1 | MODULE diffusion_v_mod |
---|
2 | |
---|
3 | !------------------------------------------------------------------------------! |
---|
4 | ! Actual revisions: |
---|
5 | ! ----------------- |
---|
6 | ! |
---|
7 | ! |
---|
8 | ! Former revisions: |
---|
9 | ! ----------------- |
---|
10 | ! $Id: diffusion_v.f90 110 2007-10-05 05:13:14Z heinze $ |
---|
11 | ! |
---|
12 | ! 106 2007-08-16 14:30:26Z raasch |
---|
13 | ! Momentumflux at top (vswst) included as boundary condition, |
---|
14 | ! j loop is starting from nysv (needed for non-cyclic boundary conditions) |
---|
15 | ! |
---|
16 | ! 75 2007-03-22 09:54:05Z raasch |
---|
17 | ! Wall functions now include diabatic conditions, call of routine wall_fluxes, |
---|
18 | ! z0 removed from argument list, vynp eliminated |
---|
19 | ! |
---|
20 | ! 20 2007-02-26 00:12:32Z raasch |
---|
21 | ! Bugfix: ddzw dimensioned 1:nzt"+1" |
---|
22 | ! |
---|
23 | ! RCS Log replace by Id keyword, revision history cleaned up |
---|
24 | ! |
---|
25 | ! Revision 1.15 2006/02/23 10:36:00 raasch |
---|
26 | ! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner |
---|
27 | ! or nzb_diff_v, respectively, in vertical diffusion, |
---|
28 | ! wall functions added for north and south walls, +z0 in argument list, |
---|
29 | ! terms containing w(k-1,..) are removed from the Prandtl-layer equation |
---|
30 | ! because they cause errors at the edges of topography |
---|
31 | ! WARNING: loops containing the MAX function are still not properly vectorized! |
---|
32 | ! |
---|
33 | ! Revision 1.1 1997/09/12 06:24:01 raasch |
---|
34 | ! Initial revision |
---|
35 | ! |
---|
36 | ! |
---|
37 | ! Description: |
---|
38 | ! ------------ |
---|
39 | ! Diffusion term of the v-component |
---|
40 | !------------------------------------------------------------------------------! |
---|
41 | |
---|
42 | USE wall_fluxes_mod |
---|
43 | |
---|
44 | PRIVATE |
---|
45 | PUBLIC diffusion_v |
---|
46 | |
---|
47 | INTERFACE diffusion_v |
---|
48 | MODULE PROCEDURE diffusion_v |
---|
49 | MODULE PROCEDURE diffusion_v_ij |
---|
50 | END INTERFACE diffusion_v |
---|
51 | |
---|
52 | CONTAINS |
---|
53 | |
---|
54 | |
---|
55 | !------------------------------------------------------------------------------! |
---|
56 | ! Call for all grid points |
---|
57 | !------------------------------------------------------------------------------! |
---|
58 | SUBROUTINE diffusion_v( ddzu, ddzw, km, km_damp_x, tend, u, v, vsws, & |
---|
59 | vswst, w ) |
---|
60 | |
---|
61 | USE control_parameters |
---|
62 | USE grid_variables |
---|
63 | USE indices |
---|
64 | |
---|
65 | IMPLICIT NONE |
---|
66 | |
---|
67 | INTEGER :: i, j, k |
---|
68 | REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp |
---|
69 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) |
---|
70 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
---|
71 | REAL, DIMENSION(:,:), POINTER :: vsws, vswst |
---|
72 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
---|
73 | REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus |
---|
74 | |
---|
75 | ! |
---|
76 | !-- First calculate horizontal momentum flux v'u' at vertical walls, |
---|
77 | !-- if neccessary |
---|
78 | IF ( topography /= 'flat' ) THEN |
---|
79 | CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, & |
---|
80 | nzb_v_outer, wall_v ) |
---|
81 | ENDIF |
---|
82 | |
---|
83 | DO i = nxl, nxr |
---|
84 | DO j = nysv, nyn |
---|
85 | ! |
---|
86 | !-- Compute horizontal diffusion |
---|
87 | DO k = nzb_v_outer(j,i)+1, nzt |
---|
88 | ! |
---|
89 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
90 | kmxp_x = 0.25 * & |
---|
91 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
---|
92 | kmxm_x = 0.25 * & |
---|
93 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
---|
94 | kmxp_y = kmxp_x |
---|
95 | kmxm_y = kmxm_x |
---|
96 | ! |
---|
97 | !-- Increase diffusion at the outflow boundary in case of |
---|
98 | !-- non-cyclic lateral boundaries. Damping is only needed for |
---|
99 | !-- velocity components parallel to the outflow boundary in |
---|
100 | !-- the direction normal to the outflow boundary. |
---|
101 | IF ( bc_lr /= 'cyclic' ) THEN |
---|
102 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
---|
103 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
---|
104 | ENDIF |
---|
105 | |
---|
106 | tend(k,j,i) = tend(k,j,i) & |
---|
107 | & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
---|
108 | & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
---|
109 | & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
---|
110 | & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
---|
111 | & ) * ddx & |
---|
112 | & + 2.0 * ( & |
---|
113 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
---|
114 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
---|
115 | & ) * ddy2 |
---|
116 | ENDDO |
---|
117 | |
---|
118 | ! |
---|
119 | !-- Wall functions at the left and right walls, respectively |
---|
120 | IF ( wall_v(j,i) /= 0.0 ) THEN |
---|
121 | |
---|
122 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
---|
123 | kmxp_x = 0.25 * & |
---|
124 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
---|
125 | kmxm_x = 0.25 * & |
---|
126 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
---|
127 | kmxp_y = kmxp_x |
---|
128 | kmxm_y = kmxm_x |
---|
129 | ! |
---|
130 | !-- Increase diffusion at the outflow boundary in case of |
---|
131 | !-- non-cyclic lateral boundaries. Damping is only needed for |
---|
132 | !-- velocity components parallel to the outflow boundary in |
---|
133 | !-- the direction normal to the outflow boundary. |
---|
134 | IF ( bc_lr /= 'cyclic' ) THEN |
---|
135 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
---|
136 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
---|
137 | ENDIF |
---|
138 | |
---|
139 | tend(k,j,i) = tend(k,j,i) & |
---|
140 | + 2.0 * ( & |
---|
141 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
---|
142 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
---|
143 | ) * ddy2 & |
---|
144 | + ( fxp(j,i) * ( & |
---|
145 | kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
---|
146 | + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
---|
147 | ) & |
---|
148 | - fxm(j,i) * ( & |
---|
149 | kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
---|
150 | + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
---|
151 | ) & |
---|
152 | + wall_v(j,i) * vsus(k,j,i) & |
---|
153 | ) * ddx |
---|
154 | ENDDO |
---|
155 | ENDIF |
---|
156 | |
---|
157 | ! |
---|
158 | !-- Compute vertical diffusion. In case of simulating a Prandtl |
---|
159 | !-- layer, index k starts at nzb_v_inner+2. |
---|
160 | DO k = nzb_diff_v(j,i), nzt_diff |
---|
161 | ! |
---|
162 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
163 | kmzp = 0.25 * & |
---|
164 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
165 | kmzm = 0.25 * & |
---|
166 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
167 | |
---|
168 | tend(k,j,i) = tend(k,j,i) & |
---|
169 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
---|
170 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
---|
171 | & ) & |
---|
172 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
---|
173 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
---|
174 | & ) & |
---|
175 | & ) * ddzw(k) |
---|
176 | ENDDO |
---|
177 | |
---|
178 | ! |
---|
179 | !-- Vertical diffusion at the first grid point above the surface, |
---|
180 | !-- if the momentum flux at the bottom is given by the Prandtl law |
---|
181 | !-- or if it is prescribed by the user. |
---|
182 | !-- Difference quotient of the momentum flux is not formed over |
---|
183 | !-- half of the grid spacing (2.0*ddzw(k)) any more, since the |
---|
184 | !-- comparison with other (LES) modell showed that the values of |
---|
185 | !-- the momentum flux becomes too large in this case. |
---|
186 | !-- The term containing w(k-1,..) (see above equation) is removed here |
---|
187 | !-- because the vertical velocity is assumed to be zero at the surface. |
---|
188 | IF ( use_surface_fluxes ) THEN |
---|
189 | k = nzb_v_inner(j,i)+1 |
---|
190 | ! |
---|
191 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
192 | kmzp = 0.25 * & |
---|
193 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
194 | kmzm = 0.25 * & |
---|
195 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
196 | |
---|
197 | tend(k,j,i) = tend(k,j,i) & |
---|
198 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
---|
199 | & ) * ddzw(k) & |
---|
200 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
---|
201 | & + vsws(j,i) & |
---|
202 | & ) * ddzw(k) |
---|
203 | ENDIF |
---|
204 | |
---|
205 | ! |
---|
206 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
---|
207 | !-- if the momentum flux at the top is prescribed by the user |
---|
208 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
---|
209 | k = nzt |
---|
210 | ! |
---|
211 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
212 | kmzp = 0.25 * & |
---|
213 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
214 | kmzm = 0.25 * & |
---|
215 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
216 | |
---|
217 | tend(k,j,i) = tend(k,j,i) & |
---|
218 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
---|
219 | & ) * ddzw(k) & |
---|
220 | & + ( -vswst(j,i) & |
---|
221 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
---|
222 | & ) * ddzw(k) |
---|
223 | ENDIF |
---|
224 | |
---|
225 | ENDDO |
---|
226 | ENDDO |
---|
227 | |
---|
228 | END SUBROUTINE diffusion_v |
---|
229 | |
---|
230 | |
---|
231 | !------------------------------------------------------------------------------! |
---|
232 | ! Call for grid point i,j |
---|
233 | !------------------------------------------------------------------------------! |
---|
234 | SUBROUTINE diffusion_v_ij( i, j, ddzu, ddzw, km, km_damp_x, tend, u, v, & |
---|
235 | vsws, vswst, w ) |
---|
236 | |
---|
237 | USE control_parameters |
---|
238 | USE grid_variables |
---|
239 | USE indices |
---|
240 | |
---|
241 | IMPLICIT NONE |
---|
242 | |
---|
243 | INTEGER :: i, j, k |
---|
244 | REAL :: kmxm_x, kmxm_y, kmxp_x, kmxp_y, kmzm, kmzp |
---|
245 | REAL :: ddzu(1:nzt+1), ddzw(1:nzt+1), km_damp_x(nxl-1:nxr+1) |
---|
246 | REAL :: tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) |
---|
247 | REAL, DIMENSION(nzb:nzt+1) :: vsus |
---|
248 | REAL, DIMENSION(:,:), POINTER :: vsws, vswst |
---|
249 | REAL, DIMENSION(:,:,:), POINTER :: km, u, v, w |
---|
250 | |
---|
251 | ! |
---|
252 | !-- Compute horizontal diffusion |
---|
253 | DO k = nzb_v_outer(j,i)+1, nzt |
---|
254 | ! |
---|
255 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
256 | kmxp_x = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
---|
257 | kmxm_x = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
---|
258 | kmxp_y = kmxp_x |
---|
259 | kmxm_y = kmxm_x |
---|
260 | ! |
---|
261 | !-- Increase diffusion at the outflow boundary in case of non-cyclic |
---|
262 | !-- lateral boundaries. Damping is only needed for velocity components |
---|
263 | !-- parallel to the outflow boundary in the direction normal to the |
---|
264 | !-- outflow boundary. |
---|
265 | IF ( bc_lr /= 'cyclic' ) THEN |
---|
266 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
---|
267 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
---|
268 | ENDIF |
---|
269 | |
---|
270 | tend(k,j,i) = tend(k,j,i) & |
---|
271 | & + ( kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
---|
272 | & + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
---|
273 | & - kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
---|
274 | & - kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
---|
275 | & ) * ddx & |
---|
276 | & + 2.0 * ( & |
---|
277 | & km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
---|
278 | & - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
---|
279 | & ) * ddy2 |
---|
280 | ENDDO |
---|
281 | |
---|
282 | ! |
---|
283 | !-- Wall functions at the left and right walls, respectively |
---|
284 | IF ( wall_v(j,i) /= 0.0 ) THEN |
---|
285 | |
---|
286 | ! |
---|
287 | !-- Calculate the horizontal momentum flux v'u' |
---|
288 | CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), & |
---|
289 | vsus, 0.0, 1.0, 0.0, 0.0 ) |
---|
290 | |
---|
291 | DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i) |
---|
292 | kmxp_x = 0.25 * & |
---|
293 | ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) ) |
---|
294 | kmxm_x = 0.25 * & |
---|
295 | ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) ) |
---|
296 | kmxp_y = kmxp_x |
---|
297 | kmxm_y = kmxm_x |
---|
298 | ! |
---|
299 | !-- Increase diffusion at the outflow boundary in case of |
---|
300 | !-- non-cyclic lateral boundaries. Damping is only needed for |
---|
301 | !-- velocity components parallel to the outflow boundary in |
---|
302 | !-- the direction normal to the outflow boundary. |
---|
303 | IF ( bc_lr /= 'cyclic' ) THEN |
---|
304 | kmxp_x = MAX( kmxp_x, km_damp_x(i) ) |
---|
305 | kmxm_x = MAX( kmxm_x, km_damp_x(i) ) |
---|
306 | ENDIF |
---|
307 | |
---|
308 | tend(k,j,i) = tend(k,j,i) & |
---|
309 | + 2.0 * ( & |
---|
310 | km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) & |
---|
311 | - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) & |
---|
312 | ) * ddy2 & |
---|
313 | + ( fxp(j,i) * ( & |
---|
314 | kmxp_x * ( v(k,j,i+1) - v(k,j,i) ) * ddx & |
---|
315 | + kmxp_y * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy & |
---|
316 | ) & |
---|
317 | - fxm(j,i) * ( & |
---|
318 | kmxm_x * ( v(k,j,i) - v(k,j,i-1) ) * ddx & |
---|
319 | + kmxm_y * ( u(k,j,i) - u(k,j-1,i) ) * ddy & |
---|
320 | ) & |
---|
321 | + wall_v(j,i) * vsus(k) & |
---|
322 | ) * ddx |
---|
323 | ENDDO |
---|
324 | ENDIF |
---|
325 | |
---|
326 | ! |
---|
327 | !-- Compute vertical diffusion. In case of simulating a Prandtl layer, |
---|
328 | !-- index k starts at nzb_v_inner+2. |
---|
329 | DO k = nzb_diff_v(j,i), nzt_diff |
---|
330 | ! |
---|
331 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
332 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
333 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
334 | |
---|
335 | tend(k,j,i) = tend(k,j,i) & |
---|
336 | & + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
---|
337 | & + ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
---|
338 | & ) & |
---|
339 | & - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
---|
340 | & + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
---|
341 | & ) & |
---|
342 | & ) * ddzw(k) |
---|
343 | ENDDO |
---|
344 | |
---|
345 | ! |
---|
346 | !-- Vertical diffusion at the first grid point above the surface, if the |
---|
347 | !-- momentum flux at the bottom is given by the Prandtl law or if it is |
---|
348 | !-- prescribed by the user. |
---|
349 | !-- Difference quotient of the momentum flux is not formed over half of |
---|
350 | !-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with |
---|
351 | !-- other (LES) modell showed that the values of the momentum flux becomes |
---|
352 | !-- too large in this case. |
---|
353 | !-- The term containing w(k-1,..) (see above equation) is removed here |
---|
354 | !-- because the vertical velocity is assumed to be zero at the surface. |
---|
355 | IF ( use_surface_fluxes ) THEN |
---|
356 | k = nzb_v_inner(j,i)+1 |
---|
357 | ! |
---|
358 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
359 | kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
360 | kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
361 | |
---|
362 | tend(k,j,i) = tend(k,j,i) & |
---|
363 | & + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy & |
---|
364 | & ) * ddzw(k) & |
---|
365 | & + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) & |
---|
366 | & + vsws(j,i) & |
---|
367 | & ) * ddzw(k) |
---|
368 | ENDIF |
---|
369 | |
---|
370 | ! |
---|
371 | !-- Vertical diffusion at the first gridpoint below the top boundary, |
---|
372 | !-- if the momentum flux at the top is prescribed by the user |
---|
373 | IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN |
---|
374 | k = nzt |
---|
375 | ! |
---|
376 | !-- Interpolate eddy diffusivities on staggered gridpoints |
---|
377 | kmzp = 0.25 * & |
---|
378 | ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) ) |
---|
379 | kmzm = 0.25 * & |
---|
380 | ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) ) |
---|
381 | |
---|
382 | tend(k,j,i) = tend(k,j,i) & |
---|
383 | & - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy & |
---|
384 | & ) * ddzw(k) & |
---|
385 | & + ( -vswst(j,i) & |
---|
386 | & - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) & |
---|
387 | & ) * ddzw(k) |
---|
388 | ENDIF |
---|
389 | |
---|
390 | END SUBROUTINE diffusion_v_ij |
---|
391 | |
---|
392 | END MODULE diffusion_v_mod |
---|