[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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| 5 | CONTAINS |
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| 6 | |
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[22] | 7 | !========================================================================== |
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[17] | 8 | |
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[22] | 9 | SUBROUTINE init_advect(normal,tangent) |
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| 10 | USE domain_mod |
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| 11 | USE dimensions |
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| 12 | USE geometry |
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| 13 | USE metric |
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| 14 | USE vector |
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| 15 | IMPLICIT NONE |
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| 16 | REAL(rstd),INTENT(OUT) :: normal(3*iim*jjm,3) |
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| 17 | REAL(rstd),INTENT(OUT) :: tangent(3*iim*jjm,3) |
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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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| 42 | END DO |
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| 43 | ENDDO |
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| 44 | |
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[17] | 45 | END SUBROUTINE init_advect |
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| 46 | |
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[22] | 47 | !======================================================================================= |
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[17] | 48 | |
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[22] | 49 | SUBROUTINE compute_gradq3d(qi,gradq3d) |
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| 50 | USE domain_mod |
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| 51 | USE dimensions |
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| 52 | USE geometry |
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| 53 | USE metric |
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| 54 | IMPLICIT NONE |
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| 55 | REAL(rstd),INTENT(IN) :: qi(iim*jjm,llm) |
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[23] | 56 | REAL(rstd),INTENT(OUT) :: gradq3d(iim*jjm,llm,3) |
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[17] | 57 | REAL(rstd) :: maxq,minq,minq_c,maxq_c |
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| 58 | REAL(rstd) :: alphamx,alphami,alpha ,maggrd,leng |
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| 59 | REAL(rstd) :: leng1,leng2 |
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| 60 | REAL(rstd) :: arr(2*iim*jjm) |
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| 61 | REAL(rstd) :: gradtri(2*iim*jjm,llm,3) |
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| 62 | REAL(rstd) :: ar |
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| 63 | INTEGER :: i,j,n,k,ind,l |
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[22] | 64 | !========================================================================================== GRADIENT |
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| 65 | Do l = 1,llm |
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| 66 | DO j=jj_begin-1,jj_end+1 |
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| 67 | DO i=ii_begin-1,ii_end+1 |
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| 68 | n=(j-1)*iim+i |
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| 69 | CALL gradq(n,n+t_rup,n+t_lup,n+z_up,qi(:,l),gradtri(n+z_up,l,:),arr(n+z_up)) |
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| 70 | CALL gradq(n,n+t_ldown,n+t_rdown,n+z_down,qi(:,l),gradtri(n+z_down,l,:),arr(n+z_down)) |
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| 71 | END DO |
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[17] | 72 | END DO |
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[22] | 73 | END DO |
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[17] | 74 | |
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[22] | 75 | ! Do l =1,llm |
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| 76 | DO j=jj_begin,jj_end |
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| 77 | DO i=ii_begin,ii_end |
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| 78 | n=(j-1)*iim+i |
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| 79 | gradq3d(n,:,:) = gradtri(n+z_up,:,:) + gradtri(n+z_down,:,:) + & |
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| 80 | gradtri(n+z_rup,:,:) + gradtri(n+z_ldown,:,:) + & |
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| 81 | gradtri(n+z_lup,:,:)+ gradtri(n+z_rdown,:,:) |
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| 82 | ar = arr(n+z_up)+arr(n+z_lup)+arr(n+z_ldown)+arr(n+z_down)+arr(n+z_rdown)+arr(n+z_rup) |
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| 83 | gradq3d(n,:,:) = gradq3d(n,:,:)/(ar+1.e-50) |
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| 84 | END DO |
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| 85 | END DO |
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| 86 | ! END DO |
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| 87 | |
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| 88 | !============================================================================================= LIMITING |
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| 89 | ! GO TO 120 |
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| 90 | DO l =1,llm |
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| 91 | DO j=jj_begin,jj_end |
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[17] | 92 | DO i=ii_begin,ii_end |
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| 93 | n=(j-1)*iim+i |
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[22] | 94 | maggrd = dot_product(gradq3d(n,l,:),gradq3d(n,l,:)) |
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| 95 | maggrd = sqrt(maggrd) |
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| 96 | leng = 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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| 97 | sum((xyz_v(n+z_rup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_rdown,:) - xyz_i(n,:))**2), & |
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| 98 | sum((xyz_v(n+z_lup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_ldown,:) - xyz_i(n,:))**2)) |
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| 99 | maxq_c = qi(n,l) + maggrd*sqrt(leng) |
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| 100 | minq_c = qi(n,l) - maggrd*sqrt(leng) |
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| 101 | 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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| 102 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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| 103 | 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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| 104 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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| 105 | alphamx = (maxq - qi(n,l)) ; alphamx = alphamx/(maxq_c - qi(n,l) ) |
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| 106 | alphamx = max(alphamx,0.0) |
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| 107 | alphami = (minq - qi(n,l)); alphami = alphami/(minq_c - qi(n,l)) |
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| 108 | alphami = max(alphami,0.0) |
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| 109 | alpha = min(alphamx,alphami,1.0) |
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| 110 | gradq3d(n,l,:) = alpha*gradq3d(n,l,:) |
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| 111 | END DO |
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| 112 | END DO |
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[17] | 113 | END DO |
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[22] | 114 | END SUBROUTINE compute_gradq3d |
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| 115 | |
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| 116 | !=================================================================================================== |
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[136] | 117 | SUBROUTINE compute_advect_horiz(update_mass, normal,tangent,qi,gradq3d,him,ue,he,bigt) |
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[22] | 118 | USE domain_mod |
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| 119 | USE dimensions |
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| 120 | USE geometry |
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| 121 | USE metric |
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| 122 | IMPLICIT NONE |
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[136] | 123 | LOGICAL, INTENT(IN) :: update_mass |
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[22] | 124 | REAL(rstd),INTENT(IN) :: normal(3*iim*jjm,3) |
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| 125 | REAL(rstd),INTENT(IN) :: tangent(3*iim*jjm,3) |
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[17] | 126 | REAL(rstd),INTENT(INOUT) :: qi(iim*jjm,llm) |
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[23] | 127 | REAL(rstd),INTENT(IN) :: gradq3d(iim*jjm,llm,3) |
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[17] | 128 | REAL(rstd),INTENT(INOUT) :: him(iim*jjm,llm) |
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[22] | 129 | REAL(rstd),INTENT(IN) :: ue(iim*3*jjm,llm) |
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| 130 | REAL(rstd),INTENT(IN) :: he(3*iim*jjm,llm) ! mass flux |
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| 131 | REAL(rstd),INTENT(IN) :: bigt |
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| 132 | |
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[17] | 133 | REAL(rstd) :: dqi(iim*jjm,llm),dhi(iim*jjm,llm) |
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[136] | 134 | REAL(rstd) :: cc(3*iim*jjm,llm,3) ! barycenter of quadrilateral, where q is evaluated (1-point quadrature) |
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[17] | 135 | REAL(rstd) :: v_e(3*iim*jjm,llm,3) |
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| 136 | REAL(rstd) :: up_e |
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[22] | 137 | |
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[17] | 138 | REAL(rstd) :: qe(3*iim*jjm,llm) |
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| 139 | REAL(rstd) :: ed(3) |
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| 140 | REAL(rstd) :: flxx(3*iim*jjm,llm) |
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| 141 | INTEGER :: i,j,n,k,l |
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| 142 | REAL(rstd):: him_old(llm) |
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| 143 | |
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| 144 | |
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[136] | 145 | ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*dt/2 |
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| 146 | ! TODO : this does not depend on q and should be done only once, not for each tracer |
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[22] | 147 | DO l = 1,llm |
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[69] | 148 | DO j=jj_begin-1,jj_end+1 |
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| 149 | DO i=ii_begin-1,ii_end+1 |
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[22] | 150 | n=(j-1)*iim+i |
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[17] | 151 | |
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[22] | 152 | up_e =1/de(n+u_right)*( & |
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| 153 | wee(n+u_right,1,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 154 | wee(n+u_right,2,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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| 155 | wee(n+u_right,3,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 156 | wee(n+u_right,4,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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| 157 | wee(n+u_right,5,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 158 | wee(n+u_right,1,2)*le(n+t_right+u_ldown)*ue(n+t_right+u_ldown,l)+ & |
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| 159 | wee(n+u_right,2,2)*le(n+t_right+u_rdown)*ue(n+t_right+u_rdown,l)+ & |
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| 160 | wee(n+u_right,3,2)*le(n+t_right+u_right)*ue(n+t_right+u_right,l)+ & |
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| 161 | wee(n+u_right,4,2)*le(n+t_right+u_rup)*ue(n+t_right+u_rup,l)+ & |
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| 162 | wee(n+u_right,5,2)*le(n+t_right+u_lup)*ue(n+t_right+u_lup,l) & |
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| 163 | ) |
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| 164 | v_e(n+u_right,l,:)= ue(n+u_right,l)*normal(n+u_right,:) + up_e*tangent(n+u_right,:) |
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[17] | 165 | |
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[22] | 166 | up_e=1/de(n+u_lup)*( & |
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| 167 | wee(n+u_lup,1,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 168 | wee(n+u_lup,2,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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| 169 | wee(n+u_lup,3,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 170 | wee(n+u_lup,4,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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| 171 | wee(n+u_lup,5,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 172 | wee(n+u_lup,1,2)*le(n+t_lup+u_right)*ue(n+t_lup+u_right,l)+ & |
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| 173 | wee(n+u_lup,2,2)*le(n+t_lup+u_rup)*ue(n+t_lup+u_rup,l)+ & |
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| 174 | wee(n+u_lup,3,2)*le(n+t_lup+u_lup)*ue(n+t_lup+u_lup,l)+ & |
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| 175 | wee(n+u_lup,4,2)*le(n+t_lup+u_left)*ue(n+t_lup+u_left,l)+ & |
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| 176 | wee(n+u_lup,5,2)*le(n+t_lup+u_ldown)*ue(n+t_lup+u_ldown,l) & |
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| 177 | ) |
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| 178 | v_e(n+u_lup,l,:)= ue(n+u_lup,l)*normal(n+u_lup,:) + up_e*tangent(n+u_lup,:) |
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| 179 | |
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| 180 | up_e=1/de(n+u_ldown)*( & |
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| 181 | wee(n+u_ldown,1,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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| 182 | wee(n+u_ldown,2,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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| 183 | wee(n+u_ldown,3,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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| 184 | wee(n+u_ldown,4,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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| 185 | wee(n+u_ldown,5,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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| 186 | wee(n+u_ldown,1,2)*le(n+t_ldown+u_lup)*ue(n+t_ldown+u_lup,l)+ & |
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| 187 | wee(n+u_ldown,2,2)*le(n+t_ldown+u_left)*ue(n+t_ldown+u_left,l)+ & |
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| 188 | wee(n+u_ldown,3,2)*le(n+t_ldown+u_ldown)*ue(n+t_ldown+u_ldown,l)+ & |
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| 189 | wee(n+u_ldown,4,2)*le(n+t_ldown+u_rdown)*ue(n+t_ldown+u_rdown,l)+ & |
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| 190 | wee(n+u_ldown,5,2)*le(n+t_ldown+u_right)*ue(n+t_ldown+u_right,l) & |
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| 191 | ) |
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| 192 | v_e(n+u_ldown,l,:)= ue(n+u_ldown,l)*normal(n+u_ldown,:) + up_e*tangent(n+u_ldown,:) |
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| 193 | |
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| 194 | cc(n+u_right,l,:) = xyz_e(n+u_right,:) - v_e(n+u_right,l,:)*0.5*bigt !! redge is mid point of edge i |
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| 195 | cc(n+u_lup,l,:) = xyz_e(n+u_lup,:) - v_e(n+u_lup,l,:)*0.5*bigt |
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| 196 | cc(n+u_ldown,l,:) = xyz_e(n+u_ldown,:) - v_e(n+u_ldown,l,:)*0.5*bigt |
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| 197 | ENDDO |
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[17] | 198 | ENDDO |
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| 199 | END DO |
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[136] | 200 | ! end of tracer-independant computations |
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| 201 | |
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| 202 | ! evaluate traver field at point cc usin piecewise linear reconstruction |
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| 203 | ! q(cc)= q0 + gradq.(cc-xyz_i) with xi centroid of hexagon |
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[17] | 204 | DO l = 1,llm |
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[22] | 205 | DO j=jj_begin-1,jj_end+1 |
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| 206 | DO i=ii_begin-1,ii_end+1 |
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| 207 | n=(j-1)*iim+i |
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| 208 | if (ne(n,right)*ue(n+u_right,l)>0) then |
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| 209 | ed = cc(n+u_right,l,:) - xyz_i(n,:) |
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| 210 | qe(n+u_right,l)=qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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| 211 | else |
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| 212 | ed = cc(n+u_right,l,:) - xyz_i(n+t_right,:) |
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| 213 | qe(n+u_right,l)=qi(n+t_right,l)+sum2(gradq3d(n+t_right,l,:),ed) |
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| 214 | endif |
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| 215 | if (ne(n,lup)*ue(n+u_lup,l)>0) then |
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| 216 | ed = cc(n+u_lup,l,:) - xyz_i(n,:) |
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| 217 | qe(n+u_lup,l)=qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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| 218 | else |
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| 219 | ed = cc(n+u_lup,l,:) - xyz_i(n+t_lup,:) |
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| 220 | qe(n+u_lup,l)=qi(n+t_lup,l)+sum2(gradq3d(n+t_lup,l,:),ed) |
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| 221 | endif |
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| 222 | if (ne(n,ldown)*ue(n+u_ldown,l)>0) then |
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| 223 | ed = cc(n+u_ldown,l,:) - xyz_i(n,:) |
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| 224 | qe(n+u_ldown,l)=qi(n,l)+ sum2(gradq3d(n,l,:),ed) |
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| 225 | else |
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| 226 | ed = cc(n+u_ldown,l,:) - xyz_i(n+t_ldown,:) |
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| 227 | qe(n+u_ldown,l)=qi(n+t_ldown,l)+sum2(gradq3d(n+t_ldown,l,:),ed) |
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| 228 | endif |
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| 229 | end do |
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| 230 | end do |
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| 231 | END DO |
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[17] | 232 | |
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[136] | 233 | ! evaluate q flux as mass flux * qe |
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| 234 | ! TODO : loop over k ! |
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| 235 | ! TODO : merge with previous loop and eliminate unnecessary temporary qe |
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[22] | 236 | DO j=jj_begin-1,jj_end+1 |
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| 237 | DO i=ii_begin-1,ii_end+1 |
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| 238 | n=(j-1)*iim+i |
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| 239 | flxx(n+u_right,:) = he(n+u_right,:)*qe(n+u_right,:)*ne(n,right) |
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| 240 | flxx(n+u_lup,:) = he(n+u_lup,:)*qe(n+u_lup,:)*ne(n,lup) |
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| 241 | flxx(n+u_ldown,:) = he(n+u_ldown,:)*qe(n+u_ldown,:)*ne(n,ldown) |
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| 242 | ENDDO |
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| 243 | ENDDO |
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| 244 | |
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[136] | 245 | ! update q and, if update_mass, mass |
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| 246 | ! TODO : loop over k ! |
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[22] | 247 | DO j=jj_begin,jj_end |
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[17] | 248 | DO i=ii_begin,ii_end |
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[22] | 249 | n=(j-1)*iim+i |
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[17] | 250 | |
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[22] | 251 | dhi(n,:)= -(1/Ai(n))*(he(n+u_right,:)*ne(n,right) + he(n+u_lup,:)*ne(n,lup) & |
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| 252 | + he(n+u_ldown,:)*ne(n,ldown) + he(n+u_rup,:)*ne(n,rup) & |
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| 253 | + he(n+u_left,:)*ne(n,left) + he(n+u_rdown,:)*ne(n,rdown) ) |
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[17] | 254 | |
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[22] | 255 | dqi(n,:)= -(1/Ai(n))*(flxx(n+u_right,:)+flxx(n+u_lup,:) & |
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| 256 | +flxx(n+u_ldown,:) - flxx(n+u_rup,:) & |
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| 257 | - flxx(n+u_left,:) - flxx(n+u_rdown,:) ) |
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| 258 | him_old(:) = him(n,:) |
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| 259 | him(n,:) = him(n,:) + dhi(n,:) |
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| 260 | qi(n,:) = (qi(n,:)*him_old(:) + dqi(n,:))/him(n,:) |
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| 261 | |
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[17] | 262 | END DO |
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[22] | 263 | END DO |
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[17] | 264 | |
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[22] | 265 | CONTAINS |
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| 266 | !==================================================================================== |
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| 267 | REAL FUNCTION sum2(a1,a2) |
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| 268 | IMPLICIT NONE |
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| 269 | REAL,INTENT(IN):: a1(3), a2(3) |
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| 270 | sum2 = a1(1)*a2(1)+a1(2)*a2(2)+a1(3)*a2(3) |
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| 271 | END FUNCTION sum2 |
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| 272 | |
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| 273 | END SUBROUTINE compute_advect_horiz |
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| 274 | !========================================================================== |
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[17] | 275 | SUBROUTINE gradq(n0,n1,n2,n3,q,dq,det) |
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[22] | 276 | USE geometry |
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| 277 | USE metric |
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| 278 | USE dimensions |
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| 279 | IMPLICIT NONE |
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[17] | 280 | INTEGER, INTENT(IN) :: n0,n1,n2,n3 |
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| 281 | REAL,INTENT(IN) :: q(iim*jjm) |
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| 282 | REAL,INTENT(OUT) :: dq(3) |
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| 283 | REAL(rstd) ::det,detx,dety,detz |
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| 284 | INTEGER :: info |
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| 285 | INTEGER :: IPIV(3) |
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| 286 | |
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| 287 | REAL(rstd) :: A(3,3) |
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| 288 | REAL(rstd) :: B(3) |
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| 289 | |
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| 290 | 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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| 291 | 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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| 292 | 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] | 293 | |
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| 294 | |
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[17] | 295 | dq(1) = q(n1)-q(n0) |
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| 296 | dq(2) = q(n2)-q(n0) |
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| 297 | dq(3) = 0.0 |
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[22] | 298 | ! CALL DGESV(3,1,A,3,IPIV,dq(:),3,info) |
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| 299 | CALL determinant(A(:,1),A(:,2),A(:,3),det) |
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| 300 | CALL determinant(dq,A(:,2),A(:,3),detx) |
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| 301 | CALL determinant(A(:,1),dq,A(:,3),dety) |
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| 302 | CALL determinant(A(:,1),A(:,2),dq,detz) |
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| 303 | dq(1) = detx |
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| 304 | dq(2) = dety |
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| 305 | dq(3) = detz |
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[17] | 306 | END SUBROUTINE gradq |
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[22] | 307 | !========================================================================== |
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| 308 | SUBROUTINE determinant(a1,a2,a3,det) |
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| 309 | IMPLICIT NONE |
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| 310 | REAL, DIMENSION(3) :: a1, a2,a3 |
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| 311 | REAL :: det,x1,x2,x3 |
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| 312 | x1 = a1(1) * (a2(2) * a3(3) - a2(3) * a3(2)) |
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| 313 | x2 = a1(2) * (a2(1) * a3(3) - a2(3) * a3(1)) |
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| 314 | x3 = a1(3) * (a2(1) * a3(2) - a2(2) * a3(1)) |
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| 315 | det = x1 - x2 + x3 |
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| 316 | END SUBROUTINE determinant |
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| 317 | |
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| 318 | END MODULE advect_mod |
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