| 1 | MODULE sedmat |
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| 2 | #if defined key_sed |
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| 3 | !!====================================================================== |
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| 4 | !! *** MODULE sedmat *** |
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| 5 | !! Sediment : linear system of equations |
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| 6 | !!===================================================================== |
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| 7 | !! * Modules used |
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| 8 | !!---------------------------------------------------------------------- |
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| 9 | |
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| 10 | USE sed ! sediment global variable |
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| 11 | |
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| 12 | IMPLICIT NONE |
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| 13 | PRIVATE |
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| 14 | |
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| 15 | PUBLIC sed_mat |
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| 16 | |
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| 17 | INTERFACE sed_mat |
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| 18 | MODULE PROCEDURE sed_mat_dsr, sed_mat_btb |
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| 19 | END INTERFACE |
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| 20 | |
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| 21 | INTEGER, PARAMETER :: nmax = 30 |
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| 22 | |
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| 23 | |
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| 24 | CONTAINS |
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| 25 | |
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| 26 | SUBROUTINE sed_mat_dsr( nvar, ndim, nlev, preac, psol ) |
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| 27 | !!--------------------------------------------------------------------- |
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| 28 | !! *** ROUTINE sed_mat_dsr *** |
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| 29 | !! |
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| 30 | !! ** Purpose : solves tridiagonal system of linear equations |
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| 31 | !! |
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| 32 | !! ** Method : |
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| 33 | !! 1 - computes left hand side of linear system of equations |
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| 34 | !! for dissolution reaction |
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| 35 | !! For mass balance in kbot+sediment : |
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| 36 | !! dz3d (:,1) = dz(1) = 0.5 cm |
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| 37 | !! volw3d(:,1) = dzkbot ( see sedini.F90 ) |
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| 38 | !! dz(2) = 0.3 cm |
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| 39 | !! dz3d(:,2) = 0.3 + dzdep ( see seddsr.F90 ) |
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| 40 | !! volw3d(:,2) and vols3d(l,2) are thickened ( see seddsr.F90 ) |
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| 41 | !! |
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| 42 | !! 2 - forward/backward substitution. |
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| 43 | !! |
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| 44 | !! History : |
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| 45 | !! ! 04-10 (N. Emprin, M. Gehlen ) original |
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| 46 | !! ! 06-04 (C. Ethe) Module Re-organization |
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| 47 | !!---------------------------------------------------------------------- |
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| 48 | !! * Arguments |
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| 49 | INTEGER , INTENT(in) :: nvar ! number of variables |
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| 50 | INTEGER , INTENT(in) :: ndim ! number of points |
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| 51 | INTEGER , INTENT(in) :: nlev ! number of sediment levels |
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| 52 | |
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| 53 | REAL(wp), DIMENSION(ndim,nlev,nvar), INTENT(in ) :: preac ! reaction rates |
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| 54 | REAL(wp), DIMENSION(ndim,nlev,nvar), INTENT(inout) :: psol ! solution ( undersaturation values ) |
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| 55 | |
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| 56 | !---Local declarations |
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| 57 | INTEGER :: ji, jk, jn |
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| 58 | REAL(wp), DIMENSION(ndim,nlev) :: za, zb, zc, zr |
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| 59 | REAL(wp), DIMENSION(ndim) :: zbet |
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| 60 | REAL(wp), DIMENSION(ndim,nmax) :: zgamm |
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| 61 | |
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| 62 | REAL(wp) :: aplus,aminus |
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| 63 | REAL(wp) :: rplus,rminus |
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| 64 | REAL(wp) :: dxplus,dxminus |
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| 65 | |
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| 66 | !---------------------------------------------------------------------- |
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| 67 | |
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| 68 | |
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| 69 | ! Computation left hand side of linear system of |
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| 70 | ! equations for dissolution reaction |
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| 71 | !--------------------------------------------- |
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| 72 | |
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| 73 | |
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| 74 | ! first sediment level |
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| 75 | DO ji = 1, ndim |
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| 76 | aplus = ( ( volw3d(ji,1) / dz3d(ji,1) ) + & |
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| 77 | ( volw3d(ji,2) / dz3d(ji,2) ) ) / 2. |
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| 78 | dxplus = ( dz3d(ji,1) + dz3d(ji,2) ) / 2. |
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| 79 | rplus = ( dtsed / volw3d(ji,1) ) * diff(1) * aplus / dxplus |
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| 80 | |
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| 81 | za(ji,1) = 0. |
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| 82 | zb(ji,1) = 1. + rplus |
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| 83 | zc(ji,1) = -rplus |
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| 84 | ENDDO |
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| 85 | |
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| 86 | DO jk = 2, nlev - 1 |
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| 87 | DO ji = 1, ndim |
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| 88 | aminus = ( ( volw3d(ji,jk-1) / dz3d(ji,jk-1) ) + & |
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| 89 | & ( volw3d(ji,jk ) / dz3d(ji,jk ) ) ) / 2. |
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| 90 | dxminus = ( dz3d(ji,jk-1) + dz3d(ji,jk) ) / 2. |
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| 91 | |
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| 92 | aplus = ( ( volw3d(ji,jk ) / dz3d(ji,jk ) ) + & |
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| 93 | & ( volw3d(ji,jk+1) / dz3d(ji,jk+1) ) ) / 2. |
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| 94 | dxplus = ( dz3d(ji,jk) + dz3d(ji,jk+1) ) / 2 |
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| 95 | ! |
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| 96 | rminus = ( dtsed / volw3d(ji,jk) ) * diff(jk-1) * aminus / dxminus |
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| 97 | rplus = ( dtsed / volw3d(ji,jk) ) * diff(jk) * aplus / dxplus |
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| 98 | ! |
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| 99 | za(ji,jk) = -rminus |
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| 100 | zb(ji,jk) = 1. + rminus + rplus |
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| 101 | zc(ji,jk) = -rplus |
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| 102 | END DO |
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| 103 | END DO |
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| 104 | |
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| 105 | DO ji = 1, ndim |
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| 106 | aminus = ( ( volw3d(ji,nlev-1) / dz3d(ji,nlev-1) ) + & |
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| 107 | & ( volw3d(ji,nlev) / dz3d(ji,nlev) ) ) / 2. |
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| 108 | dxminus = ( dz3d(ji,nlev-1) + dz3d(ji,nlev) ) / 2. |
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| 109 | rminus = ( dtsed / volw3d(ji,nlev) ) * diff(nlev-1) * aminus / dxminus |
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| 110 | ! |
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| 111 | za(ji,nlev) = -rminus |
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| 112 | zb(ji,nlev) = 1. + rminus |
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| 113 | zc(ji,nlev) = 0. |
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| 114 | END DO |
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| 115 | |
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| 116 | |
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| 117 | ! solves tridiagonal system of linear equations |
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| 118 | ! ----------------------------------------------- |
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| 119 | |
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| 120 | DO jn = 1, nvar |
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| 121 | |
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| 122 | zr (:,:) = psol(:,:,jn) |
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| 123 | zbet(: ) = zb(:,1) + preac(:,1,jn) |
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| 124 | psol(:,1,jn) = zr(:,1) / zbet(:) |
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| 125 | ! |
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| 126 | DO jk = 2, nlev |
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| 127 | DO ji = 1, ndim |
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| 128 | zgamm(ji,jk) = zc(ji,jk-1) / zbet(ji) |
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| 129 | zbet(ji) = ( zb(ji,jk) + preac(ji,jk,jn) ) - za(ji,jk) * zgamm(ji,jk) |
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| 130 | psol(ji,jk,jn) = ( zr(ji,jk) - za(ji,jk) * psol(ji,jk-1,jn) ) / zbet(ji) |
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| 131 | END DO |
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| 132 | ENDDO |
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| 133 | ! |
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| 134 | DO jk = nlev - 1, 1, -1 |
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| 135 | DO ji = 1,ndim |
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| 136 | psol(ji,jk,jn) = psol(ji,jk,jn) - zgamm(ji,jk+1) * psol(ji,jk+1,jn) |
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| 137 | END DO |
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| 138 | ENDDO |
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| 139 | |
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| 140 | ENDDO |
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| 141 | |
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| 142 | |
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| 143 | END SUBROUTINE sed_mat_dsr |
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| 144 | |
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| 145 | |
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| 146 | SUBROUTINE sed_mat_btb( nvar, ndim, nlev, psol ) |
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| 147 | !!--------------------------------------------------------------------- |
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| 148 | !! *** ROUTINE sed_mat_btb *** |
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| 149 | !! |
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| 150 | !! ** Purpose : solves tridiagonal system of linear equations |
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| 151 | !! |
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| 152 | !! ** Method : |
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| 153 | !! 1 - computes left hand side of linear system of equations |
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| 154 | !! for dissolution reaction |
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| 155 | !! |
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| 156 | !! 2 - forward/backward substitution. |
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| 157 | !! |
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| 158 | !! History : |
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| 159 | !! ! 04-10 (N. Emprin, M. Gehlen ) original |
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| 160 | !! ! 06-04 (C. Ethe) Module Re-organization |
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| 161 | !!---------------------------------------------------------------------- |
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| 162 | !! * Arguments |
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| 163 | INTEGER , INTENT(in) :: & |
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| 164 | nvar , & ! number of variables |
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| 165 | ndim , & ! number of points |
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| 166 | nlev ! number of sediment levels |
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| 167 | |
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| 168 | REAL(wp), DIMENSION(ndim,nlev,nvar), INTENT(inout) :: & |
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| 169 | psol ! solution |
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| 170 | |
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| 171 | !---Local declarations |
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| 172 | INTEGER :: & |
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| 173 | ji, jk, jn |
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| 174 | |
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| 175 | REAL(wp) :: & |
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| 176 | aplus,aminus , & |
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| 177 | rplus,rminus , & |
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| 178 | dxplus,dxminus |
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| 179 | |
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| 180 | REAL(wp), DIMENSION(nlev) :: za, zb, zc |
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| 181 | REAL(wp), DIMENSION(ndim,nlev) :: zr |
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| 182 | REAL(wp), DIMENSION(nmax) :: zgamm |
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| 183 | REAL(wp) :: zbet |
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| 184 | |
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| 185 | |
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| 186 | !---------------------------------------------------------------------- |
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| 187 | |
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| 188 | ! Computation left hand side of linear system of |
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| 189 | ! equations for dissolution reaction |
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| 190 | !--------------------------------------------- |
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| 191 | |
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| 192 | |
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| 193 | ! first sediment level |
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| 194 | aplus = ( ( vols(2) / dz(2) ) + ( vols(3) / dz(3) ) ) / 2. |
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| 195 | dxplus = ( dz(2) + dz(3) ) / 2. |
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| 196 | rplus = ( dtsed / vols(2) ) * db * aplus / dxplus |
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| 197 | |
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| 198 | za(1) = 0. |
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| 199 | zb(1) = 1. + rplus |
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| 200 | zc(1) = -rplus |
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| 201 | |
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| 202 | |
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| 203 | DO jk = 2, nlev - 1 |
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| 204 | aminus = ( ( vols(jk) / dz(jk) ) + ( vols(jk+1) / dz(jk+1) ) ) / 2. |
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| 205 | dxminus = ( dz(jk) + dz(jk+1) ) / 2. |
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| 206 | rminus = ( dtsed / vols(jk+1) ) * db * aminus / dxminus |
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| 207 | ! |
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| 208 | aplus = ( ( vols(jk+1) / dz(jk+1 ) ) + ( vols(jk+2) / dz(jk+2) ) ) / 2. |
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| 209 | dxplus = ( dz(jk+1) + dz(jk+2) ) / 2. |
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| 210 | rplus = ( dtsed / vols(jk+1) ) * db * aplus / dxplus |
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| 211 | ! |
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| 212 | za(jk) = -rminus |
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| 213 | zb(jk) = 1. + rminus + rplus |
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| 214 | zc(jk) = -rplus |
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| 215 | ENDDO |
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| 216 | |
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| 217 | aminus = ( ( vols(nlev) / dz(nlev) ) + ( vols(nlev+1) / dz(nlev+1) ) ) / 2. |
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| 218 | dxminus = ( dz(nlev) + dz(nlev+1) ) / 2. |
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| 219 | rminus = ( dtsed / vols(nlev+1) ) * db * aminus / dxminus |
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| 220 | ! |
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| 221 | |
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| 222 | za(nlev) = -rminus |
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| 223 | zb(nlev) = 1. + rminus |
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| 224 | zc(nlev) = 0. |
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| 225 | |
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| 226 | |
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| 227 | ! solves tridiagonal system of linear equations |
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| 228 | ! ----------------------------------------------- |
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| 229 | DO jn = 1, nvar |
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| 230 | |
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| 231 | zr (:,:) = psol(:,:,jn) |
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| 232 | zbet = zb(1) |
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| 233 | psol(:,1,jn) = zr(:,1) / zbet |
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| 234 | ! |
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| 235 | DO jk = 2, nlev |
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| 236 | zgamm(jk) = zc(jk-1) / zbet |
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| 237 | zbet = zb(jk) - za(jk) * zgamm(jk) |
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| 238 | DO ji = 1, ndim |
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| 239 | psol(ji,jk,jn) = ( zr(ji,jk) - za(jk) * psol(ji,jk-1,jn) ) / zbet |
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| 240 | END DO |
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| 241 | ENDDO |
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| 242 | ! |
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| 243 | DO jk = nlev - 1, 1, -1 |
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| 244 | DO ji = 1,ndim |
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| 245 | psol(ji,jk,jn) = psol(ji,jk,jn) - zgamm(jk+1) * psol(ji,jk+1,jn) |
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| 246 | END DO |
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| 247 | ENDDO |
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| 248 | |
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| 249 | ENDDO |
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| 250 | |
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| 251 | |
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| 252 | END SUBROUTINE sed_mat_btb |
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| 253 | |
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| 254 | |
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| 255 | #else |
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| 256 | !!====================================================================== |
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| 257 | !! MODULE sedmat : Dummy module |
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| 258 | !!====================================================================== |
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| 259 | CONTAINS |
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| 260 | SUBROUTINE sed_mat ! Empty routine |
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| 261 | END SUBROUTINE sed_mat |
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| 262 | !!====================================================================== |
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| 263 | #endif |
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| 264 | |
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| 265 | END MODULE sedmat |
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