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