| [1] | 1 | MODULE diffusion_v_mod |
|---|
| 2 | |
|---|
| 3 | !------------------------------------------------------------------------------! |
|---|
| 4 | ! Actual revisions: |
|---|
| 5 | ! ----------------- |
|---|
| [20] | 6 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
|---|
| [1] | 7 | ! |
|---|
| 8 | ! Former revisions: |
|---|
| 9 | ! ----------------- |
|---|
| [3] | 10 | ! $Id: diffusion_v.f90 20 2007-02-26 00:12:32Z raasch $ |
|---|
| 11 | ! RCS Log replace by Id keyword, revision history cleaned up |
|---|
| 12 | ! |
|---|
| [1] | 13 | ! Revision 1.15 2006/02/23 10:36:00 raasch |
|---|
| 14 | ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner |
|---|
| 15 | ! or nzb_diff_v, respectively, in vertical diffusion, |
|---|
| 16 | ! wall functions added for north and south walls, +z0 in argument list, |
|---|
| 17 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
|---|
| 18 | ! because they cause errors at the edges of topography |
|---|
| 19 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
|---|
| 20 | ! |
|---|
| 21 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
|---|
| 22 | ! Initial revision |
|---|
| 23 | ! |
|---|
| 24 | ! |
|---|
| 25 | ! Description: |
|---|
| 26 | ! ------------ |
|---|
| 27 | ! Diffusion term of the v-component |
|---|
| 28 | !------------------------------------------------------------------------------! |
|---|
| 29 | |
|---|
| 30 | PRIVATE |
|---|
| 31 | PUBLIC diffusion_v |
|---|
| 32 | |
|---|
| 33 | INTERFACE diffusion_v |
|---|
| 34 | MODULE PROCEDURE diffusion_v |
|---|
| 35 | MODULE PROCEDURE diffusion_v_ij |
|---|
| 36 | END INTERFACE diffusion_v |
|---|
| 37 | |
|---|
| 38 | CONTAINS |
|---|
| 39 | |
|---|
| 40 | |
|---|
| 41 | !------------------------------------------------------------------------------! |
|---|
| 42 | ! Call for all grid points |
|---|
| 43 | !------------------------------------------------------------------------------! |
|---|
| 44 | SUBROUTINE diffusion_v( ddzu, ddzw, km, km_damp_x, tend, u, v, vsws, w, z0 ) |
|---|
| 45 | |
|---|
| 46 | USE control_parameters |
|---|
| 47 | USE grid_variables |
|---|
| 48 | USE indices |
|---|
| 49 | |
|---|
| 50 | IMPLICIT NONE |
|---|
| 51 | |
|---|
| 52 | INTEGER :: i, j, k |
|---|
| 53 | REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp, vsus |
|---|
| [20] | 54 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) |
|---|
| [1] | 55 | REAL :: z0(nys-1:nyn+1,nxl-1:nxr+1) |
|---|
| 56 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
|---|
| 57 | REAL, DIMENSION(:,:), POINTER :: vsws |
|---|
| 58 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
|---|
| 59 | |
|---|
| 60 | DO i = nxl, nxr |
|---|
| 61 | DO j = nys, nyn+vynp |
|---|
| 62 | ! |
|---|
| 63 | !-- Compute horizontal diffusion |
|---|
| 64 | DO k = nzb_v_outer(j,i)+1, nzt |
|---|
| 65 | ! |
|---|
| 66 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 67 | kmxp_x = 0.25 * & |
|---|
| 68 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
|---|
| 69 | kmxm_x = 0.25 * & |
|---|
| 70 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
|---|
| 71 | kmxp_y = kmxp_x |
|---|
| 72 | kmxm_y = kmxm_x |
|---|
| 73 | ! |
|---|
| 74 | !-- Increase diffusion at the outflow boundary in case of |
|---|
| 75 | !-- non-cyclic lateral boundaries. Damping is only needed for |
|---|
| 76 | !-- velocity components parallel to the outflow boundary in |
|---|
| 77 | !-- the direction normal to the outflow boundary. |
|---|
| 78 | IF ( bc_lr /= 'cyclic' ) THEN |
|---|
| 79 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
|---|
| 80 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
|---|
| 81 | ENDIF |
|---|
| 82 | |
|---|
| 83 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 84 | & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
|---|
| 85 | & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
|---|
| 86 | & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 87 | & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 88 | & ) * ddx & |
|---|
| 89 | & + 2.0 * ( & |
|---|
| 90 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
|---|
| 91 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
|---|
| 92 | & ) * ddy2 |
|---|
| 93 | ENDDO |
|---|
| 94 | |
|---|
| 95 | ! |
|---|
| 96 | !-- Wall functions at the left and right walls, respectively |
|---|
| 97 | IF ( wall_v(j,i) /= 0.0 ) THEN |
|---|
| 98 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
|---|
| 99 | vsus = kappa * v(k,j,i) / LOG( 0.5 * dx / z0(j,i)) |
|---|
| 100 | vsus = -vsus * ABS( vsus ) |
|---|
| 101 | kmxp_x = 0.25 * & |
|---|
| 102 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
|---|
| 103 | kmxm_x = 0.25 * & |
|---|
| 104 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
|---|
| 105 | kmxp_y = kmxp_x |
|---|
| 106 | kmxm_y = kmxm_x |
|---|
| 107 | ! |
|---|
| 108 | !-- Increase diffusion at the outflow boundary in case of |
|---|
| 109 | !-- non-cyclic lateral boundaries. Damping is only needed for |
|---|
| 110 | !-- velocity components parallel to the outflow boundary in |
|---|
| 111 | !-- the direction normal to the outflow boundary. |
|---|
| 112 | IF ( bc_lr /= 'cyclic' ) THEN |
|---|
| 113 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
|---|
| 114 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
|---|
| 115 | ENDIF |
|---|
| 116 | |
|---|
| 117 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 118 | + 2.0 * ( & |
|---|
| 119 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
|---|
| 120 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
|---|
| 121 | ) * ddy2 & |
|---|
| 122 | + ( fxp(j,i) * ( & |
|---|
| 123 | kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
|---|
| 124 | + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
|---|
| 125 | ) & |
|---|
| 126 | - fxm(j,i) * ( & |
|---|
| 127 | kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 128 | + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 129 | ) & |
|---|
| 130 | + wall_v(j,i) * vsus & |
|---|
| 131 | ) * ddx |
|---|
| 132 | ENDDO |
|---|
| 133 | ENDIF |
|---|
| 134 | |
|---|
| 135 | ! |
|---|
| 136 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
|---|
| 137 | !-- layer, index k starts at nzb_v_inner+2. |
|---|
| 138 | DO k = nzb_diff_v(j,i), nzt |
|---|
| 139 | ! |
|---|
| 140 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 141 | kmzp = 0.25 * & |
|---|
| 142 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
|---|
| 143 | kmzm = 0.25 * & |
|---|
| 144 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
|---|
| 145 | |
|---|
| 146 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 147 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
|---|
| 148 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
|---|
| 149 | & ) & |
|---|
| 150 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
|---|
| 151 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
|---|
| 152 | & ) & |
|---|
| 153 | & ) * ddzw(k) |
|---|
| 154 | ENDDO |
|---|
| 155 | |
|---|
| 156 | ! |
|---|
| 157 | !-- Vertical diffusion at the first grid point above the surface, |
|---|
| 158 | !-- if the momentum flux at the bottom is given by the Prandtl law |
|---|
| 159 | !-- or if it is prescribed by the user. |
|---|
| 160 | !-- Difference quotient of the momentum flux is not formed over |
|---|
| 161 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
|---|
| 162 | !-- comparison with other (LES) modell showed that the values of |
|---|
| 163 | !-- the momentum flux becomes too large in this case. |
|---|
| 164 | !-- The term containing w(k-1,..) (see above equation) is removed here |
|---|
| 165 | !-- because the vertical velocity is assumed to be zero at the surface. |
|---|
| 166 | IF ( use_surface_fluxes ) THEN |
|---|
| 167 | k = nzb_v_inner(j,i)+1 |
|---|
| 168 | ! |
|---|
| 169 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 170 | kmzp = 0.25 * & |
|---|
| 171 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
|---|
| 172 | kmzm = 0.25 * & |
|---|
| 173 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
|---|
| 174 | |
|---|
| 175 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 176 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
|---|
| 177 | & ) * ddzw(k) & |
|---|
| 178 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
|---|
| 179 | & + vsws(j,i) & |
|---|
| 180 | & ) * ddzw(k) |
|---|
| 181 | ENDIF |
|---|
| 182 | |
|---|
| 183 | ENDDO |
|---|
| 184 | ENDDO |
|---|
| 185 | |
|---|
| 186 | END SUBROUTINE diffusion_v |
|---|
| 187 | |
|---|
| 188 | |
|---|
| 189 | !------------------------------------------------------------------------------! |
|---|
| 190 | ! Call for grid point i,j |
|---|
| 191 | !------------------------------------------------------------------------------! |
|---|
| 192 | SUBROUTINE diffusion_v_ij( i, j, ddzu, ddzw, km, km_damp_x, tend, u, v, & |
|---|
| 193 | vsws, w, z0 ) |
|---|
| 194 | |
|---|
| 195 | USE control_parameters |
|---|
| 196 | USE grid_variables |
|---|
| 197 | USE indices |
|---|
| 198 | |
|---|
| 199 | IMPLICIT NONE |
|---|
| 200 | |
|---|
| 201 | INTEGER :: i, j, k |
|---|
| 202 | REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp, vsus |
|---|
| [20] | 203 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) |
|---|
| [1] | 204 | REAL :: z0(nys-1:nyn+1,nxl-1:nxr+1) |
|---|
| 205 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
|---|
| 206 | REAL, DIMENSION(:,:), POINTER :: vsws |
|---|
| 207 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
|---|
| 208 | |
|---|
| 209 | ! |
|---|
| 210 | !-- Compute horizontal diffusion |
|---|
| 211 | DO k = nzb_v_outer(j,i)+1, nzt |
|---|
| 212 | ! |
|---|
| 213 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 214 | kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
|---|
| 215 | kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
|---|
| 216 | kmxp_y = kmxp_x |
|---|
| 217 | kmxm_y = kmxm_x |
|---|
| 218 | ! |
|---|
| 219 | !-- Increase diffusion at the outflow boundary in case of non-cyclic |
|---|
| 220 | !-- lateral boundaries. Damping is only needed for velocity components |
|---|
| 221 | !-- parallel to the outflow boundary in the direction normal to the |
|---|
| 222 | !-- outflow boundary. |
|---|
| 223 | IF ( bc_lr /= 'cyclic' ) THEN |
|---|
| 224 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
|---|
| 225 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
|---|
| 226 | ENDIF |
|---|
| 227 | |
|---|
| 228 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 229 | & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
|---|
| 230 | & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
|---|
| 231 | & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 232 | & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 233 | & ) * ddx & |
|---|
| 234 | & + 2.0 * ( & |
|---|
| 235 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
|---|
| 236 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
|---|
| 237 | & ) * ddy2 |
|---|
| 238 | ENDDO |
|---|
| 239 | |
|---|
| 240 | ! |
|---|
| 241 | !-- Wall functions at the left and right walls, respectively |
|---|
| 242 | IF ( wall_v(j,i) /= 0.0 ) THEN |
|---|
| 243 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
|---|
| 244 | vsus = kappa * v(k,j,i) / LOG( 0.5 * dx / z0(j,i)) |
|---|
| 245 | vsus = -vsus * ABS( vsus ) |
|---|
| 246 | kmxp_x = 0.25 * & |
|---|
| 247 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
|---|
| 248 | kmxm_x = 0.25 * & |
|---|
| 249 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
|---|
| 250 | kmxp_y = kmxp_x |
|---|
| 251 | kmxm_y = kmxm_x |
|---|
| 252 | ! |
|---|
| 253 | !-- Increase diffusion at the outflow boundary in case of |
|---|
| 254 | !-- non-cyclic lateral boundaries. Damping is only needed for |
|---|
| 255 | !-- velocity components parallel to the outflow boundary in |
|---|
| 256 | !-- the direction normal to the outflow boundary. |
|---|
| 257 | IF ( bc_lr /= 'cyclic' ) THEN |
|---|
| 258 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
|---|
| 259 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
|---|
| 260 | ENDIF |
|---|
| 261 | |
|---|
| 262 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 263 | + 2.0 * ( & |
|---|
| 264 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
|---|
| 265 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
|---|
| 266 | ) * ddy2 & |
|---|
| 267 | + ( fxp(j,i) * ( & |
|---|
| 268 | kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
|---|
| 269 | + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
|---|
| 270 | ) & |
|---|
| 271 | - fxm(j,i) * ( & |
|---|
| 272 | kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
|---|
| 273 | + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
|---|
| 274 | ) & |
|---|
| 275 | + wall_v(j,i) * vsus & |
|---|
| 276 | ) * ddx |
|---|
| 277 | ENDDO |
|---|
| 278 | ENDIF |
|---|
| 279 | |
|---|
| 280 | ! |
|---|
| 281 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
|---|
| 282 | !-- index k starts at nzb_v_inner+2. |
|---|
| 283 | DO k = nzb_diff_v(j,i), nzt |
|---|
| 284 | ! |
|---|
| 285 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 286 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
|---|
| 287 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
|---|
| 288 | |
|---|
| 289 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 290 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
|---|
| 291 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
|---|
| 292 | & ) & |
|---|
| 293 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
|---|
| 294 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
|---|
| 295 | & ) & |
|---|
| 296 | & ) * ddzw(k) |
|---|
| 297 | ENDDO |
|---|
| 298 | |
|---|
| 299 | ! |
|---|
| 300 | !-- Vertical diffusion at the first grid point above the surface, if the |
|---|
| 301 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
|---|
| 302 | !-- prescribed by the user. |
|---|
| 303 | !-- Difference quotient of the momentum flux is not formed over half of |
|---|
| 304 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
|---|
| 305 | !-- other (LES) modell showed that the values of the momentum flux becomes |
|---|
| 306 | !-- too large in this case. |
|---|
| 307 | !-- The term containing w(k-1,..) (see above equation) is removed here |
|---|
| 308 | !-- because the vertical velocity is assumed to be zero at the surface. |
|---|
| 309 | IF ( use_surface_fluxes ) THEN |
|---|
| 310 | k = nzb_v_inner(j,i)+1 |
|---|
| 311 | ! |
|---|
| 312 | !-- Interpolate eddy diffusivities on staggered gridpoints |
|---|
| 313 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
|---|
| 314 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
|---|
| 315 | |
|---|
| 316 | tend(k,j,i) = tend(k,j,i) & |
|---|
| 317 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
|---|
| 318 | & ) * ddzw(k) & |
|---|
| 319 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
|---|
| 320 | & + vsws(j,i) & |
|---|
| 321 | & ) * ddzw(k) |
|---|
| 322 | ENDIF |
|---|
| 323 | |
|---|
| 324 | END SUBROUTINE diffusion_v_ij |
|---|
| 325 | |
|---|
| 326 | END MODULE diffusion_v_mod |
|---|
