| 1 | MODULE diffusion_v_mod |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! |
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| 7 | ! |
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| 8 | ! Former revisions: |
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| 9 | ! ----------------- |
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| 10 | ! $Id: diffusion_v.f90 1017 2012-09-27 11:28:50Z raasch $ |
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| 11 | ! |
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| 12 | ! 1015 2012-09-27 09:23:24Z raasch |
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| 13 | ! accelerator version (*_acc) added |
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| 14 | ! |
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| 15 | ! 1001 2012-09-13 14:08:46Z raasch |
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| 16 | ! arrays comunicated by module instead of parameter list |
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| 17 | ! |
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| 18 | ! 978 2012-08-09 08:28:32Z fricke |
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| 19 | ! outflow damping layer removed |
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| 20 | ! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp |
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| 21 | ! |
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| 22 | ! 667 2010-12-23 12:06:00Z suehring/gryschka |
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| 23 | ! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng |
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| 24 | ! |
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| 25 | ! 366 2009-08-25 08:06:27Z raasch |
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| 26 | ! bc_lr replaced by bc_lr_cyc |
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| 27 | ! |
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| 28 | ! 106 2007-08-16 14:30:26Z raasch |
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| 29 | ! Momentumflux at top (vswst) included as boundary condition, |
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| 30 | ! j loop is starting from nysv (needed for non-cyclic boundary conditions) |
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| 31 | ! |
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| 32 | ! 75 2007-03-22 09:54:05Z raasch |
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| 33 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes, |
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| 34 | ! z0 removed from argument list, vynp eliminated |
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| 35 | ! |
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| 36 | ! 20 2007-02-26 00:12:32Z raasch |
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| 37 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 38 | ! |
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| 39 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 40 | ! |
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| 41 | ! Revision 1.15 2006/02/23 10:36:00 raasch |
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| 42 | ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner |
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| 43 | ! or nzb_diff_v, respectively, in vertical diffusion, |
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| 44 | ! wall functions added for north and south walls, +z0 in argument list, |
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| 45 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
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| 46 | ! because they cause errors at the edges of topography |
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| 47 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
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| 48 | ! |
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| 49 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
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| 50 | ! Initial revision |
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| 51 | ! |
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| 52 | ! |
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| 53 | ! Description: |
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| 54 | ! ------------ |
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| 55 | ! Diffusion term of the v-component |
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| 56 | !------------------------------------------------------------------------------! |
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| 57 | |
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| 58 | USE wall_fluxes_mod |
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| 59 | |
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| 60 | PRIVATE |
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| 61 | PUBLIC diffusion_v, diffusion_v_acc |
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| 62 | |
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| 63 | INTERFACE diffusion_v |
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| 64 | MODULE PROCEDURE diffusion_v |
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| 65 | MODULE PROCEDURE diffusion_v_ij |
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| 66 | END INTERFACE diffusion_v |
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| 67 | |
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| 68 | INTERFACE diffusion_v_acc |
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| 69 | MODULE PROCEDURE diffusion_v_acc |
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| 70 | END INTERFACE diffusion_v_acc |
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| 71 | |
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| 72 | CONTAINS |
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| 73 | |
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| 74 | |
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| 75 | !------------------------------------------------------------------------------! |
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| 76 | ! Call for all grid points |
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| 77 | !------------------------------------------------------------------------------! |
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| 78 | SUBROUTINE diffusion_v |
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| 79 | |
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| 80 | USE arrays_3d |
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| 81 | USE control_parameters |
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| 82 | USE grid_variables |
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| 83 | USE indices |
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| 84 | |
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| 85 | IMPLICIT NONE |
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| 86 | |
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| 87 | INTEGER :: i, j, k |
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| 88 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 89 | |
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| 90 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
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| 91 | |
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| 92 | ! |
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| 93 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 94 | !-- if neccessary |
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| 95 | IF ( topography /= 'flat' ) THEN |
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| 96 | CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
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| 97 | nzb_v_outer, wall_v ) |
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| 98 | ENDIF |
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| 99 | |
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| 100 | DO i = nxl, nxr |
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| 101 | DO j = nysv, nyn |
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| 102 | ! |
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| 103 | !-- Compute horizontal diffusion |
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| 104 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 105 | ! |
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| 106 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 107 | kmxp = 0.25 * & |
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| 108 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 109 | kmxm = 0.25 * & |
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| 110 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 111 | |
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| 112 | tend(k,j,i) = tend(k,j,i) & |
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| 113 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 114 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 115 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 116 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 117 | & ) * ddx & |
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| 118 | & + 2.0 * ( & |
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| 119 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 120 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 121 | & ) * ddy2 |
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| 122 | ENDDO |
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| 123 | |
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| 124 | ! |
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| 125 | !-- Wall functions at the left and right walls, respectively |
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| 126 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 127 | |
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| 128 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 129 | kmxp = 0.25 * & |
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| 130 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 131 | kmxm = 0.25 * & |
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| 132 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 133 | |
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| 134 | tend(k,j,i) = tend(k,j,i) & |
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| 135 | + 2.0 * ( & |
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| 136 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 137 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 138 | ) * ddy2 & |
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| 139 | + ( fxp(j,i) * ( & |
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| 140 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 141 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 142 | ) & |
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| 143 | - fxm(j,i) * ( & |
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| 144 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 145 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 146 | ) & |
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| 147 | + wall_v(j,i) * vsus(k,j,i) & |
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| 148 | ) * ddx |
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| 149 | ENDDO |
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| 150 | ENDIF |
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| 151 | |
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| 152 | ! |
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| 153 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 154 | !-- layer, index k starts at nzb_v_inner+2. |
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| 155 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 156 | ! |
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| 157 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 158 | kmzp = 0.25 * & |
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| 159 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 160 | kmzm = 0.25 * & |
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| 161 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 162 | |
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| 163 | tend(k,j,i) = tend(k,j,i) & |
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| 164 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 165 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 166 | & ) & |
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| 167 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 168 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 169 | & ) & |
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| 170 | & ) * ddzw(k) |
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| 171 | ENDDO |
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| 172 | |
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| 173 | ! |
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| 174 | !-- Vertical diffusion at the first grid point above the surface, |
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| 175 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 176 | !-- or if it is prescribed by the user. |
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| 177 | !-- Difference quotient of the momentum flux is not formed over |
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| 178 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 179 | !-- comparison with other (LES) modell showed that the values of |
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| 180 | !-- the momentum flux becomes too large in this case. |
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| 181 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 182 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 183 | IF ( use_surface_fluxes ) THEN |
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| 184 | k = nzb_v_inner(j,i)+1 |
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| 185 | ! |
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| 186 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 187 | kmzp = 0.25 * & |
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| 188 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 189 | kmzm = 0.25 * & |
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| 190 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 191 | |
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| 192 | tend(k,j,i) = tend(k,j,i) & |
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| 193 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 194 | & ) * ddzw(k) & |
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| 195 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 196 | & + vsws(j,i) & |
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| 197 | & ) * ddzw(k) |
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| 198 | ENDIF |
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| 199 | |
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| 200 | ! |
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| 201 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 202 | !-- if the momentum flux at the top is prescribed by the user |
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| 203 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 204 | k = nzt |
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| 205 | ! |
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| 206 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 207 | kmzp = 0.25 * & |
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| 208 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 209 | kmzm = 0.25 * & |
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| 210 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 211 | |
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| 212 | tend(k,j,i) = tend(k,j,i) & |
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| 213 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 214 | & ) * ddzw(k) & |
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| 215 | & + ( -vswst(j,i) & |
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| 216 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 217 | & ) * ddzw(k) |
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| 218 | ENDIF |
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| 219 | |
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| 220 | ENDDO |
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| 221 | ENDDO |
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| 222 | |
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| 223 | END SUBROUTINE diffusion_v |
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| 224 | |
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| 225 | |
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| 226 | !------------------------------------------------------------------------------! |
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| 227 | ! Call for all grid points - accelerator version |
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| 228 | !------------------------------------------------------------------------------! |
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| 229 | SUBROUTINE diffusion_v_acc |
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| 230 | |
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| 231 | USE arrays_3d |
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| 232 | USE control_parameters |
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| 233 | USE grid_variables |
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| 234 | USE indices |
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| 235 | |
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| 236 | IMPLICIT NONE |
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| 237 | |
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| 238 | INTEGER :: i, j, k |
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| 239 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 240 | |
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| 241 | !$acc declare create ( vsus ) |
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| 242 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
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| 243 | |
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| 244 | ! |
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| 245 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
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| 246 | !-- if neccessary |
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| 247 | IF ( topography /= 'flat' ) THEN |
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| 248 | CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
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| 249 | nzb_v_outer, wall_v ) |
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| 250 | ENDIF |
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| 251 | |
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| 252 | !$acc kernels present ( u, v, w, km, tend, vsws, vswst ) & |
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| 253 | !$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) & |
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| 254 | !$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v ) |
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| 255 | !$acc loop |
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| 256 | DO i = nxl, nxr |
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| 257 | DO j = nysv, nyn |
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| 258 | ! |
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| 259 | !-- Compute horizontal diffusion |
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| 260 | !$acc loop vector(32) |
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| 261 | DO k = 1, nzt |
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| 262 | IF ( k > nzb_v_outer(j,i) ) THEN |
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| 263 | ! |
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| 264 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 265 | kmxp = 0.25 * & |
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| 266 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 267 | kmxm = 0.25 * & |
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| 268 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 269 | |
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| 270 | tend(k,j,i) = tend(k,j,i) & |
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| 271 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 272 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 273 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 274 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 275 | & ) * ddx & |
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| 276 | & + 2.0 * ( & |
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| 277 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 278 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 279 | & ) * ddy2 |
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| 280 | ENDIF |
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| 281 | ENDDO |
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| 282 | |
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| 283 | ! |
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| 284 | !-- Wall functions at the left and right walls, respectively |
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| 285 | !$acc loop vector(32) |
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| 286 | DO k = 1, nzt |
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| 287 | IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. & |
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| 288 | wall_v(j,i) /= 0.0 ) THEN |
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| 289 | |
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| 290 | kmxp = 0.25 * & |
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| 291 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 292 | kmxm = 0.25 * & |
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| 293 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 294 | |
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| 295 | tend(k,j,i) = tend(k,j,i) & |
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| 296 | + 2.0 * ( & |
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| 297 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 298 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 299 | ) * ddy2 & |
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| 300 | + ( fxp(j,i) * ( & |
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| 301 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 302 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 303 | ) & |
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| 304 | - fxm(j,i) * ( & |
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| 305 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 306 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 307 | ) & |
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| 308 | + wall_v(j,i) * vsus(k,j,i) & |
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| 309 | ) * ddx |
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| 310 | ENDIF |
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| 311 | ENDDO |
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| 312 | |
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| 313 | ! |
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| 314 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
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| 315 | !-- layer, index k starts at nzb_v_inner+2. |
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| 316 | !$acc loop vector(32) |
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| 317 | DO k = 1, nzt_diff |
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| 318 | IF ( k >= nzb_diff_v(j,i) ) THEN |
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| 319 | ! |
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| 320 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 321 | kmzp = 0.25 * & |
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| 322 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 323 | kmzm = 0.25 * & |
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| 324 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 325 | |
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| 326 | tend(k,j,i) = tend(k,j,i) & |
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| 327 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)& |
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| 328 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 329 | & ) & |
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| 330 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)& |
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| 331 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 332 | & ) & |
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| 333 | & ) * ddzw(k) |
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| 334 | ENDIF |
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| 335 | ENDDO |
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| 336 | |
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| 337 | ENDDO |
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| 338 | ENDDO |
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| 339 | |
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| 340 | ! |
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| 341 | !-- Vertical diffusion at the first grid point above the surface, |
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| 342 | !-- if the momentum flux at the bottom is given by the Prandtl law |
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| 343 | !-- or if it is prescribed by the user. |
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| 344 | !-- Difference quotient of the momentum flux is not formed over |
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| 345 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
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| 346 | !-- comparison with other (LES) modell showed that the values of |
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| 347 | !-- the momentum flux becomes too large in this case. |
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| 348 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 349 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 350 | IF ( use_surface_fluxes ) THEN |
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| 351 | |
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| 352 | !$acc loop |
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| 353 | DO i = nxl, nxr |
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| 354 | !$acc loop vector(32) |
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| 355 | DO j = nysv, nyn |
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| 356 | |
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| 357 | k = nzb_v_inner(j,i)+1 |
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| 358 | ! |
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| 359 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 360 | kmzp = 0.25 * & |
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| 361 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 362 | kmzm = 0.25 * & |
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| 363 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 364 | |
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| 365 | tend(k,j,i) = tend(k,j,i) & |
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| 366 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 367 | & ) * ddzw(k) & |
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| 368 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 369 | & + vsws(j,i) & |
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| 370 | & ) * ddzw(k) |
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| 371 | ENDDO |
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| 372 | ENDDO |
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| 373 | |
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| 374 | ENDIF |
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| 375 | |
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| 376 | ! |
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| 377 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 378 | !-- if the momentum flux at the top is prescribed by the user |
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| 379 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 380 | |
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| 381 | k = nzt |
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| 382 | |
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| 383 | !$acc loop |
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| 384 | DO i = nxl, nxr |
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| 385 | !$acc loop vector(32) |
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| 386 | DO j = nysv, nyn |
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| 387 | |
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| 388 | ! |
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| 389 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 390 | kmzp = 0.25 * & |
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| 391 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 392 | kmzm = 0.25 * & |
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| 393 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 394 | |
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| 395 | tend(k,j,i) = tend(k,j,i) & |
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| 396 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 397 | & ) * ddzw(k) & |
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| 398 | & + ( -vswst(j,i) & |
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| 399 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 400 | & ) * ddzw(k) |
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| 401 | ENDDO |
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| 402 | ENDDO |
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| 403 | |
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| 404 | ENDIF |
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| 405 | !$acc end kernels |
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| 406 | |
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| 407 | END SUBROUTINE diffusion_v_acc |
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| 408 | |
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| 409 | |
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| 410 | !------------------------------------------------------------------------------! |
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| 411 | ! Call for grid point i,j |
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| 412 | !------------------------------------------------------------------------------! |
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| 413 | SUBROUTINE diffusion_v_ij( i, j ) |
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| 414 | |
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| 415 | USE arrays_3d |
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| 416 | USE control_parameters |
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| 417 | USE grid_variables |
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| 418 | USE indices |
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| 419 | |
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| 420 | IMPLICIT NONE |
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| 421 | |
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| 422 | INTEGER :: i, j, k |
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| 423 | REAL :: kmxm, kmxp, kmzm, kmzp |
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| 424 | |
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| 425 | REAL, DIMENSION(nzb:nzt+1) :: vsus |
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| 426 | |
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| 427 | ! |
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| 428 | !-- Compute horizontal diffusion |
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| 429 | DO k = nzb_v_outer(j,i)+1, nzt |
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| 430 | ! |
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| 431 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 432 | kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 433 | kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 434 | |
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| 435 | tend(k,j,i) = tend(k,j,i) & |
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| 436 | & + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 437 | & + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 438 | & - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 439 | & - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 440 | & ) * ddx & |
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| 441 | & + 2.0 * ( & |
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| 442 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 443 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 444 | & ) * ddy2 |
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| 445 | ENDDO |
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| 446 | |
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| 447 | ! |
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| 448 | !-- Wall functions at the left and right walls, respectively |
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| 449 | IF ( wall_v(j,i) /= 0.0 ) THEN |
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| 450 | |
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| 451 | ! |
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| 452 | !-- Calculate the horizontal momentum flux v'u' |
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| 453 | CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & |
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| 454 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
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| 455 | |
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| 456 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
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| 457 | kmxp = 0.25 * & |
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| 458 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
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| 459 | kmxm = 0.25 * & |
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| 460 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
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| 461 | |
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| 462 | tend(k,j,i) = tend(k,j,i) & |
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| 463 | + 2.0 * ( & |
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| 464 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
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| 465 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
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| 466 | ) * ddy2 & |
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| 467 | + ( fxp(j,i) * ( & |
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| 468 | kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
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| 469 | + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
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| 470 | ) & |
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| 471 | - fxm(j,i) * ( & |
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| 472 | kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 473 | + kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 474 | ) & |
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| 475 | + wall_v(j,i) * vsus(k) & |
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| 476 | ) * ddx |
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| 477 | ENDDO |
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| 478 | ENDIF |
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| 479 | |
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| 480 | ! |
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| 481 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 482 | !-- index k starts at nzb_v_inner+2. |
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| 483 | DO k = nzb_diff_v(j,i), nzt_diff |
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| 484 | ! |
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| 485 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 486 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 487 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 488 | |
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| 489 | tend(k,j,i) = tend(k,j,i) & |
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| 490 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 491 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 492 | & ) & |
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| 493 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 494 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 495 | & ) & |
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| 496 | & ) * ddzw(k) |
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| 497 | ENDDO |
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| 498 | |
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| 499 | ! |
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| 500 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 501 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 502 | !-- prescribed by the user. |
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| 503 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 504 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 505 | !-- other (LES) modell showed that the values of the momentum flux becomes |
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| 506 | !-- too large in this case. |
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| 507 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 508 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 509 | IF ( use_surface_fluxes ) THEN |
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| 510 | k = nzb_v_inner(j,i)+1 |
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| 511 | ! |
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| 512 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 513 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 514 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 515 | |
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| 516 | tend(k,j,i) = tend(k,j,i) & |
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| 517 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
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| 518 | & ) * ddzw(k) & |
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| 519 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
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| 520 | & + vsws(j,i) & |
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| 521 | & ) * ddzw(k) |
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| 522 | ENDIF |
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| 523 | |
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| 524 | ! |
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| 525 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
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| 526 | !-- if the momentum flux at the top is prescribed by the user |
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| 527 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
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| 528 | k = nzt |
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| 529 | ! |
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| 530 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 531 | kmzp = 0.25 * & |
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| 532 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
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| 533 | kmzm = 0.25 * & |
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| 534 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
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| 535 | |
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| 536 | tend(k,j,i) = tend(k,j,i) & |
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| 537 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
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| 538 | & ) * ddzw(k) & |
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| 539 | & + ( -vswst(j,i) & |
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| 540 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
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| 541 | & ) * ddzw(k) |
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| 542 | ENDIF |
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| 543 | |
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| 544 | END SUBROUTINE diffusion_v_ij |
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| 545 | |
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| 546 | END MODULE diffusion_v_mod |
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