[221] | 1 | MODULE advect_mod |
---|
| 2 | USE icosa |
---|
| 3 | IMPLICIT NONE |
---|
| 4 | |
---|
| 5 | PRIVATE |
---|
| 6 | |
---|
| 7 | PUBLIC :: init_advect, compute_backward_traj, compute_gradq3d, compute_advect_horiz |
---|
| 8 | |
---|
| 9 | CONTAINS |
---|
| 10 | |
---|
| 11 | !========================================================================== |
---|
| 12 | |
---|
[267] | 13 | SUBROUTINE init_advect(normal,tangent,sqrt_leng) |
---|
[221] | 14 | IMPLICIT NONE |
---|
| 15 | REAL(rstd),INTENT(OUT) :: normal(3*iim*jjm,3) |
---|
| 16 | REAL(rstd),INTENT(OUT) :: tangent(3*iim*jjm,3) |
---|
[267] | 17 | REAL(rstd),INTENT(OUT) :: sqrt_leng(iim*jjm) |
---|
[221] | 18 | |
---|
| 19 | INTEGER :: ij |
---|
| 20 | |
---|
| 21 | !$SIMD |
---|
| 22 | DO ij=ij_begin,ij_end |
---|
| 23 | |
---|
| 24 | CALL cross_product2(xyz_v(ij+z_rdown,:),xyz_v(ij+z_rup,:),normal(ij+u_right,:)) |
---|
| 25 | normal(ij+u_right,:)=normal(ij+u_right,:)/sqrt(sum(normal(ij+u_right,:)**2)+1e-50)*ne(ij,right) |
---|
| 26 | |
---|
| 27 | CALL cross_product2(xyz_v(ij+z_up,:),xyz_v(ij+z_lup,:),normal(ij+u_lup,:)) |
---|
| 28 | normal(ij+u_lup,:)=normal(ij+u_lup,:)/sqrt(sum(normal(ij+u_lup,:)**2)+1e-50)*ne(ij,lup) |
---|
| 29 | |
---|
| 30 | CALL cross_product2(xyz_v(ij+z_ldown,:),xyz_v(ij+z_down,:),normal(ij+u_ldown,:)) |
---|
| 31 | normal(ij+u_ldown,:)=normal(ij+u_ldown,:)/sqrt(sum(normal(ij+u_ldown,:)**2)+1e-50)*ne(ij,ldown) |
---|
| 32 | |
---|
| 33 | tangent(ij+u_right,:)=xyz_v(ij+z_rup,:)-xyz_v(ij+z_rdown,:) |
---|
| 34 | tangent(ij+u_right,:)=tangent(ij+u_right,:)/sqrt(sum(tangent(ij+u_right,:)**2)+1e-50) |
---|
| 35 | |
---|
| 36 | tangent(ij+u_lup,:)=xyz_v(ij+z_lup,:)-xyz_v(ij+z_up,:) |
---|
| 37 | tangent(ij+u_lup,:)=tangent(ij+u_lup,:)/sqrt(sum(tangent(ij+u_lup,:)**2)+1e-50) |
---|
| 38 | |
---|
| 39 | tangent(ij+u_ldown,:)=xyz_v(ij+z_down,:)-xyz_v(ij+z_ldown,:) |
---|
| 40 | tangent(ij+u_ldown,:)=tangent(ij+u_ldown,:)/sqrt(sum(tangent(ij+u_ldown,:)**2)+1e-50) |
---|
| 41 | |
---|
[267] | 42 | sqrt_leng(ij) = sqrt(max(sum((xyz_v(ij+z_up,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_down,:) - xyz_i(ij,:))**2), & |
---|
| 43 | sum((xyz_v(ij+z_rup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_rdown,:) - xyz_i(ij,:))**2), & |
---|
| 44 | sum((xyz_v(ij+z_lup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_ldown,:) - xyz_i(ij,:))**2)) ) |
---|
[221] | 45 | ENDDO |
---|
| 46 | |
---|
| 47 | END SUBROUTINE init_advect |
---|
| 48 | |
---|
| 49 | !======================================================================================= |
---|
| 50 | |
---|
[267] | 51 | SUBROUTINE compute_gradq3d(qi_in,sqrt_leng_in,gradq3d_out,xyz_i,xyz_v) |
---|
[221] | 52 | USE trace |
---|
| 53 | USE omp_para |
---|
| 54 | IMPLICIT NONE |
---|
| 55 | REAL(rstd),INTENT(IN) :: qi_in(iim*jjm,llm) |
---|
[267] | 56 | REAL(rstd),INTENT(IN) :: sqrt_leng_in(iim*jjm) |
---|
[221] | 57 | REAL(rstd),INTENT(IN) :: xyz_i(iim*jjm,3) |
---|
| 58 | REAL(rstd),INTENT(IN) :: xyz_v(2*iim*jjm,3) |
---|
| 59 | REAL(rstd),INTENT(OUT) :: gradq3d_out(iim*jjm,llm,3) |
---|
| 60 | REAL(rstd) :: maxq,minq,minq_c,maxq_c |
---|
| 61 | REAL(rstd) :: alphamx,alphami,alpha ,maggrd |
---|
| 62 | REAL(rstd) :: leng1,leng2 |
---|
| 63 | REAL(rstd) :: arr(2*iim*jjm) |
---|
| 64 | REAL(rstd) :: ar(iim*jjm) |
---|
| 65 | REAL(rstd) :: gradtri(2*iim*jjm,llm,3) |
---|
| 66 | INTEGER :: ij,k,ind,l |
---|
| 67 | REAL(rstd) :: qi(iim*jjm,llm) |
---|
[267] | 68 | REAL(rstd) :: sqrt_leng(iim*jjm) |
---|
[221] | 69 | REAL(rstd) :: gradq3d(iim*jjm,llm,3) |
---|
| 70 | REAL(rstd) :: detx,dety,detz,det |
---|
| 71 | REAL(rstd) :: A(3,3), a11,a12,a13,a21,a22,a23,a31,a32,a33 |
---|
| 72 | REAL(rstd) :: x1,x2,x3 |
---|
| 73 | REAL(rstd) :: dq(3) |
---|
| 74 | |
---|
| 75 | qi=qi_in |
---|
[267] | 76 | sqrt_leng=sqrt_leng_in |
---|
[221] | 77 | |
---|
| 78 | CALL trace_start("compute_gradq3d1") |
---|
| 79 | |
---|
| 80 | ! TODO : precompute ar, drop arr as output argument of gradq ? |
---|
| 81 | |
---|
| 82 | !========================================================================================== GRADIENT |
---|
| 83 | ! Compute gradient at triangles solving a linear system |
---|
| 84 | ! arr = area of triangle joining centroids of hexagons |
---|
| 85 | ! DO l = ll_begin,ll_end |
---|
| 86 | !!$SIMD |
---|
| 87 | ! DO ij=ij_begin_ext,ij_end_ext |
---|
| 88 | !! CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,:),arr(ij+z_up)) |
---|
| 89 | !! CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,:),arr(ij+z_down)) |
---|
| 90 | ! CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,1),gradtri(ij+z_up,l,2),gradtri(ij+z_up,l,3),arr(ij+z_up)) |
---|
| 91 | ! CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,1),gradtri(ij+z_down,l,2),gradtri(ij+z_down,l,3),arr(ij+z_down)) |
---|
| 92 | ! END DO |
---|
| 93 | ! END DO |
---|
| 94 | |
---|
| 95 | DO l = ll_begin,ll_end |
---|
| 96 | !$SIMD |
---|
| 97 | DO ij=ij_begin_ext,ij_end_ext |
---|
| 98 | ! CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,1),gradtri(ij+z_up,l,2),gradtri(ij+z_up,l,3),arr(ij+z_up)) |
---|
| 99 | |
---|
| 100 | |
---|
| 101 | A(1,1)=xyz_i(ij+t_rup,1)-xyz_i(ij,1); A(1,2)=xyz_i(ij+t_rup,2)-xyz_i(ij,2); A(1,3)=xyz_i(ij+t_rup,3)-xyz_i(ij,3) |
---|
| 102 | A(2,1)=xyz_i(ij+t_lup,1)-xyz_i(ij,1); A(2,2)=xyz_i(ij+t_lup,2)-xyz_i(ij,2); A(2,3)=xyz_i(ij+t_lup,3)-xyz_i(ij,3) |
---|
| 103 | A(3,1)=xyz_v(ij+z_up,1); A(3,2)= xyz_v(ij+z_up,2); A(3,3)=xyz_v(ij+z_up,3) |
---|
| 104 | |
---|
| 105 | dq(1) = qi(ij+t_rup,l)-qi(ij,l) |
---|
| 106 | dq(2) = qi(ij+t_lup,l)-qi(ij,l) |
---|
| 107 | dq(3) = 0.0 |
---|
| 108 | |
---|
| 109 | |
---|
| 110 | ! CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det) |
---|
| 111 | |
---|
| 112 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 113 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 114 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 115 | |
---|
| 116 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 117 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 118 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 119 | det = x1 - x2 + x3 |
---|
| 120 | |
---|
| 121 | ! CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),detx) |
---|
| 122 | |
---|
| 123 | a11=dq(1) ; a12=dq(2) ; a13=dq(3) |
---|
| 124 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 125 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 126 | |
---|
| 127 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 128 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 129 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 130 | detx = x1 - x2 + x3 |
---|
| 131 | |
---|
| 132 | ! CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dety) |
---|
| 133 | |
---|
| 134 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 135 | a21=dq(1) ; a22=dq(2) ; a23=dq(3) |
---|
| 136 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 137 | |
---|
| 138 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 139 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 140 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 141 | dety = x1 - x2 + x3 |
---|
| 142 | |
---|
| 143 | ! CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),detz) |
---|
| 144 | |
---|
| 145 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 146 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 147 | a31=dq(1) ; a32=dq(2) ; a33=dq(3) |
---|
| 148 | |
---|
| 149 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 150 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 151 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 152 | detz = x1 - x2 + x3 |
---|
| 153 | |
---|
| 154 | gradtri(ij+z_up,l,1) = detx |
---|
| 155 | gradtri(ij+z_up,l,2) = dety |
---|
| 156 | gradtri(ij+z_up,l,3) = detz |
---|
| 157 | arr(ij+z_up) = det |
---|
| 158 | |
---|
| 159 | ENDDO |
---|
| 160 | |
---|
| 161 | DO ij=ij_begin_ext,ij_end_ext |
---|
| 162 | |
---|
| 163 | |
---|
| 164 | ! CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,1),gradtri(ij+z_down,l,2),gradtri(ij+z_down,l,3),arr(ij+z_down)) |
---|
| 165 | |
---|
| 166 | A(1,1)=xyz_i(ij+t_ldown,1)-xyz_i(ij,1); A(1,2)=xyz_i(ij+t_ldown,2)-xyz_i(ij,2); A(1,3)=xyz_i(ij+t_ldown,3)-xyz_i(ij,3) |
---|
| 167 | A(2,1)=xyz_i(ij+t_rdown,1)-xyz_i(ij,1); A(2,2)=xyz_i(ij+t_rdown,2)-xyz_i(ij,2); A(2,3)=xyz_i(ij+t_rdown,3)-xyz_i(ij,3) |
---|
| 168 | A(3,1)=xyz_v(ij+z_down,1); A(3,2)= xyz_v(ij+z_down,2); A(3,3)=xyz_v(ij+z_down,3) |
---|
| 169 | |
---|
| 170 | dq(1) = qi(ij+t_ldown,l)-qi(ij,l) |
---|
| 171 | dq(2) = qi(ij+t_rdown,l)-qi(ij,l) |
---|
| 172 | dq(3) = 0.0 |
---|
| 173 | |
---|
| 174 | |
---|
| 175 | ! CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det) |
---|
| 176 | |
---|
| 177 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 178 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 179 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 180 | |
---|
| 181 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 182 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 183 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 184 | det = x1 - x2 + x3 |
---|
| 185 | |
---|
| 186 | ! CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),detx) |
---|
| 187 | |
---|
| 188 | a11=dq(1) ; a12=dq(2) ; a13=dq(3) |
---|
| 189 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 190 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 191 | |
---|
| 192 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 193 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 194 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 195 | detx = x1 - x2 + x3 |
---|
| 196 | |
---|
| 197 | ! CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dety) |
---|
| 198 | |
---|
| 199 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 200 | a21=dq(1) ; a22=dq(2) ; a23=dq(3) |
---|
| 201 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
---|
| 202 | |
---|
| 203 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 204 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 205 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 206 | dety = x1 - x2 + x3 |
---|
| 207 | |
---|
| 208 | ! CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),detz) |
---|
| 209 | |
---|
| 210 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
---|
| 211 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
---|
| 212 | a31=dq(1) ; a32=dq(2) ; a33=dq(3) |
---|
| 213 | |
---|
| 214 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 215 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 216 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 217 | detz = x1 - x2 + x3 |
---|
| 218 | |
---|
| 219 | gradtri(ij+z_down,l,1) = detx |
---|
| 220 | gradtri(ij+z_down,l,2) = dety |
---|
| 221 | gradtri(ij+z_down,l,3) = detz |
---|
| 222 | arr(ij+z_down) = det |
---|
| 223 | |
---|
| 224 | END DO |
---|
| 225 | END DO |
---|
| 226 | |
---|
| 227 | !$SIMD |
---|
| 228 | DO ij=ij_begin,ij_end |
---|
| 229 | ar(ij) = arr(ij+z_up)+arr(ij+z_lup)+arr(ij+z_ldown)+arr(ij+z_down)+arr(ij+z_rdown)+arr(ij+z_rup)+1.e-50 |
---|
| 230 | ENDDO |
---|
| 231 | CALL trace_end("compute_gradq3d1") |
---|
| 232 | CALL trace_start2("compute_gradq3d2") |
---|
| 233 | |
---|
| 234 | DO k=1,3 |
---|
| 235 | DO l =ll_begin,ll_end |
---|
| 236 | !$SIMD |
---|
| 237 | DO ij=ij_begin,ij_end |
---|
| 238 | gradq3d(ij,l,k) = ( gradtri(ij+z_up,l,k) + gradtri(ij+z_down,l,k) + & |
---|
| 239 | gradtri(ij+z_rup,l,k) + gradtri(ij+z_ldown,l,k) + & |
---|
| 240 | gradtri(ij+z_lup,l,k)+ gradtri(ij+z_rdown,l,k) ) / ar(ij) |
---|
| 241 | END DO |
---|
| 242 | END DO |
---|
| 243 | ENDDO |
---|
| 244 | CALL trace_end2("compute_gradq3d2") |
---|
| 245 | CALL trace_start("compute_gradq3d3") |
---|
| 246 | |
---|
| 247 | !============================================================================================= LIMITING |
---|
| 248 | DO l =ll_begin,ll_end |
---|
| 249 | !$SIMD |
---|
| 250 | DO ij=ij_begin,ij_end |
---|
| 251 | ! maggrd = dot_product(gradq3d(ij,l,:),gradq3d(ij,l,:)) |
---|
| 252 | maggrd = gradq3d(ij,l,1)*gradq3d(ij,l,1) + gradq3d(ij,l,2)*gradq3d(ij,l,2) + gradq3d(ij,l,3)*gradq3d(ij,l,3) |
---|
| 253 | maggrd = sqrt(maggrd) |
---|
[267] | 254 | maxq_c = qi(ij,l) + maggrd*sqrt_leng(ij) |
---|
| 255 | minq_c = qi(ij,l) - maggrd*sqrt_leng(ij) |
---|
[221] | 256 | maxq = max(qi(ij,l),qi(ij+t_right,l),qi(ij+t_lup,l),qi(ij+t_rup,l),qi(ij+t_left,l), & |
---|
| 257 | qi(ij+t_rdown,l),qi(ij+t_ldown,l)) |
---|
| 258 | minq = min(qi(ij,l),qi(ij+t_right,l),qi(ij+t_lup,l),qi(ij+t_rup,l),qi(ij+t_left,l), & |
---|
| 259 | qi(ij+t_rdown,l),qi(ij+t_ldown,l)) |
---|
| 260 | alphamx = (maxq - qi(ij,l)) ; alphamx = alphamx/(maxq_c - qi(ij,l) ) |
---|
| 261 | alphamx = max(alphamx,0.0) |
---|
| 262 | alphami = (minq - qi(ij,l)); alphami = alphami/(minq_c - qi(ij,l)) |
---|
| 263 | alphami = max(alphami,0.0) |
---|
| 264 | alpha = min(alphamx,alphami,1.0) |
---|
| 265 | ! gradq3d(ij,l,:) = alpha*gradq3d(ij,l,:) |
---|
| 266 | gradq3d(ij,l,1) = alpha*gradq3d(ij,l,1) |
---|
| 267 | gradq3d(ij,l,2) = alpha*gradq3d(ij,l,2) |
---|
| 268 | gradq3d(ij,l,3) = alpha*gradq3d(ij,l,3) |
---|
| 269 | END DO |
---|
| 270 | END DO |
---|
| 271 | |
---|
| 272 | CALL trace_end("compute_gradq3d3") |
---|
| 273 | |
---|
| 274 | gradq3d_out=gradq3d |
---|
| 275 | |
---|
| 276 | CONTAINS |
---|
| 277 | |
---|
| 278 | SUBROUTINE gradq(n0,l,n1,n2,n3,q,dq1,dq2,dq3,det) |
---|
| 279 | IMPLICIT NONE |
---|
| 280 | INTEGER, INTENT(IN) :: n0,l,n1,n2,n3 |
---|
| 281 | REAL(rstd), INTENT(IN) :: q(iim*jjm,llm) |
---|
| 282 | ! REAL(rstd), INTENT(OUT) :: dq(3), det |
---|
| 283 | REAL(rstd), INTENT(OUT) :: dq1,dq2,dq3,det |
---|
| 284 | REAL(rstd) :: dq(3) |
---|
| 285 | |
---|
| 286 | REAL(rstd) ::detx,dety,detz |
---|
| 287 | INTEGER :: info |
---|
| 288 | INTEGER :: IPIV(3) |
---|
| 289 | |
---|
| 290 | REAL(rstd) :: A(3,3) |
---|
| 291 | REAL(rstd) :: B(3) |
---|
| 292 | |
---|
| 293 | ! TODO : replace A by A1,A2,A3 |
---|
| 294 | A(1,1)=xyz_i(n1,1)-xyz_i(n0,1); A(1,2)=xyz_i(n1,2)-xyz_i(n0,2); A(1,3)=xyz_i(n1,3)-xyz_i(n0,3) |
---|
| 295 | A(2,1)=xyz_i(n2,1)-xyz_i(n0,1); A(2,2)=xyz_i(n2,2)-xyz_i(n0,2); A(2,3)=xyz_i(n2,3)-xyz_i(n0,3) |
---|
| 296 | A(3,1)=xyz_v(n3,1); A(3,2)= xyz_v(n3,2); A(3,3)=xyz_v(n3,3) |
---|
| 297 | |
---|
| 298 | dq(1) = q(n1,l)-q(n0,l) |
---|
| 299 | dq(2) = q(n2,l)-q(n0,l) |
---|
| 300 | dq(3) = 0.0 |
---|
| 301 | |
---|
| 302 | ! CALL DGESV(3,1,A,3,IPIV,dq(:),3,info) |
---|
| 303 | ! CALL determinant(A(:,1),A(:,2),A(:,3),det) |
---|
| 304 | ! CALL determinant(dq,A(:,2),A(:,3),detx) |
---|
| 305 | ! CALL determinant(A(:,1),dq,A(:,3),dety) |
---|
| 306 | ! CALL determinant(A(:,1),A(:,2),dq,detz) |
---|
| 307 | ! dq(1) = detx |
---|
| 308 | ! dq(2) = dety |
---|
| 309 | ! dq(3) = detz |
---|
| 310 | |
---|
| 311 | CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),det) |
---|
| 312 | CALL determinant(dq(1),dq(2),dq(3),A(1,2),A(2,2),A(3,2),A(1,3),A(2,3),A(3,3),dq1) |
---|
| 313 | CALL determinant(A(1,1),A(2,1),A(3,1),dq(1),dq(2),dq(3),A(1,3),A(2,3),A(3,3),dq2) |
---|
| 314 | CALL determinant(A(1,1),A(2,1),A(3,1),A(1,2),A(2,2),A(3,2),dq(1),dq(2),dq(3),dq3) |
---|
| 315 | |
---|
| 316 | END SUBROUTINE gradq |
---|
| 317 | |
---|
| 318 | !========================================================================== |
---|
| 319 | ! PURE SUBROUTINE determinant(a1,a2,a3,det) |
---|
| 320 | ! IMPLICIT NONE |
---|
| 321 | ! REAL(rstd), DIMENSION(3), INTENT(IN) :: a1,a2,a3 |
---|
| 322 | ! REAL(rstd), INTENT(OUT) :: det |
---|
| 323 | ! REAL(rstd) :: x1,x2,x3 |
---|
| 324 | ! x1 = a1(1) * (a2(2) * a3(3) - a2(3) * a3(2)) |
---|
| 325 | ! x2 = a1(2) * (a2(1) * a3(3) - a2(3) * a3(1)) |
---|
| 326 | ! x3 = a1(3) * (a2(1) * a3(2) - a2(2) * a3(1)) |
---|
| 327 | ! det = x1 - x2 + x3 |
---|
| 328 | ! END SUBROUTINE determinant |
---|
| 329 | |
---|
| 330 | SUBROUTINE determinant(a11,a12,a13,a21,a22,a23,a31,a32,a33,det) |
---|
| 331 | IMPLICIT NONE |
---|
| 332 | REAL(rstd), INTENT(IN) :: a11,a12,a13,a21,a22,a23,a31,a32,a33 |
---|
| 333 | REAL(rstd), INTENT(OUT) :: det |
---|
| 334 | REAL(rstd) :: x1,x2,x3 |
---|
| 335 | x1 = a11 * (a22 * a33 - a23 * a32) |
---|
| 336 | x2 = a12 * (a21 * a33 - a23 * a31) |
---|
| 337 | x3 = a13 * (a21 * a32 - a22 * a31) |
---|
| 338 | det = x1 - x2 + x3 |
---|
| 339 | END SUBROUTINE determinant |
---|
| 340 | |
---|
| 341 | |
---|
| 342 | END SUBROUTINE compute_gradq3d |
---|
| 343 | |
---|
| 344 | ! Backward trajectories, for use with Miura approach |
---|
| 345 | SUBROUTINE compute_backward_traj(normal,tangent,ue,tau, cc) |
---|
| 346 | USE trace |
---|
| 347 | USE omp_para |
---|
| 348 | IMPLICIT NONE |
---|
| 349 | REAL(rstd),INTENT(IN) :: normal(3*iim*jjm,3) |
---|
| 350 | REAL(rstd),INTENT(IN) :: tangent(3*iim*jjm,3) |
---|
| 351 | REAL(rstd),INTENT(IN) :: ue(iim*3*jjm,llm) |
---|
| 352 | REAL(rstd),INTENT(OUT) :: cc(3*iim*jjm,llm,3) ! start of backward trajectory |
---|
| 353 | REAL(rstd),INTENT(IN) :: tau |
---|
| 354 | |
---|
| 355 | REAL(rstd) :: v_e(3), up_e, qe, ed(3) |
---|
| 356 | INTEGER :: ij,l |
---|
| 357 | |
---|
| 358 | CALL trace_start("compute_backward_traj") |
---|
| 359 | |
---|
| 360 | ! TODO : compute normal displacement ue*tau as hfluxt / mass(upwind) then reconstruct tangential displacement |
---|
| 361 | |
---|
| 362 | ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*tau |
---|
| 363 | DO l = ll_begin,ll_end |
---|
| 364 | !$SIMD |
---|
| 365 | DO ij=ij_begin,ij_end |
---|
| 366 | up_e =1/de(ij+u_right)*( & |
---|
| 367 | wee(ij+u_right,1,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
---|
| 368 | wee(ij+u_right,2,1)*le(ij+u_lup)*ue(ij+u_lup,l)+ & |
---|
| 369 | wee(ij+u_right,3,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
---|
| 370 | wee(ij+u_right,4,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+ & |
---|
| 371 | wee(ij+u_right,5,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
---|
| 372 | wee(ij+u_right,1,2)*le(ij+t_right+u_ldown)*ue(ij+t_right+u_ldown,l)+ & |
---|
| 373 | wee(ij+u_right,2,2)*le(ij+t_right+u_rdown)*ue(ij+t_right+u_rdown,l)+ & |
---|
| 374 | wee(ij+u_right,3,2)*le(ij+t_right+u_right)*ue(ij+t_right+u_right,l)+ & |
---|
| 375 | wee(ij+u_right,4,2)*le(ij+t_right+u_rup)*ue(ij+t_right+u_rup,l)+ & |
---|
| 376 | wee(ij+u_right,5,2)*le(ij+t_right+u_lup)*ue(ij+t_right+u_lup,l) & |
---|
| 377 | ) |
---|
| 378 | v_e = ue(ij+u_right,l)*normal(ij+u_right,:) + up_e*tangent(ij+u_right,:) |
---|
| 379 | cc(ij+u_right,l,:) = xyz_e(ij+u_right,:) - v_e*tau |
---|
| 380 | |
---|
| 381 | up_e=1/de(ij+u_lup)*( & |
---|
| 382 | wee(ij+u_lup,1,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
---|
| 383 | wee(ij+u_lup,2,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+ & |
---|
| 384 | wee(ij+u_lup,3,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
---|
| 385 | wee(ij+u_lup,4,1)*le(ij+u_right)*ue(ij+u_right,l)+ & |
---|
| 386 | wee(ij+u_lup,5,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
---|
| 387 | wee(ij+u_lup,1,2)*le(ij+t_lup+u_right)*ue(ij+t_lup+u_right,l)+ & |
---|
| 388 | wee(ij+u_lup,2,2)*le(ij+t_lup+u_rup)*ue(ij+t_lup+u_rup,l)+ & |
---|
| 389 | wee(ij+u_lup,3,2)*le(ij+t_lup+u_lup)*ue(ij+t_lup+u_lup,l)+ & |
---|
| 390 | wee(ij+u_lup,4,2)*le(ij+t_lup+u_left)*ue(ij+t_lup+u_left,l)+ & |
---|
| 391 | wee(ij+u_lup,5,2)*le(ij+t_lup+u_ldown)*ue(ij+t_lup+u_ldown,l) & |
---|
| 392 | ) |
---|
| 393 | v_e = ue(ij+u_lup,l)*normal(ij+u_lup,:) + up_e*tangent(ij+u_lup,:) |
---|
| 394 | cc(ij+u_lup,l,:) = xyz_e(ij+u_lup,:) - v_e*tau |
---|
| 395 | |
---|
| 396 | |
---|
| 397 | up_e=1/de(ij+u_ldown)*( & |
---|
| 398 | wee(ij+u_ldown,1,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
---|
| 399 | wee(ij+u_ldown,2,1)*le(ij+u_right)*ue(ij+u_right,l)+ & |
---|
| 400 | wee(ij+u_ldown,3,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
---|
| 401 | wee(ij+u_ldown,4,1)*le(ij+u_lup)*ue(ij+u_lup,l)+ & |
---|
| 402 | wee(ij+u_ldown,5,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
---|
| 403 | wee(ij+u_ldown,1,2)*le(ij+t_ldown+u_lup)*ue(ij+t_ldown+u_lup,l)+ & |
---|
| 404 | wee(ij+u_ldown,2,2)*le(ij+t_ldown+u_left)*ue(ij+t_ldown+u_left,l)+ & |
---|
| 405 | wee(ij+u_ldown,3,2)*le(ij+t_ldown+u_ldown)*ue(ij+t_ldown+u_ldown,l)+ & |
---|
| 406 | wee(ij+u_ldown,4,2)*le(ij+t_ldown+u_rdown)*ue(ij+t_ldown+u_rdown,l)+ & |
---|
| 407 | wee(ij+u_ldown,5,2)*le(ij+t_ldown+u_right)*ue(ij+t_ldown+u_right,l) & |
---|
| 408 | ) |
---|
| 409 | v_e = ue(ij+u_ldown,l)*normal(ij+u_ldown,:) + up_e*tangent(ij+u_ldown,:) |
---|
| 410 | cc(ij+u_ldown,l,:) = xyz_e(ij+u_ldown,:) - v_e*tau |
---|
| 411 | ENDDO |
---|
| 412 | END DO |
---|
| 413 | |
---|
| 414 | CALL trace_end("compute_backward_traj") |
---|
| 415 | |
---|
| 416 | END SUBROUTINE compute_backward_traj |
---|
| 417 | |
---|
| 418 | ! Horizontal transport (S. Dubey, T. Dubos) |
---|
| 419 | ! Slope-limited van Leer approach with hexagons |
---|
| 420 | SUBROUTINE compute_advect_horiz(update_mass,hfluxt,cc,gradq3d, mass,qi) |
---|
| 421 | USE trace |
---|
| 422 | USE omp_para |
---|
| 423 | IMPLICIT NONE |
---|
| 424 | LOGICAL, INTENT(IN) :: update_mass |
---|
| 425 | REAL(rstd), INTENT(IN) :: gradq3d(iim*jjm,llm,3) |
---|
| 426 | REAL(rstd), INTENT(IN) :: hfluxt(3*iim*jjm,llm) ! mass flux |
---|
| 427 | REAL(rstd), INTENT(IN) :: cc(3*iim*jjm,llm,3) ! barycenter of quadrilateral, where q is evaluated (1-point quadrature) |
---|
| 428 | REAL(rstd), INTENT(INOUT) :: mass(iim*jjm,llm) |
---|
| 429 | REAL(rstd), INTENT(INOUT) :: qi(iim*jjm,llm) |
---|
| 430 | |
---|
| 431 | REAL(rstd) :: dq,dmass,qe,ed(3), newmass |
---|
| 432 | REAL(rstd) :: qflux(3*iim*jjm,llm) |
---|
| 433 | INTEGER :: ij,k,l |
---|
| 434 | |
---|
| 435 | CALL trace_start("compute_advect_horiz") |
---|
| 436 | |
---|
| 437 | ! evaluate tracer field at point cc using piecewise linear reconstruction |
---|
| 438 | ! q(cc)= q0 + gradq.(cc-xyz_i) with xi centroid of hexagon |
---|
| 439 | ! ne*hfluxt>0 iff outgoing |
---|
| 440 | DO l = ll_begin,ll_end |
---|
| 441 | |
---|
| 442 | !$SIMD |
---|
| 443 | DO ij=ij_begin_ext,ij_end_ext |
---|
| 444 | |
---|
| 445 | IF (ne(ij,right)*hfluxt(ij+u_right,l)>0) THEN |
---|
| 446 | ed = cc(ij+u_right,l,:) - xyz_i(ij,:) |
---|
| 447 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
---|
| 448 | qe = qi(ij,l)+gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
---|
| 449 | ELSE |
---|
| 450 | ed = cc(ij+u_right,l,:) - xyz_i(ij+t_right,:) |
---|
| 451 | ! qe = qi(ij+t_right,l)+sum2(gradq3d(ij+t_right,l,:),ed) |
---|
| 452 | qe = qi(ij+t_right,l) + gradq3d(ij+t_right,l,1)*ed(1)+gradq3d(ij+t_right,l,2)*ed(2)+gradq3d(ij+t_right,l,3)*ed(3) |
---|
| 453 | ENDIF |
---|
| 454 | qflux(ij+u_right,l) = hfluxt(ij+u_right,l)*qe |
---|
| 455 | |
---|
| 456 | IF (ne(ij,lup)*hfluxt(ij+u_lup,l)>0) THEN |
---|
| 457 | ed = cc(ij+u_lup,l,:) - xyz_i(ij,:) |
---|
| 458 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
---|
| 459 | qe = qi(ij,l) + gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
---|
| 460 | ELSE |
---|
| 461 | ed = cc(ij+u_lup,l,:) - xyz_i(ij+t_lup,:) |
---|
| 462 | ! qe = qi(ij+t_lup,l)+sum2(gradq3d(ij+t_lup,l,:),ed) |
---|
| 463 | qe = qi(ij+t_lup,l) + gradq3d(ij+t_lup,l,1)*ed(1)+gradq3d(ij+t_lup,l,2)*ed(2)+gradq3d(ij+t_lup,l,3)*ed(3) |
---|
| 464 | ENDIF |
---|
| 465 | qflux(ij+u_lup,l) = hfluxt(ij+u_lup,l)*qe |
---|
| 466 | |
---|
| 467 | IF (ne(ij,ldown)*hfluxt(ij+u_ldown,l)>0) THEN |
---|
| 468 | ed = cc(ij+u_ldown,l,:) - xyz_i(ij,:) |
---|
| 469 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
---|
| 470 | qe = qi(ij,l) + gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
---|
| 471 | ELSE |
---|
| 472 | ed = cc(ij+u_ldown,l,:) - xyz_i(ij+t_ldown,:) |
---|
| 473 | ! qe = qi(ij+t_ldown,l)+sum2(gradq3d(ij+t_ldown,l,:),ed) |
---|
| 474 | qe = qi(ij+t_ldown,l)+gradq3d(ij+t_ldown,l,1)*ed(1)+gradq3d(ij+t_ldown,l,2)*ed(2)+gradq3d(ij+t_ldown,l,3)*ed(3) |
---|
| 475 | ENDIF |
---|
| 476 | qflux(ij+u_ldown,l) = hfluxt(ij+u_ldown,l)*qe |
---|
| 477 | END DO |
---|
| 478 | END DO |
---|
| 479 | |
---|
| 480 | ! update q and, if update_mass, update mass |
---|
| 481 | DO l = ll_begin,ll_end |
---|
| 482 | !$SIMD |
---|
| 483 | DO ij=ij_begin,ij_end |
---|
| 484 | ! sign convention as Ringler et al. (2010) eq. 21 |
---|
| 485 | dmass = hfluxt(ij+u_right,l)*ne(ij,right) & |
---|
| 486 | + hfluxt(ij+u_lup,l) *ne(ij,lup) & |
---|
| 487 | + hfluxt(ij+u_ldown,l)*ne(ij,ldown) & |
---|
| 488 | + hfluxt(ij+u_rup,l) *ne(ij,rup) & |
---|
| 489 | + hfluxt(ij+u_left,l) *ne(ij,left) & |
---|
| 490 | + hfluxt(ij+u_rdown,l)*ne(ij,rdown) |
---|
| 491 | |
---|
| 492 | dq = qflux(ij+u_right,l) *ne(ij,right) & |
---|
| 493 | + qflux(ij+u_lup,l) *ne(ij,lup) & |
---|
| 494 | + qflux(ij+u_ldown,l) *ne(ij,ldown) & |
---|
| 495 | + qflux(ij+u_rup,l) *ne(ij,rup) & |
---|
| 496 | + qflux(ij+u_left,l) *ne(ij,left) & |
---|
| 497 | + qflux(ij+u_rdown,l) *ne(ij,rdown) |
---|
| 498 | |
---|
| 499 | |
---|
| 500 | newmass = mass(ij,l) - dmass/Ai(ij) |
---|
| 501 | qi(ij,l) = (qi(ij,l)*mass(ij,l) - dq/Ai(ij) ) / newmass |
---|
| 502 | IF(update_mass) mass(ij,l) = newmass |
---|
| 503 | |
---|
| 504 | END DO |
---|
| 505 | END DO |
---|
| 506 | |
---|
| 507 | CALL trace_end("compute_advect_horiz") |
---|
| 508 | CONTAINS |
---|
| 509 | |
---|
| 510 | !==================================================================================== |
---|
| 511 | PURE REAL(rstd) FUNCTION sum2(a1,a2) |
---|
| 512 | IMPLICIT NONE |
---|
| 513 | REAL(rstd),INTENT(IN):: a1(3), a2(3) |
---|
| 514 | sum2 = a1(1)*a2(1)+a1(2)*a2(2)+a1(3)*a2(3) |
---|
| 515 | ! sum2 = 0. ! Godunov scheme |
---|
| 516 | END FUNCTION sum2 |
---|
| 517 | |
---|
| 518 | END SUBROUTINE compute_advect_horiz |
---|
| 519 | |
---|
| 520 | |
---|
| 521 | END MODULE advect_mod |
---|