[22] | 1 | MODULE advect_mod |
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| 2 | USE icosa |
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| 3 | IMPLICIT NONE |
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[17] | 4 | |
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[138] | 5 | PRIVATE |
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| 6 | |
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| 7 | PUBLIC :: init_advect, compute_backward_traj, compute_gradq3d, compute_advect_horiz |
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| 8 | |
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[17] | 9 | CONTAINS |
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| 10 | |
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[22] | 11 | !========================================================================== |
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[17] | 12 | |
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[148] | 13 | SUBROUTINE init_advect(normal,tangent,one_over_sqrt_leng) |
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[22] | 14 | IMPLICIT NONE |
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| 15 | REAL(rstd),INTENT(OUT) :: normal(3*iim*jjm,3) |
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| 16 | REAL(rstd),INTENT(OUT) :: tangent(3*iim*jjm,3) |
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[148] | 17 | REAL(rstd),INTENT(OUT) :: one_over_sqrt_leng(iim*jjm) |
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[17] | 18 | |
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[22] | 19 | INTEGER :: i,j,n |
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| 20 | |
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[17] | 21 | DO j=jj_begin-1,jj_end+1 |
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[22] | 22 | DO i=ii_begin-1,ii_end+1 |
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| 23 | n=(j-1)*iim+i |
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| 24 | |
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| 25 | CALL cross_product2(xyz_v(n+z_rdown,:),xyz_v(n+z_rup,:),normal(n+u_right,:)) |
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| 26 | normal(n+u_right,:)=normal(n+u_right,:)/sqrt(sum(normal(n+u_right,:)**2)+1e-50)*ne(n,right) |
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| 27 | |
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| 28 | CALL cross_product2(xyz_v(n+z_up,:),xyz_v(n+z_lup,:),normal(n+u_lup,:)) |
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| 29 | normal(n+u_lup,:)=normal(n+u_lup,:)/sqrt(sum(normal(n+u_lup,:)**2)+1e-50)*ne(n,lup) |
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| 30 | |
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| 31 | CALL cross_product2(xyz_v(n+z_ldown,:),xyz_v(n+z_down,:),normal(n+u_ldown,:)) |
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| 32 | normal(n+u_ldown,:)=normal(n+u_ldown,:)/sqrt(sum(normal(n+u_ldown,:)**2)+1e-50)*ne(n,ldown) |
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| 33 | |
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| 34 | tangent(n+u_right,:)=xyz_v(n+z_rup,:)-xyz_v(n+z_rdown,:) |
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| 35 | tangent(n+u_right,:)=tangent(n+u_right,:)/sqrt(sum(tangent(n+u_right,:)**2)+1e-50) |
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| 36 | |
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| 37 | tangent(n+u_lup,:)=xyz_v(n+z_lup,:)-xyz_v(n+z_up,:) |
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| 38 | tangent(n+u_lup,:)=tangent(n+u_lup,:)/sqrt(sum(tangent(n+u_lup,:)**2)+1e-50) |
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| 39 | |
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| 40 | tangent(n+u_ldown,:)=xyz_v(n+z_down,:)-xyz_v(n+z_ldown,:) |
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| 41 | tangent(n+u_ldown,:)=tangent(n+u_ldown,:)/sqrt(sum(tangent(n+u_ldown,:)**2)+1e-50) |
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[148] | 42 | |
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| 43 | one_over_sqrt_leng(n) = 1./sqrt(max(sum((xyz_v(n+z_up,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_down,:) - xyz_i(n,:))**2), & |
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| 44 | sum((xyz_v(n+z_rup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_rdown,:) - xyz_i(n,:))**2), & |
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| 45 | sum((xyz_v(n+z_lup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_ldown,:) - xyz_i(n,:))**2)) ) |
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| 46 | ENDDO |
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[22] | 47 | ENDDO |
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| 48 | |
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[17] | 49 | END SUBROUTINE init_advect |
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| 50 | |
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[22] | 51 | !======================================================================================= |
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[17] | 52 | |
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[148] | 53 | SUBROUTINE compute_gradq3d(qi,one_over_sqrt_leng,gradq3d) |
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| 54 | USE trace |
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[151] | 55 | USE omp_para |
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[22] | 56 | IMPLICIT NONE |
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| 57 | REAL(rstd),INTENT(IN) :: qi(iim*jjm,llm) |
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[148] | 58 | REAL(rstd),INTENT(IN) :: one_over_sqrt_leng(iim*jjm) |
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[23] | 59 | REAL(rstd),INTENT(OUT) :: gradq3d(iim*jjm,llm,3) |
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[17] | 60 | REAL(rstd) :: maxq,minq,minq_c,maxq_c |
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[148] | 61 | REAL(rstd) :: alphamx,alphami,alpha ,maggrd |
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[17] | 62 | REAL(rstd) :: leng1,leng2 |
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| 63 | REAL(rstd) :: arr(2*iim*jjm) |
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[148] | 64 | REAL(rstd) :: ar(iim*jjm) |
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[17] | 65 | REAL(rstd) :: gradtri(2*iim*jjm,llm,3) |
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| 66 | INTEGER :: i,j,n,k,ind,l |
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[138] | 67 | |
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[148] | 68 | CALL trace_start("compute_gradq3d") |
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| 69 | |
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[138] | 70 | ! TODO : precompute ar, drop arr as output argument of gradq ? |
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| 71 | |
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[22] | 72 | !========================================================================================== GRADIENT |
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[138] | 73 | ! Compute gradient at triangles solving a linear system |
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| 74 | ! arr = area of triangle joining centroids of hexagons |
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[151] | 75 | DO l = ll_begin,ll_end |
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[22] | 76 | DO j=jj_begin-1,jj_end+1 |
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| 77 | DO i=ii_begin-1,ii_end+1 |
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| 78 | n=(j-1)*iim+i |
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[148] | 79 | CALL gradq(n,l,n+t_rup,n+t_lup,n+z_up,qi,gradtri(n+z_up,l,:),arr(n+z_up)) |
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| 80 | CALL gradq(n,l,n+t_ldown,n+t_rdown,n+z_down,qi,gradtri(n+z_down,l,:),arr(n+z_down)) |
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[22] | 81 | END DO |
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[17] | 82 | END DO |
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[22] | 83 | END DO |
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[17] | 84 | |
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[148] | 85 | DO j=jj_begin-1,jj_end+1 |
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| 86 | DO i=ii_begin-1,ii_end+1 |
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| 87 | n=(j-1)*iim+i |
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| 88 | ar(n) = arr(n+z_up)+arr(n+z_lup)+arr(n+z_ldown)+arr(n+z_down)+arr(n+z_rdown)+arr(n+z_rup)+1.e-50 |
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| 89 | ENDDO |
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| 90 | ENDDO |
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| 91 | |
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| 92 | DO k=1,3 |
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[151] | 93 | DO l =ll_begin,ll_end |
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[148] | 94 | DO j=jj_begin,jj_end |
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| 95 | DO i=ii_begin,ii_end |
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| 96 | n=(j-1)*iim+i |
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| 97 | gradq3d(n,l,k) = ( gradtri(n+z_up,l,k) + gradtri(n+z_down,l,k) + & |
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| 98 | gradtri(n+z_rup,l,k) + gradtri(n+z_ldown,l,k) + & |
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| 99 | gradtri(n+z_lup,l,k)+ gradtri(n+z_rdown,l,k) ) / ar(n) |
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| 100 | END DO |
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| 101 | END DO |
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| 102 | END DO |
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| 103 | ENDDO |
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[22] | 104 | |
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| 105 | !============================================================================================= LIMITING |
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[151] | 106 | DO l =ll_begin,ll_end |
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[22] | 107 | DO j=jj_begin,jj_end |
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[17] | 108 | DO i=ii_begin,ii_end |
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| 109 | n=(j-1)*iim+i |
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[22] | 110 | maggrd = dot_product(gradq3d(n,l,:),gradq3d(n,l,:)) |
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| 111 | maggrd = sqrt(maggrd) |
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[148] | 112 | maxq_c = qi(n,l) + maggrd*one_over_sqrt_leng(n) |
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| 113 | minq_c = qi(n,l) - maggrd*one_over_sqrt_leng(n) |
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[22] | 114 | maxq = max(qi(n,l),qi(n+t_right,l),qi(n+t_lup,l),qi(n+t_rup,l),qi(n+t_left,l), & |
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| 115 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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| 116 | minq = min(qi(n,l),qi(n+t_right,l),qi(n+t_lup,l),qi(n+t_rup,l),qi(n+t_left,l), & |
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| 117 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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| 118 | alphamx = (maxq - qi(n,l)) ; alphamx = alphamx/(maxq_c - qi(n,l) ) |
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| 119 | alphamx = max(alphamx,0.0) |
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| 120 | alphami = (minq - qi(n,l)); alphami = alphami/(minq_c - qi(n,l)) |
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| 121 | alphami = max(alphami,0.0) |
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| 122 | alpha = min(alphamx,alphami,1.0) |
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| 123 | gradq3d(n,l,:) = alpha*gradq3d(n,l,:) |
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| 124 | END DO |
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| 125 | END DO |
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[17] | 126 | END DO |
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[148] | 127 | |
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| 128 | CALL trace_end("compute_gradq3d") |
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[22] | 129 | END SUBROUTINE compute_gradq3d |
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| 130 | |
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[138] | 131 | ! Backward trajectories, for use with Miura approach |
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[137] | 132 | SUBROUTINE compute_backward_traj(normal,tangent,ue,tau, cc) |
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[148] | 133 | USE trace |
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[151] | 134 | USE omp_para |
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[22] | 135 | IMPLICIT NONE |
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[137] | 136 | REAL(rstd),INTENT(IN) :: normal(3*iim*jjm,3) |
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| 137 | REAL(rstd),INTENT(IN) :: tangent(3*iim*jjm,3) |
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| 138 | REAL(rstd),INTENT(IN) :: ue(iim*3*jjm,llm) |
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| 139 | REAL(rstd),INTENT(OUT) :: cc(3*iim*jjm,llm,3) ! start of backward trajectory |
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| 140 | REAL(rstd),INTENT(IN) :: tau |
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| 141 | |
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[138] | 142 | REAL(rstd) :: v_e(3), up_e, qe, ed(3) |
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[137] | 143 | INTEGER :: i,j,n,l |
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| 144 | |
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[148] | 145 | CALL trace_start("compute_backward_traj") |
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| 146 | |
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[138] | 147 | ! TODO : compute normal displacement ue*tau as hfluxt / mass(upwind) then reconstruct tangential displacement |
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| 148 | |
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[137] | 149 | ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*tau |
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[151] | 150 | DO l = ll_begin,ll_end |
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[137] | 151 | DO j=jj_begin-1,jj_end+1 |
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| 152 | DO i=ii_begin-1,ii_end+1 |
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| 153 | n=(j-1)*iim+i |
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| 154 | |
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| 155 | up_e =1/de(n+u_right)*( & |
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| 156 | wee(n+u_right,1,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 157 | wee(n+u_right,2,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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| 158 | wee(n+u_right,3,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 159 | wee(n+u_right,4,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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| 160 | wee(n+u_right,5,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 161 | wee(n+u_right,1,2)*le(n+t_right+u_ldown)*ue(n+t_right+u_ldown,l)+ & |
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| 162 | wee(n+u_right,2,2)*le(n+t_right+u_rdown)*ue(n+t_right+u_rdown,l)+ & |
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| 163 | wee(n+u_right,3,2)*le(n+t_right+u_right)*ue(n+t_right+u_right,l)+ & |
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| 164 | wee(n+u_right,4,2)*le(n+t_right+u_rup)*ue(n+t_right+u_rup,l)+ & |
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| 165 | wee(n+u_right,5,2)*le(n+t_right+u_lup)*ue(n+t_right+u_lup,l) & |
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| 166 | ) |
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| 167 | v_e = ue(n+u_right,l)*normal(n+u_right,:) + up_e*tangent(n+u_right,:) |
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| 168 | cc(n+u_right,l,:) = xyz_e(n+u_right,:) - v_e*tau |
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| 169 | |
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| 170 | up_e=1/de(n+u_lup)*( & |
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| 171 | wee(n+u_lup,1,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 172 | wee(n+u_lup,2,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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| 173 | wee(n+u_lup,3,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 174 | wee(n+u_lup,4,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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| 175 | wee(n+u_lup,5,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 176 | wee(n+u_lup,1,2)*le(n+t_lup+u_right)*ue(n+t_lup+u_right,l)+ & |
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| 177 | wee(n+u_lup,2,2)*le(n+t_lup+u_rup)*ue(n+t_lup+u_rup,l)+ & |
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| 178 | wee(n+u_lup,3,2)*le(n+t_lup+u_lup)*ue(n+t_lup+u_lup,l)+ & |
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| 179 | wee(n+u_lup,4,2)*le(n+t_lup+u_left)*ue(n+t_lup+u_left,l)+ & |
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| 180 | wee(n+u_lup,5,2)*le(n+t_lup+u_ldown)*ue(n+t_lup+u_ldown,l) & |
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| 181 | ) |
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| 182 | v_e = ue(n+u_lup,l)*normal(n+u_lup,:) + up_e*tangent(n+u_lup,:) |
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| 183 | cc(n+u_lup,l,:) = xyz_e(n+u_lup,:) - v_e*tau |
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| 184 | |
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| 185 | up_e=1/de(n+u_ldown)*( & |
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| 186 | wee(n+u_ldown,1,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 187 | wee(n+u_ldown,2,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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| 188 | wee(n+u_ldown,3,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 189 | wee(n+u_ldown,4,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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| 190 | wee(n+u_ldown,5,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 191 | wee(n+u_ldown,1,2)*le(n+t_ldown+u_lup)*ue(n+t_ldown+u_lup,l)+ & |
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| 192 | wee(n+u_ldown,2,2)*le(n+t_ldown+u_left)*ue(n+t_ldown+u_left,l)+ & |
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| 193 | wee(n+u_ldown,3,2)*le(n+t_ldown+u_ldown)*ue(n+t_ldown+u_ldown,l)+ & |
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| 194 | wee(n+u_ldown,4,2)*le(n+t_ldown+u_rdown)*ue(n+t_ldown+u_rdown,l)+ & |
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| 195 | wee(n+u_ldown,5,2)*le(n+t_ldown+u_right)*ue(n+t_ldown+u_right,l) & |
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| 196 | ) |
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| 197 | v_e = ue(n+u_ldown,l)*normal(n+u_ldown,:) + up_e*tangent(n+u_ldown,:) |
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| 198 | cc(n+u_ldown,l,:) = xyz_e(n+u_ldown,:) - v_e*tau |
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| 199 | ENDDO |
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| 200 | ENDDO |
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| 201 | END DO |
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[148] | 202 | |
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| 203 | CALL trace_end("compute_backward_traj") |
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| 204 | |
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[137] | 205 | END SUBROUTINE compute_backward_traj |
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| 206 | |
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| 207 | ! Horizontal transport (S. Dubey, T. Dubos) |
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| 208 | ! Slope-limited van Leer approach with hexagons |
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[138] | 209 | SUBROUTINE compute_advect_horiz(update_mass,hfluxt,cc,gradq3d, mass,qi) |
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[148] | 210 | USE trace |
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[151] | 211 | USE omp_para |
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[137] | 212 | IMPLICIT NONE |
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[138] | 213 | LOGICAL, INTENT(IN) :: update_mass |
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| 214 | REAL(rstd), INTENT(IN) :: gradq3d(iim*jjm,llm,3) |
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| 215 | REAL(rstd), INTENT(IN) :: hfluxt(3*iim*jjm,llm) ! mass flux |
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| 216 | REAL(rstd), INTENT(IN) :: cc(3*iim*jjm,llm,3) ! barycenter of quadrilateral, where q is evaluated (1-point quadrature) |
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| 217 | REAL(rstd), INTENT(INOUT) :: mass(iim*jjm,llm) |
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| 218 | REAL(rstd), INTENT(INOUT) :: qi(iim*jjm,llm) |
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[22] | 219 | |
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[138] | 220 | REAL(rstd) :: dq,dmass,qe,ed(3), newmass |
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| 221 | REAL(rstd) :: qflux(3*iim*jjm,llm) |
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[17] | 222 | INTEGER :: i,j,n,k,l |
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| 223 | |
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[148] | 224 | CALL trace_start("compute_advect_horiz") |
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| 225 | |
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[138] | 226 | ! evaluate tracer field at point cc using piecewise linear reconstruction |
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[136] | 227 | ! q(cc)= q0 + gradq.(cc-xyz_i) with xi centroid of hexagon |
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[138] | 228 | ! ne*hfluxt>0 iff outgoing |
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[151] | 229 | DO l = ll_begin,ll_end |
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[22] | 230 | DO j=jj_begin-1,jj_end+1 |
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| 231 | DO i=ii_begin-1,ii_end+1 |
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| 232 | n=(j-1)*iim+i |
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[138] | 233 | if (ne(n,right)*hfluxt(n+u_right,l)>0) then |
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[22] | 234 | ed = cc(n+u_right,l,:) - xyz_i(n,:) |
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[138] | 235 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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[22] | 236 | else |
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| 237 | ed = cc(n+u_right,l,:) - xyz_i(n+t_right,:) |
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[138] | 238 | qe = qi(n+t_right,l)+sum2(gradq3d(n+t_right,l,:),ed) |
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[22] | 239 | endif |
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[138] | 240 | qflux(n+u_right,l) = hfluxt(n+u_right,l)*qe |
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[137] | 241 | |
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[138] | 242 | if (ne(n,lup)*hfluxt(n+u_lup,l)>0) then |
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[22] | 243 | ed = cc(n+u_lup,l,:) - xyz_i(n,:) |
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[138] | 244 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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[22] | 245 | else |
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| 246 | ed = cc(n+u_lup,l,:) - xyz_i(n+t_lup,:) |
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[138] | 247 | qe = qi(n+t_lup,l)+sum2(gradq3d(n+t_lup,l,:),ed) |
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[22] | 248 | endif |
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[138] | 249 | qflux(n+u_lup,l) = hfluxt(n+u_lup,l)*qe |
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[137] | 250 | |
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[138] | 251 | if (ne(n,ldown)*hfluxt(n+u_ldown,l)>0) then |
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[22] | 252 | ed = cc(n+u_ldown,l,:) - xyz_i(n,:) |
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[138] | 253 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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[22] | 254 | else |
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| 255 | ed = cc(n+u_ldown,l,:) - xyz_i(n+t_ldown,:) |
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[138] | 256 | qe = qi(n+t_ldown,l)+sum2(gradq3d(n+t_ldown,l,:),ed) |
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[22] | 257 | endif |
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[138] | 258 | qflux(n+u_ldown,l) = hfluxt(n+u_ldown,l)*qe |
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[22] | 259 | end do |
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| 260 | end do |
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| 261 | END DO |
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[17] | 262 | |
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[138] | 263 | ! update q and, if update_mass, update mass |
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[151] | 264 | DO l = ll_begin,ll_end |
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[138] | 265 | DO j=jj_begin,jj_end |
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| 266 | DO i=ii_begin,ii_end |
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| 267 | n=(j-1)*iim+i |
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| 268 | ! sign convention as Ringler et al. (2010) eq. 21 |
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| 269 | dmass = hfluxt(n+u_right,l)*ne(n,right) & |
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| 270 | + hfluxt(n+u_lup,l) *ne(n,lup) & |
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| 271 | + hfluxt(n+u_ldown,l)*ne(n,ldown) & |
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| 272 | + hfluxt(n+u_rup,l) *ne(n,rup) & |
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| 273 | + hfluxt(n+u_left,l) *ne(n,left) & |
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| 274 | + hfluxt(n+u_rdown,l)*ne(n,rdown) |
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[22] | 275 | |
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[138] | 276 | dq = qflux(n+u_right,l) *ne(n,right) & |
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| 277 | + qflux(n+u_lup,l) *ne(n,lup) & |
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| 278 | + qflux(n+u_ldown,l) *ne(n,ldown) & |
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| 279 | + qflux(n+u_rup,l) *ne(n,rup) & |
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| 280 | + qflux(n+u_left,l) *ne(n,left) & |
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| 281 | + qflux(n+u_rdown,l) *ne(n,rdown) |
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[17] | 282 | |
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[138] | 283 | newmass = mass(n,l) - dmass/Ai(n) |
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| 284 | qi(n,l) = (qi(n,l)*mass(n,l) - dq/Ai(n) ) / newmass |
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| 285 | IF(update_mass) mass(n,l) = newmass |
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| 286 | END DO |
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[17] | 287 | END DO |
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[22] | 288 | END DO |
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[17] | 289 | |
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[148] | 290 | CALL trace_end("compute_advect_horiz") |
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[22] | 291 | CONTAINS |
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[138] | 292 | |
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[22] | 293 | !==================================================================================== |
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[138] | 294 | PURE REAL(rstd) FUNCTION sum2(a1,a2) |
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[22] | 295 | IMPLICIT NONE |
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[138] | 296 | REAL(rstd),INTENT(IN):: a1(3), a2(3) |
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[22] | 297 | sum2 = a1(1)*a2(1)+a1(2)*a2(2)+a1(3)*a2(3) |
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[141] | 298 | ! sum2 = 0. ! Godunov scheme |
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[22] | 299 | END FUNCTION sum2 |
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| 300 | |
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| 301 | END SUBROUTINE compute_advect_horiz |
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[138] | 302 | |
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[22] | 303 | !========================================================================== |
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[148] | 304 | PURE SUBROUTINE gradq(n0,l,n1,n2,n3,q,dq,det) |
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[22] | 305 | IMPLICIT NONE |
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[148] | 306 | INTEGER, INTENT(IN) :: n0,l,n1,n2,n3 |
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| 307 | REAL(rstd), INTENT(IN) :: q(iim*jjm,llm) |
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[138] | 308 | REAL(rstd), INTENT(OUT) :: dq(3), det |
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| 309 | |
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| 310 | REAL(rstd) ::detx,dety,detz |
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[17] | 311 | INTEGER :: info |
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| 312 | INTEGER :: IPIV(3) |
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| 313 | |
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| 314 | REAL(rstd) :: A(3,3) |
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| 315 | REAL(rstd) :: B(3) |
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| 316 | |
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[138] | 317 | ! TODO : replace A by A1,A2,A3 |
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| 318 | 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) |
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| 319 | 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) |
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| 320 | A(3,1)=xyz_v(n3,1); A(3,2)= xyz_v(n3,2); A(3,3)=xyz_v(n3,3) |
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[22] | 321 | |
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[148] | 322 | dq(1) = q(n1,l)-q(n0,l) |
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| 323 | dq(2) = q(n2,l)-q(n0,l) |
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[17] | 324 | dq(3) = 0.0 |
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[22] | 325 | ! CALL DGESV(3,1,A,3,IPIV,dq(:),3,info) |
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| 326 | CALL determinant(A(:,1),A(:,2),A(:,3),det) |
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| 327 | CALL determinant(dq,A(:,2),A(:,3),detx) |
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| 328 | CALL determinant(A(:,1),dq,A(:,3),dety) |
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| 329 | CALL determinant(A(:,1),A(:,2),dq,detz) |
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| 330 | dq(1) = detx |
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| 331 | dq(2) = dety |
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| 332 | dq(3) = detz |
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[17] | 333 | END SUBROUTINE gradq |
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[138] | 334 | |
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[22] | 335 | !========================================================================== |
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[138] | 336 | PURE SUBROUTINE determinant(a1,a2,a3,det) |
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[22] | 337 | IMPLICIT NONE |
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[138] | 338 | REAL(rstd), DIMENSION(3), INTENT(IN) :: a1,a2,a3 |
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| 339 | REAL(rstd), INTENT(OUT) :: det |
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| 340 | REAL(rstd) :: x1,x2,x3 |
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[22] | 341 | x1 = a1(1) * (a2(2) * a3(3) - a2(3) * a3(2)) |
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| 342 | x2 = a1(2) * (a2(1) * a3(3) - a2(3) * a3(1)) |
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| 343 | x3 = a1(3) * (a2(1) * a3(2) - a2(2) * a3(1)) |
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| 344 | det = x1 - x2 + x3 |
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| 345 | END SUBROUTINE determinant |
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| 346 | |
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| 347 | END MODULE advect_mod |
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