| 1 | MODULE diffusion_u_mod |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Actual 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_u.f90 39 2007-03-01 12:46:59Z raasch $ |
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| 11 | ! |
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| 12 | ! 20 2007-02-26 00:12:32Z raasch |
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| 13 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
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| 14 | ! |
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| 15 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 16 | ! |
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| 17 | ! Revision 1.15 2006/02/23 10:35:35 raasch |
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| 18 | ! nzb_2d replaced by nzb_u_outer in horizontal diffusion and by nzb_u_inner |
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| 19 | ! or nzb_diff_u, respectively, in vertical diffusion, |
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| 20 | ! wall functions added for north and south walls, +z0 in argument list, |
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| 21 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
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| 22 | ! because they cause errors at the edges of topography |
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| 23 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
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| 24 | ! |
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| 25 | ! Revision 1.1 1997/09/12 06:23:51 raasch |
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| 26 | ! Initial revision |
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| 27 | ! |
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| 28 | ! |
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| 29 | ! Description: |
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| 30 | ! ------------ |
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| 31 | ! Diffusion term of the u-component |
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| 32 | !------------------------------------------------------------------------------! |
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| 33 | |
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| 34 | PRIVATE |
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| 35 | PUBLIC diffusion_u |
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| 36 | |
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| 37 | INTERFACE diffusion_u |
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| 38 | MODULE PROCEDURE diffusion_u |
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| 39 | MODULE PROCEDURE diffusion_u_ij |
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| 40 | END INTERFACE diffusion_u |
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| 41 | |
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| 42 | CONTAINS |
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| 43 | |
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| 44 | |
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| 45 | !------------------------------------------------------------------------------! |
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| 46 | ! Call for all grid points |
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| 47 | !------------------------------------------------------------------------------! |
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| 48 | SUBROUTINE diffusion_u( ddzu, ddzw, km, km_damp_y, tend, u, usws, v, w, z0 ) |
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| 49 | |
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| 50 | USE control_parameters |
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| 51 | USE grid_variables |
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| 52 | USE indices |
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| 53 | |
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| 54 | IMPLICIT NONE |
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| 55 | |
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| 56 | INTEGER :: i, j, k |
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| 57 | REAL :: kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp, usvs |
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| 58 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_y(nys-1:nyn+1) |
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| 59 | REAL :: z0(nys-1:nyn+1,nxl-1:nxr+1) |
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| 60 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
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| 61 | REAL, DIMENSION(:,:), POINTER :: usws |
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| 62 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
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| 63 | |
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| 64 | DO i = nxl, nxr+uxrp |
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| 65 | DO j = nys,nyn |
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| 66 | ! |
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| 67 | !-- Compute horizontal diffusion |
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| 68 | DO k = nzb_u_outer(j,i)+1, nzt |
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| 69 | ! |
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| 70 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 71 | kmyp_x = 0.25 * & |
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| 72 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 73 | kmym_x = 0.25 * & |
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| 74 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 75 | kmyp_y = kmyp_x |
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| 76 | kmym_y = kmym_x |
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| 77 | ! |
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| 78 | !-- Increase diffusion at the outflow boundary in case of |
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| 79 | !-- non-cyclic lateral boundaries. Damping is only needed for |
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| 80 | !-- velocity components parallel to the outflow boundary in |
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| 81 | !-- the direction normal to the outflow boundary. |
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| 82 | IF ( bc_ns /= 'cyclic' ) THEN |
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| 83 | kmyp_y = MAX( kmyp_y, km_damp_y(j) ) |
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| 84 | kmym_y = MAX( kmym_y, km_damp_y(j) ) |
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| 85 | ENDIF |
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| 86 | |
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| 87 | tend(k,j,i) = tend(k,j,i) & |
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| 88 | & + 2.0 * ( & |
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| 89 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 90 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 91 | & ) * ddx2 & |
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| 92 | & + ( kmyp_y * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 93 | & + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 94 | & - kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 95 | & - kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 96 | & ) * ddy |
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| 97 | ENDDO |
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| 98 | |
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| 99 | ! |
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| 100 | !-- Wall functions at the north and south walls, respectively |
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| 101 | IF ( wall_u(j,i) /= 0.0 ) THEN |
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| 102 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
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| 103 | usvs = kappa * u(k,j,i) / LOG( 0.5 * dy / z0(j,i) ) |
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| 104 | usvs = -usvs * ABS( usvs ) |
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| 105 | kmyp_x = 0.25 * & |
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| 106 | ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 107 | kmym_x = 0.25 * & |
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| 108 | ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 109 | kmyp_y = kmyp_x |
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| 110 | kmym_y = kmym_x |
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| 111 | ! |
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| 112 | !-- Increase diffusion at the outflow boundary in case of |
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| 113 | !-- non-cyclic lateral boundaries. Damping is only needed for |
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| 114 | !-- velocity components parallel to the outflow boundary in |
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| 115 | !-- the direction normal to the outflow boundary. |
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| 116 | IF ( bc_ns /= 'cyclic' ) THEN |
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| 117 | kmyp_y = MAX( kmyp_y, km_damp_y(j) ) |
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| 118 | kmym_y = MAX( kmym_y, km_damp_y(j) ) |
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| 119 | ENDIF |
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| 120 | |
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| 121 | tend(k,j,i) = tend(k,j,i) & |
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| 122 | + 2.0 * ( & |
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| 123 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 124 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 125 | ) * ddx2 & |
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| 126 | + ( fyp(j,i) * ( & |
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| 127 | kmyp_y * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 128 | + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 129 | ) & |
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| 130 | - fym(j,i) * ( & |
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| 131 | kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 132 | + kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 133 | ) & |
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| 134 | + wall_u(j,i) * usvs & |
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| 135 | ) * ddy |
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| 136 | ENDDO |
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| 137 | ENDIF |
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| 138 | |
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| 139 | ! |
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| 140 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 141 | !-- index k starts at nzb_u_inner+2. |
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| 142 | DO k = nzb_diff_u(j,i), nzt |
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| 143 | ! |
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| 144 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 145 | kmzp = 0.25 * & |
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| 146 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 147 | kmzm = 0.25 * & |
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| 148 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 149 | |
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| 150 | tend(k,j,i) = tend(k,j,i) & |
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| 151 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 152 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 153 | & ) & |
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| 154 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 155 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 156 | & ) & |
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| 157 | & ) * ddzw(k) |
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| 158 | ENDDO |
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| 159 | |
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| 160 | ! |
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| 161 | !-- Vertical diffusion at the first grid point above the surface, |
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| 162 | !-- if the momentum flux at the bottom is given by the Prandtl law or |
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| 163 | !-- if it is prescribed by the user. |
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| 164 | !-- Difference quotient of the momentum flux is not formed over half |
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| 165 | !-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison |
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| 166 | !-- with other (LES) modell showed that the values of the momentum |
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| 167 | !-- flux becomes too large in this case. |
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| 168 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 169 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 170 | IF ( use_surface_fluxes ) THEN |
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| 171 | k = nzb_u_inner(j,i)+1 |
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| 172 | ! |
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| 173 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 174 | kmzp = 0.25 * & |
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| 175 | ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 176 | kmzm = 0.25 * & |
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| 177 | ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 178 | |
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| 179 | tend(k,j,i) = tend(k,j,i) & |
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| 180 | & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 181 | & ) * ddzw(k) & |
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| 182 | & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 183 | & + usws(j,i) & |
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| 184 | & ) * ddzw(k) |
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| 185 | ENDIF |
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| 186 | |
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| 187 | ENDDO |
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| 188 | ENDDO |
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| 189 | |
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| 190 | END SUBROUTINE diffusion_u |
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| 191 | |
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| 192 | |
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| 193 | !------------------------------------------------------------------------------! |
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| 194 | ! Call for grid point i,j |
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| 195 | !------------------------------------------------------------------------------! |
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| 196 | SUBROUTINE diffusion_u_ij( i, j, ddzu, ddzw, km, km_damp_y, tend, u, usws, & |
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| 197 | v, w, z0 ) |
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| 198 | |
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| 199 | USE control_parameters |
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| 200 | USE grid_variables |
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| 201 | USE indices |
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| 202 | |
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| 203 | IMPLICIT NONE |
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| 204 | |
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| 205 | INTEGER :: i, j, k |
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| 206 | REAL :: kmym_x, kmym_y, kmyp_x, kmyp_y, kmzm, kmzp, usvs |
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| 207 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_y(nys-1:nyn+1) |
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| 208 | REAL :: z0(nys-1:nyn+1,nxl-1:nxr+1) |
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| 209 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
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| 210 | REAL, DIMENSION(:,:), POINTER :: usws |
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| 211 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
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| 212 | |
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| 213 | ! |
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| 214 | !-- Compute horizontal diffusion |
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| 215 | DO k = nzb_u_outer(j,i)+1, nzt |
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| 216 | ! |
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| 217 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 218 | kmyp_x = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 219 | kmym_x = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 220 | kmyp_y = kmyp_x |
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| 221 | kmym_y = kmym_x |
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| 222 | |
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| 223 | ! |
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| 224 | !-- Increase diffusion at the outflow boundary in case of non-cyclic |
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| 225 | !-- lateral boundaries. Damping is only needed for velocity components |
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| 226 | !-- parallel to the outflow boundary in the direction normal to the |
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| 227 | !-- outflow boundary. |
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| 228 | IF ( bc_ns /= 'cyclic' ) THEN |
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| 229 | kmyp_y = MAX( kmyp_y, km_damp_y(j) ) |
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| 230 | kmym_y = MAX( kmym_y, km_damp_y(j) ) |
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| 231 | ENDIF |
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| 232 | |
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| 233 | tend(k,j,i) = tend(k,j,i) & |
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| 234 | & + 2.0 * ( & |
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| 235 | & km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 236 | & - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 237 | & ) * ddx2 & |
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| 238 | & + ( kmyp_y * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 239 | & + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 240 | & - kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 241 | & - kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 242 | & ) * ddy |
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| 243 | ENDDO |
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| 244 | |
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| 245 | ! |
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| 246 | !-- Wall functions at the north and south walls, respectively |
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| 247 | IF ( wall_u(j,i) .NE. 0.0 ) THEN |
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| 248 | DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i) |
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| 249 | usvs = kappa * u(k,j,i) / LOG( 0.5 * dy / z0(j,i) ) |
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| 250 | usvs = -usvs * ABS( usvs ) |
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| 251 | kmyp_x = 0.25 * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) ) |
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| 252 | kmym_x = 0.25 * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) ) |
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| 253 | kmyp_y = kmyp_x |
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| 254 | kmym_y = kmym_x |
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| 255 | ! |
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| 256 | !-- Increase diffusion at the outflow boundary in case of |
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| 257 | !-- non-cyclic lateral boundaries. Damping is only needed for |
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| 258 | !-- velocity components parallel to the outflow boundary in |
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| 259 | !-- the direction normal to the outflow boundary. |
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| 260 | IF ( bc_ns /= 'cyclic' ) THEN |
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| 261 | kmyp_y = MAX( kmyp_y, km_damp_y(j) ) |
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| 262 | kmym_y = MAX( kmym_y, km_damp_y(j) ) |
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| 263 | ENDIF |
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| 264 | |
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| 265 | tend(k,j,i) = tend(k,j,i) & |
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| 266 | + 2.0 * ( & |
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| 267 | km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) & |
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| 268 | - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) & |
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| 269 | ) * ddx2 & |
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| 270 | + ( fyp(j,i) * ( & |
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| 271 | kmyp_y * ( u(k,j+1,i) - u(k,j,i) ) * ddy & |
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| 272 | + kmyp_x * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx & |
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| 273 | ) & |
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| 274 | - fym(j,i) * ( & |
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| 275 | kmym_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
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| 276 | + kmym_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
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| 277 | ) & |
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| 278 | + wall_u(j,i) * usvs & |
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| 279 | ) * ddy |
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| 280 | ENDDO |
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| 281 | ENDIF |
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| 282 | |
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| 283 | ! |
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| 284 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
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| 285 | !-- index k starts at nzb_u_inner+2. |
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| 286 | DO k = nzb_diff_u(j,i), nzt |
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| 287 | ! |
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| 288 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 289 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 290 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 291 | |
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| 292 | tend(k,j,i) = tend(k,j,i) & |
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| 293 | & + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 294 | & + ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 295 | & ) & |
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| 296 | & - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) & |
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| 297 | & + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx & |
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| 298 | & ) & |
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| 299 | & ) * ddzw(k) |
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| 300 | ENDDO |
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| 301 | |
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| 302 | ! |
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| 303 | !-- Vertical diffusion at the first grid point above the surface, if the |
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| 304 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
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| 305 | !-- prescribed by the user. |
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| 306 | !-- Difference quotient of the momentum flux is not formed over half of |
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| 307 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
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| 308 | !-- other (LES) modell showed that the values of the momentum flux becomes |
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| 309 | !-- too large in this case. |
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| 310 | !-- The term containing w(k-1,..) (see above equation) is removed here |
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| 311 | !-- because the vertical velocity is assumed to be zero at the surface. |
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| 312 | IF ( use_surface_fluxes ) THEN |
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| 313 | k = nzb_u_inner(j,i)+1 |
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| 314 | ! |
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| 315 | !-- Interpolate eddy diffusivities on staggered gridpoints |
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| 316 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) ) |
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| 317 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) ) |
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| 318 | |
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| 319 | tend(k,j,i) = tend(k,j,i) & |
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| 320 | & + ( kmzp * ( w(k,j,i) - w(k,j,i-1) ) * ddx & |
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| 321 | & ) * ddzw(k) & |
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| 322 | & + ( kmzp * ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) & |
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| 323 | & + usws(j,i) & |
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| 324 | & ) * ddzw(k) |
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| 325 | ENDIF |
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| 326 | |
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| 327 | END SUBROUTINE diffusion_u_ij |
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| 328 | |
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| 329 | END MODULE diffusion_u_mod |
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