| 1 | MODULE advect_mod |
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| 2 | USE icosa |
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| 3 | IMPLICIT NONE |
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| 4 | |
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| 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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| 9 | CONTAINS |
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| 10 | |
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| 11 | !========================================================================== |
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| 12 | |
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| 13 | SUBROUTINE init_advect(normal,tangent,sqrt_leng) |
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| 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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| 17 | REAL(rstd),INTENT(OUT) :: sqrt_leng(iim*jjm) |
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| 18 | |
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| 19 | INTEGER :: ij |
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| 20 | |
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| 21 | !$SIMD |
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| 22 | DO ij=ij_begin,ij_end |
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| 23 | |
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| 24 | CALL cross_product2(xyz_v(ij+z_rdown,:),xyz_v(ij+z_rup,:),normal(ij+u_right,:)) |
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| 25 | normal(ij+u_right,:)=normal(ij+u_right,:)/sqrt(sum(normal(ij+u_right,:)**2)+1e-50)*ne(ij,right) |
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| 26 | |
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| 27 | CALL cross_product2(xyz_v(ij+z_up,:),xyz_v(ij+z_lup,:),normal(ij+u_lup,:)) |
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| 28 | normal(ij+u_lup,:)=normal(ij+u_lup,:)/sqrt(sum(normal(ij+u_lup,:)**2)+1e-50)*ne(ij,lup) |
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| 29 | |
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| 30 | CALL cross_product2(xyz_v(ij+z_ldown,:),xyz_v(ij+z_down,:),normal(ij+u_ldown,:)) |
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| 31 | normal(ij+u_ldown,:)=normal(ij+u_ldown,:)/sqrt(sum(normal(ij+u_ldown,:)**2)+1e-50)*ne(ij,ldown) |
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| 32 | |
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| 33 | tangent(ij+u_right,:)=xyz_v(ij+z_rup,:)-xyz_v(ij+z_rdown,:) |
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| 34 | tangent(ij+u_right,:)=tangent(ij+u_right,:)/sqrt(sum(tangent(ij+u_right,:)**2)+1e-50) |
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| 35 | |
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| 36 | tangent(ij+u_lup,:)=xyz_v(ij+z_lup,:)-xyz_v(ij+z_up,:) |
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| 37 | tangent(ij+u_lup,:)=tangent(ij+u_lup,:)/sqrt(sum(tangent(ij+u_lup,:)**2)+1e-50) |
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| 38 | |
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| 39 | tangent(ij+u_ldown,:)=xyz_v(ij+z_down,:)-xyz_v(ij+z_ldown,:) |
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| 40 | tangent(ij+u_ldown,:)=tangent(ij+u_ldown,:)/sqrt(sum(tangent(ij+u_ldown,:)**2)+1e-50) |
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| 41 | |
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| 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), & |
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| 43 | sum((xyz_v(ij+z_rup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_rdown,:) - xyz_i(ij,:))**2), & |
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| 44 | sum((xyz_v(ij+z_lup,:) - xyz_i(ij,:))**2),sum((xyz_v(ij+z_ldown,:) - xyz_i(ij,:))**2)) ) |
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| 45 | ENDDO |
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| 46 | |
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| 47 | END SUBROUTINE init_advect |
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| 48 | |
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| 49 | !======================================================================================= |
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| 50 | |
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| 51 | SUBROUTINE compute_gradq3d(qi_in,sqrt_leng_in,gradq3d_out,xyz_i,xyz_v) |
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| 52 | USE trace |
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| 53 | USE omp_para |
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| 54 | IMPLICIT NONE |
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| 55 | REAL(rstd),INTENT(IN) :: qi_in(iim*jjm,llm) |
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| 56 | REAL(rstd),INTENT(IN) :: sqrt_leng_in(iim*jjm) |
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| 57 | REAL(rstd),INTENT(IN) :: xyz_i(iim*jjm,3) |
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| 58 | REAL(rstd),INTENT(IN) :: xyz_v(2*iim*jjm,3) |
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| 59 | REAL(rstd),INTENT(OUT) :: gradq3d_out(iim*jjm,llm,3) |
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| 60 | REAL(rstd) :: maxq,minq,minq_c,maxq_c |
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| 61 | REAL(rstd) :: alphamx,alphami,alpha ,maggrd |
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| 62 | REAL(rstd) :: leng1,leng2 |
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| 63 | REAL(rstd) :: arr(2*iim*jjm) |
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| 64 | REAL(rstd) :: ar(iim*jjm) |
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| 65 | REAL(rstd) :: gradtri(2*iim*jjm,llm,3) |
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| 66 | INTEGER :: ij,k,ind,l |
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| 67 | REAL(rstd) :: qi(iim*jjm,llm) |
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| 68 | REAL(rstd) :: sqrt_leng(iim*jjm) |
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| 69 | REAL(rstd) :: gradq3d(iim*jjm,llm,3) |
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| 70 | REAL(rstd) :: detx,dety,detz,det |
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| 71 | REAL(rstd) :: A(3,3), a11,a12,a13,a21,a22,a23,a31,a32,a33 |
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| 72 | REAL(rstd) :: x1,x2,x3 |
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| 73 | REAL(rstd) :: dq(3) |
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| 74 | |
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| 75 | qi=qi_in |
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| 76 | sqrt_leng=sqrt_leng_in |
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| 77 | |
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| 78 | CALL trace_start("compute_gradq3d1") |
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| 79 | |
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| 80 | ! TODO : precompute ar, drop arr as output argument of gradq ? |
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| 81 | |
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| 82 | !========================================================================================== GRADIENT |
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| 83 | ! Compute gradient at triangles solving a linear system |
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| 84 | ! arr = area of triangle joining centroids of hexagons |
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| 85 | ! DO l = ll_begin,ll_end |
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| 86 | !!$SIMD |
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| 87 | ! DO ij=ij_begin_ext,ij_end_ext |
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| 88 | !! CALL gradq(ij,l,ij+t_rup,ij+t_lup,ij+z_up,qi,gradtri(ij+z_up,l,:),arr(ij+z_up)) |
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| 89 | !! CALL gradq(ij,l,ij+t_ldown,ij+t_rdown,ij+z_down,qi,gradtri(ij+z_down,l,:),arr(ij+z_down)) |
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| 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)) |
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| 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)) |
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| 92 | ! END DO |
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| 93 | ! END DO |
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| 94 | |
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| 95 | DO l = ll_begin,ll_end |
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| 96 | !$SIMD |
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| 97 | DO ij=ij_begin_ext,ij_end_ext |
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| 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)) |
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| 99 | |
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| 100 | |
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| 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) |
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| 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) |
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| 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) |
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| 104 | |
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| 105 | dq(1) = qi(ij+t_rup,l)-qi(ij,l) |
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| 106 | dq(2) = qi(ij+t_lup,l)-qi(ij,l) |
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| 107 | dq(3) = 0.0 |
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| 108 | |
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| 109 | |
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| 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) |
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| 111 | |
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| 112 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 113 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 114 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 115 | |
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| 116 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 117 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 118 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 119 | det = x1 - x2 + x3 |
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| 120 | |
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| 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) |
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| 122 | |
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| 123 | a11=dq(1) ; a12=dq(2) ; a13=dq(3) |
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| 124 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 125 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 126 | |
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| 127 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 128 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 129 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 130 | detx = x1 - x2 + x3 |
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| 131 | |
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| 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) |
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| 133 | |
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| 134 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 135 | a21=dq(1) ; a22=dq(2) ; a23=dq(3) |
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| 136 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 137 | |
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| 138 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 139 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 140 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 141 | dety = x1 - x2 + x3 |
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| 142 | |
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| 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) |
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| 144 | |
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| 145 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 146 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 147 | a31=dq(1) ; a32=dq(2) ; a33=dq(3) |
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| 148 | |
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| 149 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 150 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 151 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 152 | detz = x1 - x2 + x3 |
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| 153 | |
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| 154 | gradtri(ij+z_up,l,1) = detx |
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| 155 | gradtri(ij+z_up,l,2) = dety |
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| 156 | gradtri(ij+z_up,l,3) = detz |
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| 157 | arr(ij+z_up) = det |
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| 158 | |
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| 159 | ENDDO |
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| 160 | |
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| 161 | DO ij=ij_begin_ext,ij_end_ext |
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| 162 | |
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| 163 | |
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| 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)) |
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| 165 | |
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| 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) |
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| 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) |
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| 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) |
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| 169 | |
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| 170 | dq(1) = qi(ij+t_ldown,l)-qi(ij,l) |
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| 171 | dq(2) = qi(ij+t_rdown,l)-qi(ij,l) |
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| 172 | dq(3) = 0.0 |
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| 173 | |
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| 174 | |
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| 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) |
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| 176 | |
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| 177 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 178 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 179 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 180 | |
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| 181 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 182 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 183 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 184 | det = x1 - x2 + x3 |
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| 185 | |
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| 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) |
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| 187 | |
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| 188 | a11=dq(1) ; a12=dq(2) ; a13=dq(3) |
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| 189 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 190 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 191 | |
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| 192 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 193 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 194 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 195 | detx = x1 - x2 + x3 |
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| 196 | |
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| 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) |
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| 198 | |
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| 199 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 200 | a21=dq(1) ; a22=dq(2) ; a23=dq(3) |
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| 201 | a31=A(1,3) ; a32=A(2,3) ; a33=A(3,3) |
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| 202 | |
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| 203 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 204 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 205 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 206 | dety = x1 - x2 + x3 |
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| 207 | |
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| 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) |
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| 209 | |
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| 210 | a11=A(1,1) ; a12=A(2,1) ; a13=A(3,1) |
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| 211 | a21=A(1,2) ; a22=A(2,2) ; a23=A(3,2) |
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| 212 | a31=dq(1) ; a32=dq(2) ; a33=dq(3) |
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| 213 | |
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| 214 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 215 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 216 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 217 | detz = x1 - x2 + x3 |
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| 218 | |
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| 219 | gradtri(ij+z_down,l,1) = detx |
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| 220 | gradtri(ij+z_down,l,2) = dety |
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| 221 | gradtri(ij+z_down,l,3) = detz |
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| 222 | arr(ij+z_down) = det |
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| 223 | |
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| 224 | END DO |
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| 225 | END DO |
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| 226 | |
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| 227 | !$SIMD |
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| 228 | DO ij=ij_begin,ij_end |
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| 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 |
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| 230 | ENDDO |
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| 231 | CALL trace_end("compute_gradq3d1") |
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| 232 | CALL trace_start2("compute_gradq3d2") |
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| 233 | |
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| 234 | DO k=1,3 |
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| 235 | DO l =ll_begin,ll_end |
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| 236 | !$SIMD |
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| 237 | DO ij=ij_begin,ij_end |
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| 238 | gradq3d(ij,l,k) = ( gradtri(ij+z_up,l,k) + gradtri(ij+z_down,l,k) + & |
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| 239 | gradtri(ij+z_rup,l,k) + gradtri(ij+z_ldown,l,k) + & |
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| 240 | gradtri(ij+z_lup,l,k)+ gradtri(ij+z_rdown,l,k) ) / ar(ij) |
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| 241 | END DO |
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| 242 | END DO |
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| 243 | ENDDO |
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| 244 | CALL trace_end2("compute_gradq3d2") |
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| 245 | CALL trace_start("compute_gradq3d3") |
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| 246 | |
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| 247 | !============================================================================================= LIMITING |
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| 248 | DO l =ll_begin,ll_end |
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| 249 | !$SIMD |
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| 250 | DO ij=ij_begin,ij_end |
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| 251 | ! maggrd = dot_product(gradq3d(ij,l,:),gradq3d(ij,l,:)) |
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| 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) |
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| 253 | maggrd = sqrt(maggrd) |
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| 254 | maxq_c = qi(ij,l) + maggrd*sqrt_leng(ij) |
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| 255 | minq_c = qi(ij,l) - maggrd*sqrt_leng(ij) |
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| 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), & |
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| 257 | qi(ij+t_rdown,l),qi(ij+t_ldown,l)) |
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| 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), & |
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| 259 | qi(ij+t_rdown,l),qi(ij+t_ldown,l)) |
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| 260 | alphamx = (maxq - qi(ij,l)) ; alphamx = alphamx/(maxq_c - qi(ij,l) ) |
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| 261 | alphamx = max(alphamx,0.0) |
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| 262 | alphami = (minq - qi(ij,l)); alphami = alphami/(minq_c - qi(ij,l)) |
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| 263 | alphami = max(alphami,0.0) |
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| 264 | alpha = min(alphamx,alphami,1.0) |
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| 265 | ! gradq3d(ij,l,:) = alpha*gradq3d(ij,l,:) |
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| 266 | gradq3d(ij,l,1) = alpha*gradq3d(ij,l,1) |
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| 267 | gradq3d(ij,l,2) = alpha*gradq3d(ij,l,2) |
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| 268 | gradq3d(ij,l,3) = alpha*gradq3d(ij,l,3) |
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| 269 | END DO |
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| 270 | END DO |
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| 271 | |
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| 272 | CALL trace_end("compute_gradq3d3") |
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| 273 | |
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| 274 | |
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| 275 | DO k=1,3 |
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| 276 | DO l = ll_begin,ll_end |
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| 277 | DO ij=ij_begin,ij_end |
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| 278 | gradq3d_out(ij,l,k)=gradq3d(ij,l,k) |
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| 279 | ENDDO |
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| 280 | ENDDO |
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| 281 | ENDDO |
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| 282 | |
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| 283 | CONTAINS |
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| 284 | |
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| 285 | SUBROUTINE gradq(n0,l,n1,n2,n3,q,dq1,dq2,dq3,det) |
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| 286 | IMPLICIT NONE |
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| 287 | INTEGER, INTENT(IN) :: n0,l,n1,n2,n3 |
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| 288 | REAL(rstd), INTENT(IN) :: q(iim*jjm,llm) |
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| 289 | ! REAL(rstd), INTENT(OUT) :: dq(3), det |
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| 290 | REAL(rstd), INTENT(OUT) :: dq1,dq2,dq3,det |
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| 291 | REAL(rstd) :: dq(3) |
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| 292 | |
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| 293 | REAL(rstd) ::detx,dety,detz |
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| 294 | INTEGER :: info |
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| 295 | INTEGER :: IPIV(3) |
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| 296 | |
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| 297 | REAL(rstd) :: A(3,3) |
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| 298 | REAL(rstd) :: B(3) |
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| 299 | |
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| 300 | ! TODO : replace A by A1,A2,A3 |
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| 301 | 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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| 302 | 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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| 303 | 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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| 304 | |
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| 305 | dq(1) = q(n1,l)-q(n0,l) |
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| 306 | dq(2) = q(n2,l)-q(n0,l) |
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| 307 | dq(3) = 0.0 |
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| 308 | |
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| 309 | ! CALL DGESV(3,1,A,3,IPIV,dq(:),3,info) |
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| 310 | ! CALL determinant(A(:,1),A(:,2),A(:,3),det) |
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| 311 | ! CALL determinant(dq,A(:,2),A(:,3),detx) |
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| 312 | ! CALL determinant(A(:,1),dq,A(:,3),dety) |
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| 313 | ! CALL determinant(A(:,1),A(:,2),dq,detz) |
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| 314 | ! dq(1) = detx |
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| 315 | ! dq(2) = dety |
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| 316 | ! dq(3) = detz |
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| 317 | |
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| 318 | 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) |
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| 319 | 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) |
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| 320 | 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) |
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| 321 | 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) |
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| 322 | |
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| 323 | END SUBROUTINE gradq |
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| 324 | |
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| 325 | !========================================================================== |
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| 326 | ! PURE SUBROUTINE determinant(a1,a2,a3,det) |
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| 327 | ! IMPLICIT NONE |
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| 328 | ! REAL(rstd), DIMENSION(3), INTENT(IN) :: a1,a2,a3 |
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| 329 | ! REAL(rstd), INTENT(OUT) :: det |
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| 330 | ! REAL(rstd) :: x1,x2,x3 |
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| 331 | ! x1 = a1(1) * (a2(2) * a3(3) - a2(3) * a3(2)) |
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| 332 | ! x2 = a1(2) * (a2(1) * a3(3) - a2(3) * a3(1)) |
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| 333 | ! x3 = a1(3) * (a2(1) * a3(2) - a2(2) * a3(1)) |
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| 334 | ! det = x1 - x2 + x3 |
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| 335 | ! END SUBROUTINE determinant |
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| 336 | |
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| 337 | SUBROUTINE determinant(a11,a12,a13,a21,a22,a23,a31,a32,a33,det) |
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| 338 | IMPLICIT NONE |
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| 339 | REAL(rstd), INTENT(IN) :: a11,a12,a13,a21,a22,a23,a31,a32,a33 |
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| 340 | REAL(rstd), INTENT(OUT) :: det |
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| 341 | REAL(rstd) :: x1,x2,x3 |
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| 342 | x1 = a11 * (a22 * a33 - a23 * a32) |
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| 343 | x2 = a12 * (a21 * a33 - a23 * a31) |
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| 344 | x3 = a13 * (a21 * a32 - a22 * a31) |
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| 345 | det = x1 - x2 + x3 |
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| 346 | END SUBROUTINE determinant |
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| 347 | |
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| 348 | |
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| 349 | END SUBROUTINE compute_gradq3d |
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| 350 | |
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| 351 | ! Backward trajectories, for use with Miura approach |
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| 352 | SUBROUTINE compute_backward_traj(normal,tangent,ue,tau, cc) |
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| 353 | USE trace |
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| 354 | USE omp_para |
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| 355 | IMPLICIT NONE |
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| 356 | REAL(rstd),INTENT(IN) :: normal(3*iim*jjm,3) |
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| 357 | REAL(rstd),INTENT(IN) :: tangent(3*iim*jjm,3) |
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| 358 | REAL(rstd),INTENT(IN) :: ue(iim*3*jjm,llm) |
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| 359 | REAL(rstd),INTENT(OUT) :: cc(3*iim*jjm,llm,3) ! start of backward trajectory |
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| 360 | REAL(rstd),INTENT(IN) :: tau |
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| 361 | |
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| 362 | REAL(rstd) :: v_e(3), up_e, qe, ed(3) |
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| 363 | INTEGER :: ij,l |
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| 364 | |
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| 365 | CALL trace_start("compute_backward_traj") |
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| 366 | |
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| 367 | ! TODO : compute normal displacement ue*tau as hfluxt / mass(upwind) then reconstruct tangential displacement |
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| 368 | |
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| 369 | ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*tau |
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| 370 | DO l = ll_begin,ll_end |
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| 371 | !$SIMD |
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| 372 | DO ij=ij_begin,ij_end |
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| 373 | up_e =1/de(ij+u_right)*( & |
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| 374 | wee(ij+u_right,1,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
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| 375 | wee(ij+u_right,2,1)*le(ij+u_lup)*ue(ij+u_lup,l)+ & |
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| 376 | wee(ij+u_right,3,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
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| 377 | wee(ij+u_right,4,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+ & |
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| 378 | wee(ij+u_right,5,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
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| 379 | wee(ij+u_right,1,2)*le(ij+t_right+u_ldown)*ue(ij+t_right+u_ldown,l)+ & |
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| 380 | wee(ij+u_right,2,2)*le(ij+t_right+u_rdown)*ue(ij+t_right+u_rdown,l)+ & |
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| 381 | wee(ij+u_right,3,2)*le(ij+t_right+u_right)*ue(ij+t_right+u_right,l)+ & |
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| 382 | wee(ij+u_right,4,2)*le(ij+t_right+u_rup)*ue(ij+t_right+u_rup,l)+ & |
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| 383 | wee(ij+u_right,5,2)*le(ij+t_right+u_lup)*ue(ij+t_right+u_lup,l) & |
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| 384 | ) |
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| 385 | v_e = ue(ij+u_right,l)*normal(ij+u_right,:) + up_e*tangent(ij+u_right,:) |
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| 386 | cc(ij+u_right,l,:) = xyz_e(ij+u_right,:) - v_e*tau |
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| 387 | |
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| 388 | up_e=1/de(ij+u_lup)*( & |
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| 389 | wee(ij+u_lup,1,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
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| 390 | wee(ij+u_lup,2,1)*le(ij+u_ldown)*ue(ij+u_ldown,l)+ & |
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| 391 | wee(ij+u_lup,3,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
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| 392 | wee(ij+u_lup,4,1)*le(ij+u_right)*ue(ij+u_right,l)+ & |
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| 393 | wee(ij+u_lup,5,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
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| 394 | wee(ij+u_lup,1,2)*le(ij+t_lup+u_right)*ue(ij+t_lup+u_right,l)+ & |
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| 395 | wee(ij+u_lup,2,2)*le(ij+t_lup+u_rup)*ue(ij+t_lup+u_rup,l)+ & |
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| 396 | wee(ij+u_lup,3,2)*le(ij+t_lup+u_lup)*ue(ij+t_lup+u_lup,l)+ & |
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| 397 | wee(ij+u_lup,4,2)*le(ij+t_lup+u_left)*ue(ij+t_lup+u_left,l)+ & |
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| 398 | wee(ij+u_lup,5,2)*le(ij+t_lup+u_ldown)*ue(ij+t_lup+u_ldown,l) & |
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| 399 | ) |
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| 400 | v_e = ue(ij+u_lup,l)*normal(ij+u_lup,:) + up_e*tangent(ij+u_lup,:) |
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| 401 | cc(ij+u_lup,l,:) = xyz_e(ij+u_lup,:) - v_e*tau |
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| 402 | |
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| 403 | |
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| 404 | up_e=1/de(ij+u_ldown)*( & |
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| 405 | wee(ij+u_ldown,1,1)*le(ij+u_rdown)*ue(ij+u_rdown,l)+ & |
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| 406 | wee(ij+u_ldown,2,1)*le(ij+u_right)*ue(ij+u_right,l)+ & |
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| 407 | wee(ij+u_ldown,3,1)*le(ij+u_rup)*ue(ij+u_rup,l)+ & |
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| 408 | wee(ij+u_ldown,4,1)*le(ij+u_lup)*ue(ij+u_lup,l)+ & |
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| 409 | wee(ij+u_ldown,5,1)*le(ij+u_left)*ue(ij+u_left,l)+ & |
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| 410 | wee(ij+u_ldown,1,2)*le(ij+t_ldown+u_lup)*ue(ij+t_ldown+u_lup,l)+ & |
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| 411 | wee(ij+u_ldown,2,2)*le(ij+t_ldown+u_left)*ue(ij+t_ldown+u_left,l)+ & |
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| 412 | wee(ij+u_ldown,3,2)*le(ij+t_ldown+u_ldown)*ue(ij+t_ldown+u_ldown,l)+ & |
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| 413 | wee(ij+u_ldown,4,2)*le(ij+t_ldown+u_rdown)*ue(ij+t_ldown+u_rdown,l)+ & |
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| 414 | wee(ij+u_ldown,5,2)*le(ij+t_ldown+u_right)*ue(ij+t_ldown+u_right,l) & |
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| 415 | ) |
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| 416 | v_e = ue(ij+u_ldown,l)*normal(ij+u_ldown,:) + up_e*tangent(ij+u_ldown,:) |
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| 417 | cc(ij+u_ldown,l,:) = xyz_e(ij+u_ldown,:) - v_e*tau |
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| 418 | ENDDO |
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| 419 | END DO |
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| 420 | |
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| 421 | CALL trace_end("compute_backward_traj") |
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| 422 | |
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| 423 | END SUBROUTINE compute_backward_traj |
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| 424 | |
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| 425 | ! Horizontal transport (S. Dubey, T. Dubos) |
|---|
| 426 | ! Slope-limited van Leer approach with hexagons |
|---|
| 427 | SUBROUTINE compute_advect_horiz(update_mass,hfluxt,cc,gradq3d, mass,qi) |
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| 428 | USE trace |
|---|
| 429 | USE omp_para |
|---|
| 430 | IMPLICIT NONE |
|---|
| 431 | LOGICAL, INTENT(IN) :: update_mass |
|---|
| 432 | REAL(rstd), INTENT(IN) :: gradq3d(iim*jjm,llm,3) |
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| 433 | REAL(rstd), INTENT(IN) :: hfluxt(3*iim*jjm,llm) ! mass flux |
|---|
| 434 | REAL(rstd), INTENT(IN) :: cc(3*iim*jjm,llm,3) ! barycenter of quadrilateral, where q is evaluated (1-point quadrature) |
|---|
| 435 | REAL(rstd), INTENT(INOUT) :: mass(iim*jjm,llm) |
|---|
| 436 | REAL(rstd), INTENT(INOUT) :: qi(iim*jjm,llm) |
|---|
| 437 | |
|---|
| 438 | REAL(rstd) :: dq,dmass,qe,ed(3), newmass |
|---|
| 439 | REAL(rstd) :: qflux(3*iim*jjm,llm) |
|---|
| 440 | INTEGER :: ij,k,l |
|---|
| 441 | |
|---|
| 442 | CALL trace_start("compute_advect_horiz") |
|---|
| 443 | |
|---|
| 444 | ! evaluate tracer field at point cc using piecewise linear reconstruction |
|---|
| 445 | ! q(cc)= q0 + gradq.(cc-xyz_i) with xi centroid of hexagon |
|---|
| 446 | ! ne*hfluxt>0 iff outgoing |
|---|
| 447 | DO l = ll_begin,ll_end |
|---|
| 448 | |
|---|
| 449 | !$SIMD |
|---|
| 450 | DO ij=ij_begin_ext,ij_end_ext |
|---|
| 451 | |
|---|
| 452 | IF (ne(ij,right)*hfluxt(ij+u_right,l)>0) THEN |
|---|
| 453 | ed = cc(ij+u_right,l,:) - xyz_i(ij,:) |
|---|
| 454 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
|---|
| 455 | qe = qi(ij,l)+gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
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| 456 | ELSE |
|---|
| 457 | ed = cc(ij+u_right,l,:) - xyz_i(ij+t_right,:) |
|---|
| 458 | ! qe = qi(ij+t_right,l)+sum2(gradq3d(ij+t_right,l,:),ed) |
|---|
| 459 | 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) |
|---|
| 460 | ENDIF |
|---|
| 461 | qflux(ij+u_right,l) = hfluxt(ij+u_right,l)*qe |
|---|
| 462 | |
|---|
| 463 | IF (ne(ij,lup)*hfluxt(ij+u_lup,l)>0) THEN |
|---|
| 464 | ed = cc(ij+u_lup,l,:) - xyz_i(ij,:) |
|---|
| 465 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
|---|
| 466 | qe = qi(ij,l) + gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
|---|
| 467 | ELSE |
|---|
| 468 | ed = cc(ij+u_lup,l,:) - xyz_i(ij+t_lup,:) |
|---|
| 469 | ! qe = qi(ij+t_lup,l)+sum2(gradq3d(ij+t_lup,l,:),ed) |
|---|
| 470 | 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) |
|---|
| 471 | ENDIF |
|---|
| 472 | qflux(ij+u_lup,l) = hfluxt(ij+u_lup,l)*qe |
|---|
| 473 | |
|---|
| 474 | IF (ne(ij,ldown)*hfluxt(ij+u_ldown,l)>0) THEN |
|---|
| 475 | ed = cc(ij+u_ldown,l,:) - xyz_i(ij,:) |
|---|
| 476 | ! qe = qi(ij,l)+sum2(gradq3d(ij,l,:),ed) |
|---|
| 477 | qe = qi(ij,l) + gradq3d(ij,l,1)*ed(1)+gradq3d(ij,l,2)*ed(2)+gradq3d(ij,l,3)*ed(3) |
|---|
| 478 | ELSE |
|---|
| 479 | ed = cc(ij+u_ldown,l,:) - xyz_i(ij+t_ldown,:) |
|---|
| 480 | ! qe = qi(ij+t_ldown,l)+sum2(gradq3d(ij+t_ldown,l,:),ed) |
|---|
| 481 | 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) |
|---|
| 482 | ENDIF |
|---|
| 483 | qflux(ij+u_ldown,l) = hfluxt(ij+u_ldown,l)*qe |
|---|
| 484 | END DO |
|---|
| 485 | END DO |
|---|
| 486 | |
|---|
| 487 | ! update q and, if update_mass, update mass |
|---|
| 488 | DO l = ll_begin,ll_end |
|---|
| 489 | !$SIMD |
|---|
| 490 | DO ij=ij_begin,ij_end |
|---|
| 491 | ! sign convention as Ringler et al. (2010) eq. 21 |
|---|
| 492 | dmass = hfluxt(ij+u_right,l)*ne(ij,right) & |
|---|
| 493 | + hfluxt(ij+u_lup,l) *ne(ij,lup) & |
|---|
| 494 | + hfluxt(ij+u_ldown,l)*ne(ij,ldown) & |
|---|
| 495 | + hfluxt(ij+u_rup,l) *ne(ij,rup) & |
|---|
| 496 | + hfluxt(ij+u_left,l) *ne(ij,left) & |
|---|
| 497 | + hfluxt(ij+u_rdown,l)*ne(ij,rdown) |
|---|
| 498 | |
|---|
| 499 | dq = qflux(ij+u_right,l) *ne(ij,right) & |
|---|
| 500 | + qflux(ij+u_lup,l) *ne(ij,lup) & |
|---|
| 501 | + qflux(ij+u_ldown,l) *ne(ij,ldown) & |
|---|
| 502 | + qflux(ij+u_rup,l) *ne(ij,rup) & |
|---|
| 503 | + qflux(ij+u_left,l) *ne(ij,left) & |
|---|
| 504 | + qflux(ij+u_rdown,l) *ne(ij,rdown) |
|---|
| 505 | |
|---|
| 506 | |
|---|
| 507 | newmass = mass(ij,l) - dmass/Ai(ij) |
|---|
| 508 | qi(ij,l) = (qi(ij,l)*mass(ij,l) - dq/Ai(ij) ) / newmass |
|---|
| 509 | IF(update_mass) mass(ij,l) = newmass |
|---|
| 510 | |
|---|
| 511 | END DO |
|---|
| 512 | END DO |
|---|
| 513 | |
|---|
| 514 | CALL trace_end("compute_advect_horiz") |
|---|
| 515 | CONTAINS |
|---|
| 516 | |
|---|
| 517 | !==================================================================================== |
|---|
| 518 | PURE REAL(rstd) FUNCTION sum2(a1,a2) |
|---|
| 519 | IMPLICIT NONE |
|---|
| 520 | REAL(rstd),INTENT(IN):: a1(3), a2(3) |
|---|
| 521 | sum2 = a1(1)*a2(1)+a1(2)*a2(2)+a1(3)*a2(3) |
|---|
| 522 | ! sum2 = 0. ! Godunov scheme |
|---|
| 523 | END FUNCTION sum2 |
|---|
| 524 | |
|---|
| 525 | END SUBROUTINE compute_advect_horiz |
|---|
| 526 | |
|---|
| 527 | |
|---|
| 528 | END MODULE advect_mod |
|---|
