kn_limiter ! limiter |
---|
392 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
393 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
394 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
395 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
396 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
397 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity * A components |
---|
398 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer content at before time step |
---|
399 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
400 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt_ups ! upstream guess of tracer content |
---|
401 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
402 | ! |
---|
403 | INTEGER :: ji, jj ! dummy loop indices |
---|
404 | LOGICAL :: ll_xy = .TRUE. |
---|
405 | REAL(wp), DIMENSION(jpi,jpj) :: zzt |
---|
406 | !!---------------------------------------------------------------------- |
---|
407 | ! |
---|
408 | IF( .NOT.ll_xy ) THEN !-- no alternate directions --! |
---|
409 | ! |
---|
410 | DO jj = 1, jpjm1 |
---|
411 | DO ji = 1, fs_jpim1 |
---|
412 | pfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( pt(ji,jj) + pt(ji+1,jj) ) |
---|
413 | pfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( pt(ji,jj) + pt(ji,jj+1) ) |
---|
414 | END DO |
---|
415 | END DO |
---|
416 | IF ( kn_limiter == 1 ) THEN |
---|
417 | CALL nonosc_2d( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
418 | ELSEIF( kn_limiter == 2 ) THEN |
---|
419 | CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
420 | CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
421 | ELSEIF( kn_limiter == 3 ) THEN |
---|
422 | CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
423 | CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
424 | ENDIF |
---|
425 | ! |
---|
426 | ELSE !-- alternate directions --! |
---|
427 | ! |
---|
428 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
429 | ! |
---|
430 | ! flux in x-direction |
---|
431 | DO jj = 1, jpjm1 |
---|
432 | DO ji = 1, fs_jpim1 |
---|
433 | pfu_ho(ji,jj) = 0.5 * puc(ji,jj) * ( pt(ji,jj) + pt(ji+1,jj) ) |
---|
434 | END DO |
---|
435 | END DO |
---|
436 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
437 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
438 | |
---|
439 | ! first guess of tracer content from u-flux |
---|
440 | DO jj = 2, jpjm1 |
---|
441 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
442 | zzt(ji,jj) = ( ptc(ji,jj) - ( pfu_ho(ji,jj) - pfu_ho(ji-1,jj) ) * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
443 | END DO |
---|
444 | END DO |
---|
445 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
446 | |
---|
447 | ! flux in y-direction |
---|
448 | DO jj = 1, jpjm1 |
---|
449 | DO ji = 1, fs_jpim1 |
---|
450 | pfv_ho(ji,jj) = 0.5 * pv(ji,jj) * ( zzt(ji,jj) + zzt(ji,jj+1) ) |
---|
451 | END DO |
---|
452 | END DO |
---|
453 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
454 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
455 | |
---|
456 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
457 | ! |
---|
458 | ! flux in y-direction |
---|
459 | DO jj = 1, jpjm1 |
---|
460 | DO ji = 1, fs_jpim1 |
---|
461 | pfv_ho(ji,jj) = 0.5 * pvc(ji,jj) * ( pt(ji,jj) + pt(ji,jj+1) ) |
---|
462 | END DO |
---|
463 | END DO |
---|
464 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
465 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
466 | ! |
---|
467 | ! first guess of tracer content from v-flux |
---|
468 | DO jj = 2, jpjm1 |
---|
469 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
470 | zzt(ji,jj) = ( ptc(ji,jj) - ( pfv_ho(ji,jj) - pfv_ho(ji,jj-1) ) * pdt * r1_e1e2t(ji,jj) ) * tmask(ji,jj,1) |
---|
471 | END DO |
---|
472 | END DO |
---|
473 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
474 | ! |
---|
475 | ! flux in x-direction |
---|
476 | DO jj = 1, jpjm1 |
---|
477 | DO ji = 1, fs_jpim1 |
---|
478 | pfu_ho(ji,jj) = 0.5 * pu(ji,jj) * ( zzt(ji,jj) + zzt(ji+1,jj) ) |
---|
479 | END DO |
---|
480 | END DO |
---|
481 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
482 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
483 | |
---|
484 | ENDIF |
---|
485 | IF( kn_limiter == 1 ) CALL nonosc_2d( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
486 | |
---|
487 | ENDIF |
---|
488 | |
---|
489 | END SUBROUTINE cen2 |
---|
490 | |
---|
491 | |
---|
492 | SUBROUTINE macho( pamsk, kn_limiter, kn_umx, jt, kt, pdt, pt, pu, pv, puc, pvc, pubox, pvbox, ptc, pt_u, pt_v, pfu_ho, pfv_ho, & |
---|
493 | & pt_ups, pfu_ups, pfv_ups ) |
---|
494 | !!--------------------------------------------------------------------- |
---|
495 | !! *** ROUTINE macho *** |
---|
496 | !! |
---|
497 | !! ** Purpose : compute |
---|
498 | !! |
---|
499 | !! ** Method : ... ??? |
---|
500 | !! TIM = transient interpolation Modeling |
---|
501 | !! |
---|
502 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
503 | !!---------------------------------------------------------------------- |
---|
504 | REAL(wp) , INTENT(in ) :: pamsk ! advection of concentration (1) or other tracers (0) |
---|
505 | INTEGER , INTENT(in ) :: kn_limiter ! limiter |
---|
506 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
507 | INTEGER , INTENT(in ) :: jt ! number of sub-iteration |
---|
508 | INTEGER , INTENT(in ) :: kt ! number of iteration |
---|
509 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
510 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
511 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu, pv ! 2 ice velocity components |
---|
512 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc, pvc ! 2 ice velocity * A components |
---|
513 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pubox, pvbox ! upstream velocity |
---|
514 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ptc ! tracer content at before time step |
---|
515 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u, pt_v ! tracer at u- and v-points |
---|
516 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho, pfv_ho ! high order fluxes |
---|
517 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt_ups ! upstream guess of tracer content |
---|
518 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pfu_ups, pfv_ups ! upstream fluxes |
---|
519 | ! |
---|
520 | INTEGER :: ji, jj ! dummy loop indices |
---|
521 | REAL(wp) :: ztra |
---|
522 | REAL(wp), DIMENSION(jpi,jpj) :: zzt, zzfu_ho, zzfv_ho |
---|
523 | !!---------------------------------------------------------------------- |
---|
524 | ! |
---|
525 | IF( MOD( (kt - 1) / nn_fsbc , 2 ) == MOD( (jt - 1) , 2 ) ) THEN !== odd ice time step: adv_x then adv_y ==! |
---|
526 | ! |
---|
527 | ! !-- ultimate interpolation of pt at u-point --! |
---|
528 | CALL ultimate_x( kn_umx, pdt, pt, pu, puc, pt_u, pfu_ho ) |
---|
529 | ! !-- limiter in x --! |
---|
530 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
531 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
532 | ! !-- advective form update in zzt --! |
---|
533 | DO jj = 2, jpjm1 |
---|
534 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
535 | zzt(ji,jj) = pt(ji,jj) - pubox(ji,jj) * pdt * ( pt_u(ji,jj) - pt_u(ji-1,jj) ) * r1_e1t(ji,jj) & |
---|
536 | & - pt (ji,jj) * pdt * ( pu (ji,jj) - pu (ji-1,jj) ) * r1_e1e2t(ji,jj) * pamsk |
---|
537 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
---|
538 | END DO |
---|
539 | END DO |
---|
540 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
541 | ! !-- ultimate interpolation of pt at v-point --! |
---|
542 | CALL ultimate_y( kn_umx, pdt, zzt, pv, pvc, pt_v, pfv_ho ) |
---|
543 | ! !-- limiter in y --! |
---|
544 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
545 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
546 | ! |
---|
547 | ELSE !== even ice time step: adv_y then adv_x ==! |
---|
548 | ! |
---|
549 | ! !-- ultimate interpolation of pt at v-point --! |
---|
550 | CALL ultimate_y( kn_umx, pdt, pt, pv, pvc, pt_v, pfv_ho ) |
---|
551 | ! !-- limiter in y --! |
---|
552 | IF( kn_limiter == 2 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho ) |
---|
553 | IF( kn_limiter == 3 ) CALL limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
554 | ! !-- advective form update in zzt --! |
---|
555 | DO jj = 2, jpjm1 |
---|
556 | DO ji = fs_2, fs_jpim1 |
---|
557 | zzt(ji,jj) = pt(ji,jj) - pvbox(ji,jj) * pdt * ( pt_v(ji,jj) - pt_v(ji,jj-1) ) * r1_e2t(ji,jj) & |
---|
558 | & - pt (ji,jj) * pdt * ( pv (ji,jj) - pv (ji,jj-1) ) * r1_e1e2t(ji,jj) * pamsk |
---|
559 | zzt(ji,jj) = zzt(ji,jj) * tmask(ji,jj,1) |
---|
560 | END DO |
---|
561 | END DO |
---|
562 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
563 | ! !-- ultimate interpolation of pt at u-point --! |
---|
564 | CALL ultimate_x( kn_umx, pdt, zzt, pu, puc, pt_u, pfu_ho ) |
---|
565 | ! !-- limiter in x --! |
---|
566 | IF( kn_limiter == 2 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho ) |
---|
567 | IF( kn_limiter == 3 ) CALL limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
568 | ! |
---|
569 | ENDIF |
---|
570 | IF( kn_limiter == 1 ) THEN |
---|
571 | IF( .NOT. ll_limiter_it2 ) THEN |
---|
572 | CALL nonosc_2d ( pdt, ptc, pt_ups, pfu_ups, pfv_ups, pfu_ho, pfv_ho ) |
---|
573 | ELSE |
---|
574 | zzfu_ho(:,:) = pfu_ho(:,:) |
---|
575 | zzfv_ho(:,:) = pfv_ho(:,:) |
---|
576 | ! 1st iteration of nonosc (limit the flux with the upstream solution) |
---|
577 | CALL nonosc_2d ( pdt, ptc, pt_ups, pfu_ups, pfv_ups, zzfu_ho, zzfv_ho ) |
---|
578 | ! guess after content field with high order |
---|
579 | DO jj = 2, jpjm1 |
---|
580 | DO ji = fs_2, fs_jpim1 |
---|
581 | ztra = - ( zzfu_ho(ji,jj) - zzfu_ho(ji-1,jj) + zzfv_ho(ji,jj) - zzfv_ho(ji,jj-1) ) * r1_e1e2t(ji,jj) |
---|
582 | zzt(ji,jj) = ( ptc(ji,jj) + pdt * ztra ) * tmask(ji,jj,1) |
---|
583 | END DO |
---|
584 | END DO |
---|
585 | CALL lbc_lnk( zzt, 'T', 1. ) |
---|
586 | ! 2nd iteration of nonosc (limit the flux with the limited high order solution) |
---|
587 | CALL nonosc_2d ( pdt, ptc, zzt, zzfu_ho, zzfv_ho, pfu_ho, pfv_ho ) |
---|
588 | ENDIF |
---|
589 | ENDIF |
---|
590 | ! |
---|
591 | END SUBROUTINE macho |
---|
592 | |
---|
593 | |
---|
594 | SUBROUTINE ultimate_x( kn_umx, pdt, pt, pu, puc, pt_u, pfu_ho ) |
---|
595 | !!--------------------------------------------------------------------- |
---|
596 | !! *** ROUTINE ultimate_x *** |
---|
597 | !! |
---|
598 | !! ** Purpose : compute |
---|
599 | !! |
---|
600 | !! ** Method : ... ??? |
---|
601 | !! TIM = transient interpolation Modeling |
---|
602 | !! |
---|
603 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
604 | !!---------------------------------------------------------------------- |
---|
605 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
606 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
607 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pu ! ice i-velocity component |
---|
608 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: puc ! ice i-velocity * A component |
---|
609 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
610 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_u ! tracer at u-point |
---|
611 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfu_ho ! high order flux |
---|
612 | ! |
---|
613 | INTEGER :: ji, jj ! dummy loop indices |
---|
614 | REAL(wp) :: zcu, zdx2, zdx4 ! - - |
---|
615 | REAL(wp), DIMENSION(jpi,jpj) :: ztu1, ztu2, ztu3, ztu4 |
---|
616 | !!---------------------------------------------------------------------- |
---|
617 | ! |
---|
618 | ! !-- Laplacian in i-direction --! |
---|
619 | DO jj = 2, jpjm1 ! First derivative (gradient) |
---|
620 | DO ji = 1, fs_jpim1 |
---|
621 | ztu1(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
622 | END DO |
---|
623 | ! ! Second derivative (Laplacian) |
---|
624 | DO ji = fs_2, fs_jpim1 |
---|
625 | ztu2(ji,jj) = ( ztu1(ji,jj) - ztu1(ji-1,jj) ) * r1_e1t(ji,jj) |
---|
626 | END DO |
---|
627 | END DO |
---|
628 | CALL lbc_lnk( ztu2, 'T', 1. ) |
---|
629 | ! |
---|
630 | ! !-- BiLaplacian in i-direction --! |
---|
631 | DO jj = 2, jpjm1 ! Third derivative |
---|
632 | DO ji = 1, fs_jpim1 |
---|
633 | ztu3(ji,jj) = ( ztu2(ji+1,jj) - ztu2(ji,jj) ) * r1_e1u(ji,jj) * umask(ji,jj,1) |
---|
634 | END DO |
---|
635 | ! ! Fourth derivative |
---|
636 | DO ji = fs_2, fs_jpim1 |
---|
637 | ztu4(ji,jj) = ( ztu3(ji,jj) - ztu3(ji-1,jj) ) * r1_e1t(ji,jj) |
---|
638 | END DO |
---|
639 | END DO |
---|
640 | CALL lbc_lnk( ztu4, 'T', 1. ) |
---|
641 | ! |
---|
642 | ! |
---|
643 | SELECT CASE (kn_umx ) |
---|
644 | ! |
---|
645 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
646 | ! |
---|
647 | DO jj = 2, jpjm1 |
---|
648 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
649 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
650 | & - SIGN( 1._wp, pu(ji,jj) ) * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
651 | END DO |
---|
652 | END DO |
---|
653 | ! |
---|
654 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
655 | ! |
---|
656 | DO jj = 2, jpjm1 |
---|
657 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
658 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
659 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( pt(ji+1,jj) + pt(ji,jj) & |
---|
660 | & - zcu * ( pt(ji+1,jj) - pt(ji,jj) ) ) |
---|
661 | END DO |
---|
662 | END DO |
---|
663 | ! |
---|
664 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
665 | ! |
---|
666 | DO jj = 2, jpjm1 |
---|
667 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
668 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
669 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
670 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
671 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
672 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
673 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
674 | & - SIGN( 1._wp, zcu ) * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
675 | END DO |
---|
676 | END DO |
---|
677 | ! |
---|
678 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
679 | ! |
---|
680 | DO jj = 2, jpjm1 |
---|
681 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
682 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
683 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
684 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
685 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
686 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
687 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
688 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) ) |
---|
689 | END DO |
---|
690 | END DO |
---|
691 | ! |
---|
692 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
693 | ! |
---|
694 | DO jj = 2, jpjm1 |
---|
695 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
696 | zcu = pu(ji,jj) * r1_e2u(ji,jj) * pdt * r1_e1u(ji,jj) |
---|
697 | zdx2 = e1u(ji,jj) * e1u(ji,jj) |
---|
698 | !!rachid zdx2 = e1u(ji,jj) * e1t(ji,jj) |
---|
699 | zdx4 = zdx2 * zdx2 |
---|
700 | pt_u(ji,jj) = 0.5_wp * umask(ji,jj,1) * ( ( pt (ji+1,jj) + pt (ji,jj) & |
---|
701 | & - zcu * ( pt (ji+1,jj) - pt (ji,jj) ) ) & |
---|
702 | & + z1_6 * zdx2 * ( zcu*zcu - 1._wp ) * ( ztu2(ji+1,jj) + ztu2(ji,jj) & |
---|
703 | & - 0.5_wp * zcu * ( ztu2(ji+1,jj) - ztu2(ji,jj) ) ) & |
---|
704 | & + z1_120 * zdx4 * ( zcu*zcu - 1._wp ) * ( zcu*zcu - 4._wp ) * ( ztu4(ji+1,jj) + ztu4(ji,jj) & |
---|
705 | & - SIGN( 1._wp, zcu ) * ( ztu4(ji+1,jj) - ztu4(ji,jj) ) ) ) |
---|
706 | END DO |
---|
707 | END DO |
---|
708 | ! |
---|
709 | END SELECT |
---|
710 | ! !-- High order flux in i-direction --! |
---|
711 | DO jj = 1, jpjm1 |
---|
712 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
713 | pfu_ho(ji,jj) = puc(ji,jj) * pt_u(ji,jj) |
---|
714 | END DO |
---|
715 | END DO |
---|
716 | ! |
---|
717 | END SUBROUTINE ultimate_x |
---|
718 | |
---|
719 | |
---|
720 | SUBROUTINE ultimate_y( kn_umx, pdt, pt, pv, pvc, pt_v, pfv_ho ) |
---|
721 | !!--------------------------------------------------------------------- |
---|
722 | !! *** ROUTINE ultimate_y *** |
---|
723 | !! |
---|
724 | !! ** Purpose : compute |
---|
725 | !! |
---|
726 | !! ** Method : ... ??? |
---|
727 | !! TIM = transient interpolation Modeling |
---|
728 | !! |
---|
729 | !! Reference : Leonard, B.P., 1991, Comput. Methods Appl. Mech. Eng., 88, 17-74. |
---|
730 | !!---------------------------------------------------------------------- |
---|
731 | INTEGER , INTENT(in ) :: kn_umx ! order of the scheme (1-5=UM or 20=CEN2) |
---|
732 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
733 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pv ! ice j-velocity component |
---|
734 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pvc ! ice j-velocity*A component |
---|
735 | REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: pt ! tracer fields |
---|
736 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pt_v ! tracer at v-point |
---|
737 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out) :: pfv_ho ! high order flux |
---|
738 | ! |
---|
739 | INTEGER :: ji, jj ! dummy loop indices |
---|
740 | REAL(wp) :: zcv, zdy2, zdy4 ! - - |
---|
741 | REAL(wp), DIMENSION(jpi,jpj) :: ztv1, ztv2, ztv3, ztv4 |
---|
742 | !!---------------------------------------------------------------------- |
---|
743 | ! |
---|
744 | ! !-- Laplacian in j-direction --! |
---|
745 | DO jj = 1, jpjm1 ! First derivative (gradient) |
---|
746 | DO ji = fs_2, fs_jpim1 |
---|
747 | ztv1(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
748 | END DO |
---|
749 | END DO |
---|
750 | DO jj = 2, jpjm1 ! Second derivative (Laplacian) |
---|
751 | DO ji = fs_2, fs_jpim1 |
---|
752 | ztv2(ji,jj) = ( ztv1(ji,jj) - ztv1(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
753 | END DO |
---|
754 | END DO |
---|
755 | CALL lbc_lnk( ztv2, 'T', 1. ) |
---|
756 | ! |
---|
757 | ! !-- BiLaplacian in j-direction --! |
---|
758 | DO jj = 1, jpjm1 ! First derivative |
---|
759 | DO ji = fs_2, fs_jpim1 |
---|
760 | ztv3(ji,jj) = ( ztv2(ji,jj+1) - ztv2(ji,jj) ) * r1_e2v(ji,jj) * vmask(ji,jj,1) |
---|
761 | END DO |
---|
762 | END DO |
---|
763 | DO jj = 2, jpjm1 ! Second derivative |
---|
764 | DO ji = fs_2, fs_jpim1 |
---|
765 | ztv4(ji,jj) = ( ztv3(ji,jj) - ztv3(ji,jj-1) ) * r1_e2t(ji,jj) |
---|
766 | END DO |
---|
767 | END DO |
---|
768 | CALL lbc_lnk( ztv4, 'T', 1. ) |
---|
769 | ! |
---|
770 | ! |
---|
771 | SELECT CASE (kn_umx ) |
---|
772 | ! |
---|
773 | CASE( 1 ) !== 1st order central TIM ==! (Eq. 21) |
---|
774 | DO jj = 1, jpjm1 |
---|
775 | DO ji = fs_2, fs_jpim1 |
---|
776 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
777 | & - SIGN( 1._wp, pv(ji,jj) ) * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
778 | END DO |
---|
779 | END DO |
---|
780 | ! |
---|
781 | CASE( 2 ) !== 2nd order central TIM ==! (Eq. 23) |
---|
782 | DO jj = 1, jpjm1 |
---|
783 | DO ji = fs_2, fs_jpim1 |
---|
784 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
785 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt(ji,jj+1) + pt(ji,jj) ) & |
---|
786 | & - zcv * ( pt(ji,jj+1) - pt(ji,jj) ) ) |
---|
787 | END DO |
---|
788 | END DO |
---|
789 | CALL lbc_lnk( pt_v, 'V', 1. ) |
---|
790 | ! |
---|
791 | CASE( 3 ) !== 3rd order central TIM ==! (Eq. 24) |
---|
792 | DO jj = 1, jpjm1 |
---|
793 | DO ji = fs_2, fs_jpim1 |
---|
794 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
795 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
796 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
797 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
798 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
799 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
800 | & - SIGN( 1._wp, zcv ) * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
801 | END DO |
---|
802 | END DO |
---|
803 | ! |
---|
804 | CASE( 4 ) !== 4th order central TIM ==! (Eq. 27) |
---|
805 | DO jj = 1, jpjm1 |
---|
806 | DO ji = fs_2, fs_jpim1 |
---|
807 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
808 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
809 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
810 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
811 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
812 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
813 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) ) |
---|
814 | END DO |
---|
815 | END DO |
---|
816 | ! |
---|
817 | CASE( 5 ) !== 5th order central TIM ==! (Eq. 29) |
---|
818 | DO jj = 1, jpjm1 |
---|
819 | DO ji = fs_2, fs_jpim1 |
---|
820 | zcv = pv(ji,jj) * r1_e1v(ji,jj) * pdt * r1_e2v(ji,jj) |
---|
821 | zdy2 = e2v(ji,jj) * e2v(ji,jj) |
---|
822 | !!rachid zdy2 = e2v(ji,jj) * e2t(ji,jj) |
---|
823 | zdy4 = zdy2 * zdy2 |
---|
824 | pt_v(ji,jj) = 0.5_wp * vmask(ji,jj,1) * ( ( pt (ji,jj+1) + pt (ji,jj) & |
---|
825 | & - zcv * ( pt (ji,jj+1) - pt (ji,jj) ) ) & |
---|
826 | & + z1_6 * zdy2 * ( zcv*zcv - 1._wp ) * ( ztv2(ji,jj+1) + ztv2(ji,jj) & |
---|
827 | & - 0.5_wp * zcv * ( ztv2(ji,jj+1) - ztv2(ji,jj) ) ) & |
---|
828 | & + z1_120 * zdy4 * ( zcv*zcv - 1._wp ) * ( zcv*zcv - 4._wp ) * ( ztv4(ji,jj+1) + ztv4(ji,jj) & |
---|
829 | & - SIGN( 1._wp, zcv ) * ( ztv4(ji,jj+1) - ztv4(ji,jj) ) ) ) |
---|
830 | END DO |
---|
831 | END DO |
---|
832 | ! |
---|
833 | END SELECT |
---|
834 | ! !-- High order flux in j-direction --! |
---|
835 | DO jj = 1, jpjm1 |
---|
836 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
837 | pfv_ho(ji,jj) = pvc(ji,jj) * pt_v(ji,jj) |
---|
838 | END DO |
---|
839 | END DO |
---|
840 | ! |
---|
841 | END SUBROUTINE ultimate_y |
---|
842 | |
---|
843 | |
---|
844 | SUBROUTINE nonosc_2d( pdt, ptc, pt_low, pfu_low, pfv_low, pfu_ho, pfv_ho ) |
---|
845 | !!--------------------------------------------------------------------- |
---|
846 | !! *** ROUTINE nonosc *** |
---|
847 | !! |
---|
848 | !! ** Purpose : compute monotonic tracer fluxes from the upstream |
---|
849 | !! scheme and the before field by a nonoscillatory algorithm |
---|
850 | !! |
---|
851 | !! ** Method : ... ??? |
---|
852 | !! warning : ptc and pt_low must be masked, but the boundaries |
---|
853 | !! conditions on the fluxes are not necessary zalezak (1979) |
---|
854 | !! drange (1995) multi-dimensional forward-in-time and upstream- |
---|
855 | !! in-space based differencing for fluid |
---|
856 | !!---------------------------------------------------------------------- |
---|
857 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
858 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: ptc, pt_low ! before field & upstream guess of after field |
---|
859 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pfv_low, pfu_low ! upstream flux |
---|
860 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfv_ho, pfu_ho ! monotonic flux |
---|
861 | ! |
---|
862 | INTEGER :: ji, jj ! dummy loop indices |
---|
863 | REAL(wp) :: zpos, zneg, zbig, zsml, z1_dt ! local scalars |
---|
864 | REAL(wp) :: zau, zbu, zcu, zav, zbv, zcv, zup, zdo, zsign ! - - |
---|
865 | REAL(wp), DIMENSION(jpi,jpj) :: zbetup, zbetdo, zbup, zbdo, zti_low, ztj_low |
---|
866 | !!---------------------------------------------------------------------- |
---|
867 | zbig = 1.e+40_wp |
---|
868 | zsml = epsi20 |
---|
869 | |
---|
870 | ! antidiffusive flux : high order minus low order |
---|
871 | ! -------------------------------------------------- |
---|
872 | DO jj = 1, jpjm1 |
---|
873 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
874 | pfu_ho(ji,jj) = pfu_ho(ji,jj) - pfu_low(ji,jj) |
---|
875 | pfv_ho(ji,jj) = pfv_ho(ji,jj) - pfv_low(ji,jj) |
---|
876 | END DO |
---|
877 | END DO |
---|
878 | |
---|
879 | ! extreme case where pfu_ho has to be zero |
---|
880 | ! ---------------------------------------- |
---|
881 | ! pfu_ho |
---|
882 | ! * ---> |
---|
883 | ! | | * | | |
---|
884 | ! | | | * | |
---|
885 | ! | | | | * |
---|
886 | ! t_low : i-1 i i+1 i+2 |
---|
887 | IF( ll_prelimiter ) THEN |
---|
888 | |
---|
889 | DO jj = 2, jpjm1 |
---|
890 | DO ji = fs_2, fs_jpim1 |
---|
891 | zti_low(ji,jj)= pt_low(ji+1,jj ) |
---|
892 | ztj_low(ji,jj)= pt_low(ji ,jj+1) |
---|
893 | END DO |
---|
894 | END DO |
---|
895 | CALL lbc_lnk_multi( zti_low, 'T', 1., ztj_low, 'T', 1. ) |
---|
896 | |
---|
897 | IF( ll_prelimiter_zalesak ) THEN |
---|
898 | |
---|
899 | !! this does not work |
---|
900 | !! DO jj = 2, jpjm1 |
---|
901 | !! DO ji = fs_2, fs_jpim1 |
---|
902 | !! IF( SIGN( 1., pfu_ho(ji,jj) ) /= SIGN( 1., pt_low (ji+1,jj ) - pt_low (ji ,jj) ) .AND. & |
---|
903 | !! & SIGN( 1., pfv_ho(ji,jj) ) /= SIGN( 1., pt_low (ji ,jj+1) - pt_low (ji ,jj) ) & |
---|
904 | !! & ) THEN |
---|
905 | !! IF( SIGN( 1., pfu_ho(ji,jj) ) /= SIGN( 1., zti_low(ji+1,jj ) - zti_low(ji ,jj) ) .AND. & |
---|
906 | !! & SIGN( 1., pfv_ho(ji,jj) ) /= SIGN( 1., ztj_low(ji,jj+1 ) - ztj_low(ji ,jj) ) & |
---|
907 | !! & ) THEN |
---|
908 | !! pfu_ho(ji,jj) = 0. ; pfv_ho(ji,jj) = 0. |
---|
909 | !! ENDIF |
---|
910 | !! IF( SIGN( 1., pfu_ho(ji,jj) ) /= SIGN( 1., pt_low (ji ,jj) - pt_low (ji-1,jj ) ) .AND. & |
---|
911 | !! & SIGN( 1., pfv_ho(ji,jj) ) /= SIGN( 1., pt_low (ji ,jj) - pt_low (ji ,jj-1) ) & |
---|
912 | !! & ) THEN |
---|
913 | !! pfu_ho(ji,jj) = 0. ; pfv_ho(ji,jj) = 0. |
---|
914 | !! ENDIF |
---|
915 | !! ENDIF |
---|
916 | !! END DO |
---|
917 | !! END DO |
---|
918 | |
---|
919 | DO jj = 2, jpjm1 |
---|
920 | DO ji = fs_2, fs_jpim1 |
---|
921 | IF ( pfu_ho(ji,jj) * ( pt_low(ji+1,jj) - pt_low(ji,jj) ) <= 0. .AND. & |
---|
922 | & pfv_ho(ji,jj) * ( pt_low(ji,jj+1) - pt_low(ji,jj) ) <= 0. ) THEN |
---|
923 | ! |
---|
924 | IF( pfu_ho(ji,jj) * ( zti_low(ji+1,jj) - zti_low(ji,jj) ) <= 0 .AND. & |
---|
925 | & pfv_ho(ji,jj) * ( ztj_low(ji,jj+1) - ztj_low(ji,jj) ) <= 0) pfu_ho(ji,jj)=0. ; pfv_ho(ji,jj)=0. |
---|
926 | ! |
---|
927 | IF( pfu_ho(ji,jj) * ( pt_low(ji ,jj) - pt_low(ji-1,jj) ) <= 0 .AND. & |
---|
928 | & pfv_ho(ji,jj) * ( pt_low(ji ,jj) - pt_low(ji,jj-1) ) <= 0) pfu_ho(ji,jj)=0. ; pfv_ho(ji,jj)=0. |
---|
929 | ! |
---|
930 | ENDIF |
---|
931 | END DO |
---|
932 | END DO |
---|
933 | CALL lbc_lnk_multi( pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
934 | |
---|
935 | ELSEIF( ll_prelimiter_devore ) THEN |
---|
936 | z1_dt = 1._wp / pdt |
---|
937 | DO jj = 2, jpjm1 |
---|
938 | DO ji = fs_2, fs_jpim1 |
---|
939 | zsign = SIGN( 1., pt_low(ji+1,jj) - pt_low(ji,jj) ) |
---|
940 | pfu_ho(ji,jj) = zsign * MAX( 0. , MIN( ABS(pfu_ho(ji,jj)) , & |
---|
941 | & zsign * ( pt_low (ji ,jj) - pt_low (ji-1,jj) ) * e1e2t(ji ,jj) * z1_dt , & |
---|
942 | & zsign * ( zti_low(ji+1,jj) - zti_low(ji ,jj) ) * e1e2t(ji+1,jj) * z1_dt ) ) |
---|
943 | |
---|
944 | zsign = SIGN( 1., pt_low(ji,jj+1) - pt_low(ji,jj) ) |
---|
945 | pfv_ho(ji,jj) = zsign * MAX( 0. , MIN( ABS(pfv_ho(ji,jj)) , & |
---|
946 | & zsign * ( pt_low (ji,jj ) - pt_low (ji,jj-1) ) * e1e2t(ji,jj ) * z1_dt , & |
---|
947 | & zsign * ( ztj_low(ji,jj+1) - ztj_low(ji,jj ) ) * e1e2t(ji,jj+1) * z1_dt ) ) |
---|
948 | END DO |
---|
949 | END DO |
---|
950 | CALL lbc_lnk_multi( pfu_ho, 'U', -1., pfv_ho, 'V', -1. ) ! lateral boundary cond. |
---|
951 | |
---|
952 | ENDIF |
---|
953 | |
---|
954 | ENDIF |
---|
955 | |
---|
956 | ! Search local extrema |
---|
957 | ! -------------------- |
---|
958 | ! max/min of ptc & pt_low with large negative/positive value (-/+zbig) outside ice cover |
---|
959 | DO jj = 1, jpj |
---|
960 | DO ji = 1, jpi |
---|
961 | !!clem IF ( ptc(ji,jj) == 0._wp .AND. pt_low(ji,jj) == 0._wp ) THEN |
---|
962 | IF ( ptc(ji,jj) <= epsi20 .AND. pt_low(ji,jj) <= epsi20 ) THEN |
---|
963 | zbup(ji,jj) = -zbig |
---|
964 | zbdo(ji,jj) = zbig |
---|
965 | !!clem ELSEIF( ptc(ji,jj) == 0._wp .AND. pt_low(ji,jj) /= 0._wp ) THEN |
---|
966 | ELSEIF( ptc(ji,jj) <= epsi20 .AND. pt_low(ji,jj) > epsi20 ) THEN |
---|
967 | zbup(ji,jj) = pt_low(ji,jj) |
---|
968 | zbdo(ji,jj) = pt_low(ji,jj) |
---|
969 | !!clem ELSEIF( ptc(ji,jj) /= 0._wp .AND. pt_low(ji,jj) == 0._wp ) THEN |
---|
970 | ELSEIF( ptc(ji,jj) > epsi20 .AND. pt_low(ji,jj) <= epsi20 ) THEN |
---|
971 | zbup(ji,jj) = ptc(ji,jj) |
---|
972 | zbdo(ji,jj) = ptc(ji,jj) |
---|
973 | ELSE |
---|
974 | zbup(ji,jj) = MAX( ptc(ji,jj) , pt_low(ji,jj) ) |
---|
975 | zbdo(ji,jj) = MIN( ptc(ji,jj) , pt_low(ji,jj) ) |
---|
976 | ENDIF |
---|
977 | END DO |
---|
978 | END DO |
---|
979 | |
---|
980 | z1_dt = 1._wp / pdt |
---|
981 | DO jj = 2, jpjm1 |
---|
982 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
983 | ! |
---|
984 | !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 |
---|
985 | !zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj ), zbdo(ji+1,jj ), zbdo(ji ,jj-1), zbdo(ji ,jj+1) ) |
---|
986 | ! |
---|
987 | 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 |
---|
988 | & zbup(ji-1,jj-1), zbup(ji+1,jj+1), zbup(ji+1,jj-1), zbup(ji-1,jj+1) ) |
---|
989 | zdo = MIN( zbdo(ji,jj), zbdo(ji-1,jj ), zbdo(ji+1,jj ), zbdo(ji ,jj-1), zbdo(ji ,jj+1), & |
---|
990 | & zbdo(ji-1,jj-1), zbdo(ji+1,jj+1), zbdo(ji+1,jj-1), zbdo(ji-1,jj+1) ) |
---|
991 | ! |
---|
992 | zpos = MAX( 0., pfu_ho(ji-1,jj) ) - MIN( 0., pfu_ho(ji ,jj) ) & ! positive/negative part of the flux |
---|
993 | & + MAX( 0., pfv_ho(ji,jj-1) ) - MIN( 0., pfv_ho(ji,jj ) ) |
---|
994 | zneg = MAX( 0., pfu_ho(ji ,jj) ) - MIN( 0., pfu_ho(ji-1,jj) ) & |
---|
995 | & + MAX( 0., pfv_ho(ji,jj ) ) - MIN( 0., pfv_ho(ji,jj-1) ) |
---|
996 | ! |
---|
997 | ! ! up & down beta terms |
---|
998 | ! zbetup(ji,jj) = ( zup - pt_low(ji,jj) ) / ( zpos + zsml ) * e1e2t(ji,jj) * z1_dt |
---|
999 | ! zbetdo(ji,jj) = ( pt_low(ji,jj) - zdo ) / ( zneg + zsml ) * e1e2t(ji,jj) * z1_dt |
---|
1000 | IF( zpos >= epsi10 ) THEN ; zbetup(ji,jj) = ( zup - pt_low(ji,jj) ) / zpos * e1e2t(ji,jj) * z1_dt |
---|
1001 | ELSE ; zbetup(ji,jj) = 0. |
---|
1002 | ENDIF |
---|
1003 | ! |
---|
1004 | IF( zneg >= epsi10 ) THEN ; zbetdo(ji,jj) = ( pt_low(ji,jj) - zdo ) / zneg * e1e2t(ji,jj) * z1_dt |
---|
1005 | ELSE ; zbetdo(ji,jj) = 0. |
---|
1006 | ENDIF |
---|
1007 | ! |
---|
1008 | IF( zbetdo(ji,jj) < 0._wp ) zbetdo(ji,jj)=0. |
---|
1009 | IF( zbetup(ji,jj) < 0._wp ) zbetup(ji,jj)=0. |
---|
1010 | ! |
---|
1011 | ! |
---|
1012 | END DO |
---|
1013 | END DO |
---|
1014 | CALL lbc_lnk_multi( zbetup, 'T', 1., zbetdo, 'T', 1. ) ! lateral boundary cond. (unchanged sign) |
---|
1015 | |
---|
1016 | ! monotonic flux in the y direction |
---|
1017 | ! --------------------------------- |
---|
1018 | DO jj = 1, jpjm1 |
---|
1019 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1020 | zau = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji+1,jj) ) |
---|
1021 | zbu = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji+1,jj) ) |
---|
1022 | zcu = 0.5 + SIGN( 0.5 , pfu_ho(ji,jj) ) |
---|
1023 | ! |
---|
1024 | pfu_ho(ji,jj) = pfu_ho(ji,jj) * ( zcu * zau + ( 1._wp - zcu ) * zbu ) + pfu_low(ji,jj) |
---|
1025 | END DO |
---|
1026 | END DO |
---|
1027 | |
---|
1028 | DO jj = 1, jpjm1 |
---|
1029 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
1030 | zav = MIN( 1._wp , zbetdo(ji,jj) , zbetup(ji,jj+1) ) |
---|
1031 | zbv = MIN( 1._wp , zbetup(ji,jj) , zbetdo(ji,jj+1) ) |
---|
1032 | zcv = 0.5 + SIGN( 0.5 , pfv_ho(ji,jj) ) |
---|
1033 | ! |
---|
1034 | pfv_ho(ji,jj) = pfv_ho(ji,jj) * ( zcv * zav + ( 1._wp - zcv ) * zbv ) + pfv_low(ji,jj) |
---|
1035 | END DO |
---|
1036 | END DO |
---|
1037 | ! |
---|
1038 | END SUBROUTINE nonosc_2d |
---|
1039 | |
---|
1040 | SUBROUTINE limiter_x( pdt, pu, puc, pt, pfu_ho, pfu_ups ) |
---|
1041 | !!--------------------------------------------------------------------- |
---|
1042 | !! *** ROUTINE limiter_x *** |
---|
1043 | !! |
---|
1044 | !! ** Purpose : compute flux limiter |
---|
1045 | !!---------------------------------------------------------------------- |
---|
1046 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1047 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pu ! ice i-velocity => u*e2 |
---|
1048 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: puc ! ice i-velocity *A => u*e2*a |
---|
1049 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pt ! ice tracer |
---|
1050 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfu_ho ! high order flux |
---|
1051 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ), OPTIONAL :: pfu_ups ! upstream flux |
---|
1052 | ! |
---|
1053 | REAL(wp) :: Cr, Rjm, Rj, Rjp, uCFL, zpsi, zh3, zlimiter, Rr |
---|
1054 | INTEGER :: ji, jj ! dummy loop indices |
---|
1055 | REAL(wp), DIMENSION (jpi,jpj) :: zslpx ! tracer slopes |
---|
1056 | !!---------------------------------------------------------------------- |
---|
1057 | ! |
---|
1058 | DO jj = 2, jpjm1 |
---|
1059 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
1060 | zslpx(ji,jj) = ( pt(ji+1,jj) - pt(ji,jj) ) * umask(ji,jj,1) |
---|
1061 | END DO |
---|
1062 | END DO |
---|
1063 | CALL lbc_lnk( zslpx, 'U', -1.) ! lateral boundary cond. |
---|
1064 | |
---|
1065 | DO jj = 2, jpjm1 |
---|
1066 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
1067 | uCFL = pdt * ABS( pu(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
1068 | |
---|
1069 | Rjm = zslpx(ji-1,jj) |
---|
1070 | Rj = zslpx(ji ,jj) |
---|
1071 | Rjp = zslpx(ji+1,jj) |
---|
1072 | |
---|
1073 | IF( PRESENT(pfu_ups) ) THEN |
---|
1074 | |
---|
1075 | IF( pu(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
1076 | ELSE ; Rr = Rjp |
---|
1077 | ENDIF |
---|
1078 | |
---|
1079 | zh3 = pfu_ho(ji,jj) - pfu_ups(ji,jj) |
---|
1080 | IF( Rj > 0. ) THEN |
---|
1081 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(puc(ji,jj)), & |
---|
1082 | & MIN( 2. * Rr * 0.5 * ABS(puc(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(puc(ji,jj)) ) ) ) ) |
---|
1083 | ELSE |
---|
1084 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(puc(ji,jj)), & |
---|
1085 | & MIN(-2. * Rr * 0.5 * ABS(puc(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(puc(ji,jj)) ) ) ) ) |
---|
1086 | ENDIF |
---|
1087 | pfu_ho(ji,jj) = pfu_ups(ji,jj) + zlimiter |
---|
1088 | |
---|
1089 | ELSE |
---|
1090 | IF( Rj /= 0. ) THEN |
---|
1091 | IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
1092 | ELSE ; Cr = Rjp / Rj |
---|
1093 | ENDIF |
---|
1094 | ELSE |
---|
1095 | Cr = 0. |
---|
1096 | !IF( pu(ji,jj) > 0. ) THEN ; Cr = Rjm * 1.e20 |
---|
1097 | !ELSE ; Cr = Rjp * 1.e20 |
---|
1098 | !ENDIF |
---|
1099 | ENDIF |
---|
1100 | |
---|
1101 | ! -- superbee -- |
---|
1102 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
1103 | ! -- van albada 2 -- |
---|
1104 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
1105 | |
---|
1106 | ! -- sweby (with beta=1) -- |
---|
1107 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
1108 | ! -- van Leer -- |
---|
1109 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
1110 | ! -- ospre -- |
---|
1111 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
1112 | ! -- koren -- |
---|
1113 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
1114 | ! -- charm -- |
---|
1115 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
1116 | !ELSE ; zpsi = 0. |
---|
1117 | !ENDIF |
---|
1118 | ! -- van albada 1 -- |
---|
1119 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
1120 | ! -- smart -- |
---|
1121 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
1122 | ! -- umist -- |
---|
1123 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
1124 | |
---|
1125 | ! high order flux corrected by the limiter |
---|
1126 | pfu_ho(ji,jj) = pfu_ho(ji,jj) - ABS( puc(ji,jj) ) * ( (1.-zpsi) + uCFL*zpsi ) * Rj * 0.5 |
---|
1127 | |
---|
1128 | ENDIF |
---|
1129 | END DO |
---|
1130 | END DO |
---|
1131 | CALL lbc_lnk( pfu_ho, 'U', -1.) ! lateral boundary cond. |
---|
1132 | ! |
---|
1133 | END SUBROUTINE limiter_x |
---|
1134 | |
---|
1135 | SUBROUTINE limiter_y( pdt, pv, pvc, pt, pfv_ho, pfv_ups ) |
---|
1136 | !!--------------------------------------------------------------------- |
---|
1137 | !! *** ROUTINE limiter_y *** |
---|
1138 | !! |
---|
1139 | !! ** Purpose : compute flux limiter |
---|
1140 | !!---------------------------------------------------------------------- |
---|
1141 | REAL(wp) , INTENT(in ) :: pdt ! tracer time-step |
---|
1142 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pv ! ice i-velocity => u*e2 |
---|
1143 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pvc ! ice i-velocity *A => u*e2*a |
---|
1144 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ) :: pt ! ice tracer |
---|
1145 | REAL(wp), DIMENSION (jpi,jpj), INTENT(inout) :: pfv_ho ! high order flux |
---|
1146 | REAL(wp), DIMENSION (jpi,jpj), INTENT(in ), OPTIONAL :: pfv_ups ! upstream flux |
---|
1147 | ! |
---|
1148 | REAL(wp) :: Cr, Rjm, Rj, Rjp, vCFL, zpsi, zh3, zlimiter, Rr |
---|
1149 | INTEGER :: ji, jj ! dummy loop indices |
---|
1150 | REAL(wp), DIMENSION (jpi,jpj) :: zslpy ! tracer slopes |
---|
1151 | !!---------------------------------------------------------------------- |
---|
1152 | ! |
---|
1153 | DO jj = 2, jpjm1 |
---|
1154 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
1155 | zslpy(ji,jj) = ( pt(ji,jj+1) - pt(ji,jj) ) * vmask(ji,jj,1) |
---|
1156 | END DO |
---|
1157 | END DO |
---|
1158 | CALL lbc_lnk( zslpy, 'V', -1.) ! lateral boundary cond. |
---|
1159 | |
---|
1160 | DO jj = 2, jpjm1 |
---|
1161 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
1162 | vCFL = pdt * ABS( pv(ji,jj) ) * r1_e1e2t(ji,jj) |
---|
1163 | |
---|
1164 | Rjm = zslpy(ji,jj-1) |
---|
1165 | Rj = zslpy(ji,jj ) |
---|
1166 | Rjp = zslpy(ji,jj+1) |
---|
1167 | |
---|
1168 | IF( PRESENT(pfv_ups) ) THEN |
---|
1169 | |
---|
1170 | IF( pv(ji,jj) > 0. ) THEN ; Rr = Rjm |
---|
1171 | ELSE ; Rr = Rjp |
---|
1172 | ENDIF |
---|
1173 | |
---|
1174 | zh3 = pfv_ho(ji,jj) - pfv_ups(ji,jj) |
---|
1175 | IF( Rj > 0. ) THEN |
---|
1176 | zlimiter = MAX( 0., MIN( zh3, MAX(-Rr * 0.5 * ABS(pvc(ji,jj)), & |
---|
1177 | & MIN( 2. * Rr * 0.5 * ABS(pvc(ji,jj)), zh3, 1.5 * Rj * 0.5 * ABS(pvc(ji,jj)) ) ) ) ) |
---|
1178 | ELSE |
---|
1179 | zlimiter = -MAX( 0., MIN(-zh3, MAX( Rr * 0.5 * ABS(pvc(ji,jj)), & |
---|
1180 | & MIN(-2. * Rr * 0.5 * ABS(pvc(ji,jj)), -zh3, -1.5 * Rj * 0.5 * ABS(pvc(ji,jj)) ) ) ) ) |
---|
1181 | ENDIF |
---|
1182 | pfv_ho(ji,jj) = pfv_ups(ji,jj) + zlimiter |
---|
1183 | |
---|
1184 | ELSE |
---|
1185 | |
---|
1186 | IF( Rj /= 0. ) THEN |
---|
1187 | IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm / Rj |
---|
1188 | ELSE ; Cr = Rjp / Rj |
---|
1189 | ENDIF |
---|
1190 | ELSE |
---|
1191 | Cr = 0. |
---|
1192 | !IF( pv(ji,jj) > 0. ) THEN ; Cr = Rjm * 1.e20 |
---|
1193 | !ELSE ; Cr = Rjp * 1.e20 |
---|
1194 | !ENDIF |
---|
1195 | ENDIF |
---|
1196 | |
---|
1197 | ! -- superbee -- |
---|
1198 | zpsi = MAX( 0., MAX( MIN(1.,2.*Cr), MIN(2.,Cr) ) ) |
---|
1199 | ! -- van albada 2 -- |
---|
1200 | !!zpsi = 2.*Cr / (Cr*Cr+1.) |
---|
1201 | |
---|
1202 | ! -- sweby (with beta=1) -- |
---|
1203 | !!zpsi = MAX( 0., MAX( MIN(1.,1.*Cr), MIN(1.,Cr) ) ) |
---|
1204 | ! -- van Leer -- |
---|
1205 | !!zpsi = ( Cr + ABS(Cr) ) / ( 1. + ABS(Cr) ) |
---|
1206 | ! -- ospre -- |
---|
1207 | !!zpsi = 1.5 * ( Cr*Cr + Cr ) / ( Cr*Cr + Cr + 1. ) |
---|
1208 | ! -- koren -- |
---|
1209 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( (1.+2*Cr)/3., 2. ) ) ) |
---|
1210 | ! -- charm -- |
---|
1211 | !IF( Cr > 0. ) THEN ; zpsi = Cr * (3.*Cr + 1.) / ( (Cr + 1.) * (Cr + 1.) ) |
---|
1212 | !ELSE ; zpsi = 0. |
---|
1213 | !ENDIF |
---|
1214 | ! -- van albada 1 -- |
---|
1215 | !!zpsi = (Cr*Cr + Cr) / (Cr*Cr +1) |
---|
1216 | ! -- smart -- |
---|
1217 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, 4. ) ) ) |
---|
1218 | ! -- umist -- |
---|
1219 | !!zpsi = MAX( 0., MIN( 2.*Cr, MIN( 0.25+0.75*Cr, MIN(0.75+0.25*Cr, 2. ) ) ) ) |
---|
1220 | |
---|
1221 | ! high order flux corrected by the limiter |
---|
1222 | pfv_ho(ji,jj) = pfv_ho(ji,jj) - ABS( pvc(ji,jj) ) * ( (1.-zpsi) + vCFL*zpsi ) * Rj * 0.5 |
---|
1223 | |
---|
1224 | ENDIF |
---|
1225 | END DO |
---|
1226 | END DO |
---|
1227 | CALL lbc_lnk( pfv_ho, 'V', -1.) ! lateral boundary cond. |
---|
1228 | ! |
---|
1229 | END SUBROUTINE limiter_y |
---|
1230 | |
---|
1231 | #else |
---|
1232 | !!---------------------------------------------------------------------- |
---|
1233 | !! Default option Dummy module NO SI3 sea-ice model |
---|
1234 | !!---------------------------------------------------------------------- |
---|
1235 | #endif |
---|
1236 | |
---|
1237 | !!====================================================================== |
---|
1238 | END MODULE icedyn_adv_umx |
---|