| 1 | subroutine moldiff(pplay,pplev,pt,pdt,pq,pdq,ptimestep, |
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| 2 | & zzlay,pdteuv,pdtconduc,pdqdiff) |
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| 3 | |
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| 4 | |
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| 5 | implicit none |
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| 6 | |
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| 7 | #include "dimensions.h" |
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| 8 | #include "dimphys.h" |
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| 9 | #include "comcstfi.h" |
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| 10 | #include "callkeys.h" |
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| 11 | #include "comdiurn.h" |
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| 12 | #include "chimiedata.h" |
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| 13 | #include "tracer.h" |
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| 14 | #include "conc.h" |
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| 15 | |
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| 16 | |
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| 17 | c |
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| 18 | c Input/Output |
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| 19 | c |
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| 20 | real ptimestep |
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| 21 | real pplay(ngridmx,nlayermx) |
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| 22 | real zzlay(ngridmx,nlayermx) |
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| 23 | real pplev(ngridmx,nlayermx+1) |
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| 24 | real pq(ngridmx,nlayermx,nqmx) |
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| 25 | real pdq(ngridmx,nlayermx,nqmx) |
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| 26 | real pt(ngridmx,nlayermx) |
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| 27 | real pdt(ngridmx,nlayermx) |
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| 28 | real pdteuv(ngridmx,nlayermx) |
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| 29 | real pdtconduc(ngridmx,nlayermx) |
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| 30 | real pdqdiff(ngridmx,nlayermx,nqmx) |
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| 31 | c |
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| 32 | c Local |
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| 33 | c |
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| 34 | real hco2(ncomptot),ho |
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| 35 | |
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| 36 | integer ig,nz,l,n,nn,iq |
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| 37 | real del1,del2, tmean ,dalfinvdz, d |
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| 38 | real hh,dcoef,dcoef1,ptfac, ntot, dens, dens2, dens3 |
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| 39 | real hp(nlayermx) |
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| 40 | real tt(nlayermx) |
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| 41 | real qq(nlayermx,ncomptot) |
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| 42 | real dmmeandz(nlayermx) |
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| 43 | real qnew(nlayermx,ncomptot) |
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| 44 | real zlocal(nlayermx) |
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| 45 | real alf(ncomptot-1,ncomptot-1) |
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| 46 | real alfinv(nlayermx,ncomptot-1,ncomptot-1) |
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| 47 | real indx(ncomptot-1) |
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| 48 | real b(nlayermx,ncomptot-1) |
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| 49 | real y(ncomptot-1,ncomptot-1) |
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| 50 | real aa(nlayermx,ncomptot-1,ncomptot-1) |
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| 51 | real bb(nlayermx,ncomptot-1,ncomptot-1) |
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| 52 | real cc(nlayermx,ncomptot-1,ncomptot-1) |
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| 53 | real atri(nlayermx-2) |
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| 54 | real btri(nlayermx-2) |
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| 55 | real ctri(nlayermx-2) |
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| 56 | real rtri(nlayermx-2) |
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| 57 | real qtri(nlayermx-2) |
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| 58 | real alfdiag(ncomptot-1) |
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| 59 | real wi(ncomptot), flux(ncomptot), pote |
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| 60 | |
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| 61 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 62 | c tracer numbering in the molecular diffusion |
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| 63 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 64 | c Atomic oxygen must always be the LAST species of the list as |
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| 65 | c it is the dominant species at high altitudes. |
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| 66 | integer,parameter :: i_co = 1 |
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| 67 | integer,parameter :: i_n2 = 2 |
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| 68 | integer,parameter :: i_o2 = 3 |
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| 69 | integer,parameter :: i_co2 = 4 |
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| 70 | integer,parameter :: i_h2 = 5 |
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| 71 | integer,parameter :: i_h = 6 |
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| 72 | integer,parameter :: i_oh = 7 |
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| 73 | integer,parameter :: i_ho2 = 8 |
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| 74 | integer,parameter :: i_h2o = 9 |
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| 75 | integer,parameter :: i_h2o2 = 10 |
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| 76 | integer,parameter :: i_o1d = 11 |
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| 77 | integer,parameter :: i_o3 = 12 |
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| 78 | integer,parameter :: i_ar = 13 |
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| 79 | integer,parameter :: i_o = 14 |
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| 80 | |
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| 81 | ! Tracer indexes in the GCM: |
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| 82 | integer,save :: g_co2=0 |
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| 83 | integer,save :: g_co=0 |
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| 84 | integer,save :: g_o=0 |
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| 85 | integer,save :: g_o1d=0 |
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| 86 | integer,save :: g_o2=0 |
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| 87 | integer,save :: g_o3=0 |
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| 88 | integer,save :: g_h=0 |
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| 89 | integer,save :: g_h2=0 |
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| 90 | integer,save :: g_oh=0 |
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| 91 | integer,save :: g_ho2=0 |
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| 92 | integer,save :: g_h2o2=0 |
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| 93 | integer,save :: g_n2=0 |
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| 94 | integer,save :: g_ar=0 |
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| 95 | integer,save :: g_h2o=0 |
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| 96 | |
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| 97 | integer,save :: gcmind(ncomptot) ! array of GCM indexes |
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| 98 | integer ierr |
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| 99 | |
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| 100 | logical,save :: firstcall=.true. |
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| 101 | real abfac(ncomptot) |
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| 102 | real,save :: dij(ncomptot,ncomptot) |
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| 103 | |
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| 104 | ! Initializations at first call |
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| 105 | if (firstcall) then |
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| 106 | call moldiffcoeff(dij) |
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| 107 | print*,'MOLDIFF EXO' |
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| 108 | |
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| 109 | ! identify the indexes of the tracers we'll need |
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| 110 | g_co2=igcm_co2 |
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| 111 | if (g_co2.eq.0) then |
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| 112 | write(*,*) "moldiff: Error; no CO2 tracer !!!" |
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| 113 | stop |
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| 114 | endif |
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| 115 | g_co=igcm_co |
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| 116 | if (g_co.eq.0) then |
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| 117 | write(*,*) "moldiff: Error; no CO tracer !!!" |
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| 118 | stop |
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| 119 | endif |
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| 120 | g_o=igcm_o |
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| 121 | if (g_o.eq.0) then |
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| 122 | write(*,*) "moldiff: Error; no O tracer !!!" |
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| 123 | stop |
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| 124 | endif |
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| 125 | g_o1d=igcm_o1d |
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| 126 | if (g_o1d.eq.0) then |
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| 127 | write(*,*) "moldiff: Error; no O1D tracer !!!" |
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| 128 | stop |
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| 129 | endif |
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| 130 | g_o2=igcm_o2 |
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| 131 | if (g_o2.eq.0) then |
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| 132 | write(*,*) "moldiff: Error; no O2 tracer !!!" |
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| 133 | stop |
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| 134 | endif |
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| 135 | g_o3=igcm_o3 |
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| 136 | if (g_o3.eq.0) then |
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| 137 | write(*,*) "moldiff: Error; no O3 tracer !!!" |
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| 138 | stop |
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| 139 | endif |
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| 140 | g_h=igcm_h |
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| 141 | if (g_h.eq.0) then |
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| 142 | write(*,*) "moldiff: Error; no H tracer !!!" |
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| 143 | stop |
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| 144 | endif |
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| 145 | g_h2=igcm_h2 |
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| 146 | if (g_h2.eq.0) then |
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| 147 | write(*,*) "moldiff: Error; no H2 tracer !!!" |
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| 148 | stop |
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| 149 | endif |
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| 150 | g_oh=igcm_oh |
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| 151 | if (g_oh.eq.0) then |
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| 152 | write(*,*) "moldiff: Error; no OH tracer !!!" |
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| 153 | stop |
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| 154 | endif |
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| 155 | g_ho2=igcm_ho2 |
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| 156 | if (g_ho2.eq.0) then |
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| 157 | write(*,*) "moldiff: Error; no HO2 tracer !!!" |
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| 158 | stop |
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| 159 | endif |
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| 160 | g_h2o2=igcm_h2o2 |
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| 161 | if (g_h2o2.eq.0) then |
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| 162 | write(*,*) "moldiff: Error; no H2O2 tracer !!!" |
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| 163 | stop |
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| 164 | endif |
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| 165 | g_n2=igcm_n2 |
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| 166 | if (g_n2.eq.0) then |
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| 167 | write(*,*) "moldiff: Error; no N2 tracer !!!" |
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| 168 | stop |
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| 169 | endif |
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| 170 | g_ar=igcm_ar |
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| 171 | if (g_ar.eq.0) then |
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| 172 | write(*,*) "moldiff: Error; no AR tracer !!!" |
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| 173 | stop |
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| 174 | endif |
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| 175 | g_h2o=igcm_h2o_vap |
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| 176 | if (g_h2o.eq.0) then |
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| 177 | write(*,*) "moldiff: Error; no water vapor tracer !!!" |
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| 178 | stop |
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| 179 | endif |
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| 180 | |
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| 181 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 182 | c fill array to relate local indexes to gcm indexes |
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| 183 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 184 | |
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| 185 | gcmind(i_co) = g_co |
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| 186 | gcmind(i_n2) = g_n2 |
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| 187 | gcmind(i_o2) = g_o2 |
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| 188 | gcmind(i_co2) = g_co2 |
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| 189 | gcmind(i_h2) = g_h2 |
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| 190 | gcmind(i_h) = g_h |
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| 191 | gcmind(i_oh) = g_oh |
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| 192 | gcmind(i_ho2) = g_ho2 |
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| 193 | gcmind(i_h2o) = g_h2o |
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| 194 | gcmind(i_h2o2) = g_h2o2 |
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| 195 | gcmind(i_o1d) = g_o1d |
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| 196 | gcmind(i_o3) = g_o3 |
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| 197 | gcmind(i_o) = g_o |
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| 198 | gcmind(i_ar) = g_ar |
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| 199 | |
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| 200 | firstcall= .false. |
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| 201 | endif ! of if (firstcall) |
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| 202 | |
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| 203 | |
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| 204 | |
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| 205 | c |
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| 206 | cccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 207 | |
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| 208 | nz=nlayermx |
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| 209 | |
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| 210 | do ig=1,ngridmx |
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| 211 | |
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| 212 | do l=2,nz-1 |
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| 213 | tt(l)=pt(ig,l)+pdt(ig,l)*ptimestep |
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| 214 | & +pdteuv(ig,l)*ptimestep |
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| 215 | & +pdtconduc(ig,l)*ptimestep |
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| 216 | |
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| 217 | do nn=1,ncomptot |
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| 218 | qq(l,nn)=pq(ig,l,gcmind(nn))+pdq(ig,l,gcmind(nn))*ptimestep |
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| 219 | qq(l,nn)=max(qq(l,nn),1.e-30) |
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| 220 | enddo |
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| 221 | hp(l)=-log(pplay(ig,l+1)/pplay(ig,l-1)) |
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| 222 | dmmeandz(l)=(mmean(ig,l+1)-mmean(ig,l-1))/hp(l) |
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| 223 | enddo |
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| 224 | |
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| 225 | tt(1)=pt(ig,1) +pdt(ig,1)*ptimestep |
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| 226 | & +pdteuv(ig,1)*ptimestep |
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| 227 | & +pdtconduc(ig,1)*ptimestep |
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| 228 | tt(nz)=pt(ig,nz)+pdt(ig,nz)*ptimestep |
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| 229 | & +pdteuv(ig,nz)*ptimestep |
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| 230 | & +pdtconduc(ig,nz)*ptimestep |
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| 231 | |
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| 232 | do nn=1,ncomptot |
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| 233 | qq(1,nn)=pq(ig,1,gcmind(nn))+pdq(ig,1,gcmind(nn))*ptimestep |
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| 234 | qq(nz,nn)=pq(ig,nz,gcmind(nn))+pdq(ig,nz,gcmind(nn))*ptimestep |
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| 235 | qq(1,nn)=max(qq(1,nn),1.e-30) |
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| 236 | qq(nz,nn)=max(qq(nz,nn),1.e-30) |
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| 237 | enddo |
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| 238 | hp(1)=-log(pplay(ig,2)/pplay(ig,1)) |
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| 239 | dmmeandz(1)=(-3.*mmean(ig,1)+4.*mmean(ig,2) |
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| 240 | & -mmean(ig,3))/(2.*hp(1)) |
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| 241 | hp(nz)=-log(pplay(ig,nz)/pplay(ig,nz-1)) |
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| 242 | dmmeandz(nz)=(3.*mmean(ig,nz)-4.*mmean(ig,nz-1) |
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| 243 | & +mmean(ig,nz-2))/(2.*hp(nz)) |
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| 244 | c |
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| 245 | c Setting-up matrix of alfa coefficients from Dickinson and Ridley 1972 |
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| 246 | c |
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| 247 | do l=1,nz |
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| 248 | if(abs(dmmeandz(l)) .lt. 1.e-5) dmmeandz(l)=0.0 |
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| 249 | hh=rnew(ig,l)*tt(l)/g |
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| 250 | ptfac=(1.e5/pplay(ig,l))*(tt(l)/273)**1.75 |
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| 251 | ntot=pplay(ig,l)/(1.381e-23*tt(l)) ! in #/m3 |
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| 252 | |
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| 253 | do nn=1,ncomptot-1 ! rows |
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| 254 | alfdiag(nn)=0. |
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| 255 | dcoef1=dij(nn,i_o)*ptfac |
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| 256 | do n=1,ncomptot-1 ! columns |
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| 257 | y(nn,n)=0. |
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| 258 | dcoef=dij(nn,n)*ptfac |
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| 259 | alf(nn,n)=qq(l,nn)/ntot/1.66e-27 |
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| 260 | & *(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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| 261 | alfdiag(nn)=alfdiag(nn) |
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| 262 | & +(1./(mmol(gcmind(n))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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| 263 | & *qq(l,n) |
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| 264 | enddo |
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| 265 | dcoef=dij(nn,nn)*ptfac |
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| 266 | alfdiag(nn)=alfdiag(nn) |
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| 267 | & -(1./(mmol(gcmind(nn))*dcoef)-1./(mmol(g_o)*dcoef1)) |
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| 268 | & *qq(l,nn) |
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| 269 | alf(nn,nn)=-(alfdiag(nn) |
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| 270 | & +1./(mmol(g_o)*dcoef1))/ntot/1.66e-27 |
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| 271 | y(nn,nn)=1. |
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| 272 | b(l,nn)=-(dmmeandz(l)/mmean(ig,l) |
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| 273 | & +mmol(gcmind(nn))/mmean(ig,l)-1.) |
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| 274 | enddo |
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| 275 | |
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| 276 | c |
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| 277 | c Inverting the alfa matrix |
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| 278 | c |
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| 279 | call ludcmp(alf,ncomptot-1,ncomptot-1,indx,d,ierr) |
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| 280 | |
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| 281 | c TEMPORAIRE ***************************** |
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| 282 | if (ierr.ne.0) then |
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| 283 | write(*,*) 'In moldiff: Problem in LUDCMP with matrix alf' |
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| 284 | write(*,*) 'Singular matrix ?' |
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| 285 | c write(*,*) 'Matrix alf = ', alf |
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| 286 | write(*,*) 'ig, l=',ig, l |
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| 287 | write(*,*) 'No molecular diffusion this time !' |
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| 288 | call zerophys(ngridmx*nlayermx*nqmx,pdqdiff) |
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| 289 | return |
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| 290 | c stop |
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| 291 | end if |
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| 292 | c ******************************************* |
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| 293 | do n=1,ncomptot-1 |
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| 294 | call lubksb(alf,ncomptot-1,ncomptot-1,indx,y(1,n)) |
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| 295 | do nn=1,ncomptot-1 |
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| 296 | alfinv(l,nn,n)=y(nn,n)/hh |
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| 297 | enddo |
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| 298 | enddo |
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| 299 | enddo |
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| 300 | |
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| 301 | c |
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| 302 | c Calculating coefficients of the system |
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| 303 | c |
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| 304 | |
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| 305 | c zlocal(1)=-log(pplay(ig,1)/pplev(ig,1))* Rnew(ig,1)*tt(1)/g |
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| 306 | zlocal(1)=zzlay(ig,1) |
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| 307 | |
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| 308 | do l=2,nz-1 |
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| 309 | del1=hp(l)*pplay(ig,l)/(g*ptimestep) |
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| 310 | del2=(hp(l)/2)**2*pplay(ig,l)/(g*ptimestep) |
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| 311 | do nn=1,ncomptot-1 |
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| 312 | do n=1,ncomptot-1 |
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| 313 | dalfinvdz=(alfinv(l+1,nn,n)-alfinv(l-1,nn,n))/hp(l) |
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| 314 | aa(l,nn,n)=-dalfinvdz/del1+alfinv(l,nn,n)/del2 |
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| 315 | & +alfinv(l-1,nn,n)*b(l-1,n)/del1 |
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| 316 | bb(l,nn,n)=-2.*alfinv(l,nn,n)/del2 |
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| 317 | cc(l,nn,n)=dalfinvdz/del1+alfinv(l,nn,n)/del2 |
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| 318 | & -alfinv(l+1,nn,n)*b(l+1,n)/del1 |
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| 319 | enddo |
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| 320 | enddo |
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| 321 | |
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| 322 | c tmean=tt(l) |
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| 323 | c if(tt(l).ne.tt(l-1)) |
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| 324 | c & tmean=(tt(l)-tt(l-1))/log(tt(l)/tt(l-1)) |
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| 325 | c zlocal(l)= zlocal(l-1) |
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| 326 | c & -log(pplay(ig,l)/pplay(ig,l-1))*rnew(ig,l)*tmean/g |
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| 327 | zlocal(l)=zzlay(ig,l) |
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| 328 | enddo |
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| 329 | |
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| 330 | c zlocal(nz)= zlocal(nz-1) |
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| 331 | c & -log(pplay(ig,nz)/pplay(ig,nz-1))*rnew(ig,nz)*tmean/g |
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| 332 | zlocal(nz)=zzlay(ig,nz) |
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| 333 | |
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| 334 | ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 335 | c Escape velocity from Jeans equation for the flux of H and H2 |
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| 336 | c (Hunten 1973, eq. 5) |
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| 337 | |
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| 338 | do n=1,ncomptot |
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| 339 | wi(n)=1. |
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| 340 | flux(n)=0. |
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| 341 | abfac(n)=1. |
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| 342 | enddo |
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| 343 | |
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| 344 | dens=pplay(ig,nz)/(rnew(ig,nz)*tt(nz)) |
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| 345 | c |
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| 346 | c For H: |
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| 347 | c |
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| 348 | pote=(3398000.+zlocal(nz))/ |
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| 349 | & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h)*g)) |
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| 350 | wi(i_h)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h))) |
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| 351 | & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) |
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| 352 | flux(i_h)=qq(nz,i_h)*dens/(1.6605e-27*mmol(g_h))*wi(i_h) |
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| 353 | flux(i_h)=flux(i_h)*1.6606e-27 |
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| 354 | abfac(i_h)=0. |
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| 355 | c |
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| 356 | c For H2: |
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| 357 | c |
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| 358 | pote=(3398000.+zlocal(nz))/ |
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| 359 | & (1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2)*g)) |
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| 360 | wi(i_h2)=sqrt(2.*1.381e-23*tt(nz)/(1.6605e-27*mmol(g_h2))) |
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| 361 | & /(2.*sqrt(3.1415))*(1.+pote)*exp(-pote) |
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| 362 | flux(i_h2)=qq(nz,i_h2)*dens/(1.6605e-27*mmol(g_h2))*wi(i_h2) |
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| 363 | flux(i_h2)=flux(i_h2)*1.6606e-27 |
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| 364 | abfac(i_h2)=0. |
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| 365 | |
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| 366 | c ********* TEMPORAIRE : no escape for h and h2 |
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| 367 | c do n=1,ncomptot |
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| 368 | c wi(n)=1. |
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| 369 | c flux(n)=0. |
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| 370 | c abfac(n)=1. |
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| 371 | c enddo |
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| 372 | c ******************************************** |
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| 373 | |
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| 374 | |
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| 375 | ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
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| 376 | |
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| 377 | c |
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| 378 | c Setting coefficients for tridiagonal matrix and solving the system |
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| 379 | c |
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| 380 | |
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| 381 | do nn=1,ncomptot-1 |
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| 382 | do l=2,nz-1 |
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| 383 | atri(l-1)=aa(l,nn,nn) |
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| 384 | btri(l-1)=bb(l,nn,nn)+1. |
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| 385 | ctri(l-1)=cc(l,nn,nn) |
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| 386 | rtri(l-1)=qq(l,nn) |
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| 387 | do n=1,ncomptot-1 |
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| 388 | rtri(l-1)=rtri(l-1)-(aa(l,nn,n)*qq(l-1,n) |
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| 389 | & +bb(l,nn,n)*qq(l,n) |
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| 390 | & +cc(l,nn,n)*qq(l+1,n)) |
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| 391 | enddo |
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| 392 | rtri(l-1)=rtri(l-1)+(aa(l,nn,nn)*qq(l-1,nn) |
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| 393 | & +bb(l,nn,nn)*qq(l,nn) |
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| 394 | & +cc(l,nn,nn)*qq(l+1,nn)) |
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| 395 | enddo |
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| 396 | |
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| 397 | c |
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| 398 | c Boundary conditions: |
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| 399 | c Escape flux for H and H2 at top |
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| 400 | c Diffusive equilibrium for the other species at top |
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| 401 | c Perfect mixing for all at bottom |
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| 402 | c |
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| 403 | |
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| 404 | rtri(nz-2)=rtri(nz-2) |
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| 405 | & -ctri(nz-2)*flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) |
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| 406 | |
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| 407 | atri(nz-2)=atri(nz-2) |
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| 408 | & -abfac(nn)*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) |
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| 409 | btri(nz-2)=btri(nz-2) |
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| 410 | & +abfac(nn)*4.*ctri(nz-2)/(3.-2.*hp(nz)*b(nz,nn)) |
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| 411 | |
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| 412 | c rtri(1)=rtri(1)-atri(1)*qq(1,nn) |
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| 413 | btri(1)=btri(1)+atri(1) |
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| 414 | |
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| 415 | call tridag(atri,btri,ctri,rtri,qtri,nz-2) |
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| 416 | |
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| 417 | do l=2,nz-1 |
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| 418 | c qnew(l,nn)=qtri(l-1) |
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| 419 | qnew(l,nn)=max(qtri(l-1),1.e-30) |
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| 420 | enddo |
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| 421 | |
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| 422 | qnew(nz,nn)=flux(nn)*mmol(gcmind(nn))/(dens*wi(nn)) |
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| 423 | & +abfac(nn)*(4.*qnew(nz-1,nn)-qnew(nz-2,nn)) |
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| 424 | & /(3.-2.*hp(nz)*b(nz,nn)) |
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| 425 | c qnew(1,nn)=qq(1,nn) |
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| 426 | qnew(1,nn)=qnew(2,nn) |
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| 427 | |
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| 428 | qnew(nz,nn)=max(qnew(nz,nn),1.e-30) |
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| 429 | qnew(1,nn)=max(qnew(1,nn),1.e-30) |
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| 430 | |
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| 431 | enddo ! loop on species |
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| 432 | |
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| 433 | DO l=1,nz |
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| 434 | if(zlocal(l).gt.65000.)then |
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| 435 | pdqdiff(ig,l,g_o)=0. |
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| 436 | do n=1,ncomptot-1 |
|---|
| 437 | pdqdiff(ig,l,gcmind(n))=(qnew(l,n)-qq(l,n)) |
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| 438 | pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)-(qnew(l,n)-qq(l,n)) |
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| 439 | pdqdiff(ig,l,gcmind(n))=pdqdiff(ig,l,gcmind(n))/ptimestep |
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| 440 | enddo |
|---|
| 441 | pdqdiff(ig,l,g_o)=pdqdiff(ig,l,g_o)/ptimestep |
|---|
| 442 | endif |
|---|
| 443 | ENDDO |
|---|
| 444 | |
|---|
| 445 | c do l=2,nz |
|---|
| 446 | c do n=1,ncomptot-1 |
|---|
| 447 | c hco2(n)=qnew(l,n)*pplay(ig,l)/(rnew(ig,l)*tt(l)) / |
|---|
| 448 | c & (qnew(l-1,n)*pplay(ig,l-1)/(rnew(ig,l-1)*tt(l-1))) |
|---|
| 449 | c hco2(n)=-(zlocal(l)-zlocal(l-1))/log(hco2(n))/1000. |
|---|
| 450 | c enddo |
|---|
| 451 | c write(225,*),l,pt(1,l),(hco2(n),n=1,6) |
|---|
| 452 | c write(226,*),l,pt(1,l),(hco2(n),n=7,12) |
|---|
| 453 | c enddo |
|---|
| 454 | |
|---|
| 455 | enddo ! ig loop |
|---|
| 456 | |
|---|
| 457 | return |
|---|
| 458 | end |
|---|
| 459 | |
|---|
| 460 | c ******************************************************************** |
|---|
| 461 | c ******************************************************************** |
|---|
| 462 | c ******************************************************************** |
|---|
| 463 | |
|---|
| 464 | subroutine tridag(a,b,c,r,u,n) |
|---|
| 465 | parameter (nmax=100) |
|---|
| 466 | c dimension gam(nmax),a(n),b(n),c(n),r(n),u(n) |
|---|
| 467 | real gam(nmax),a(n),b(n),c(n),r(n),u(n) |
|---|
| 468 | if(b(1).eq.0.)then |
|---|
| 469 | stop 'tridag: error: b(1)=0 !!! ' |
|---|
| 470 | endif |
|---|
| 471 | bet=b(1) |
|---|
| 472 | u(1)=r(1)/bet |
|---|
| 473 | do 11 j=2,n |
|---|
| 474 | gam(j)=c(j-1)/bet |
|---|
| 475 | bet=b(j)-a(j)*gam(j) |
|---|
| 476 | if(bet.eq.0.) then |
|---|
| 477 | stop 'tridag: error: bet=0 !!! ' |
|---|
| 478 | endif |
|---|
| 479 | u(j)=(r(j)-a(j)*u(j-1))/bet |
|---|
| 480 | 11 continue |
|---|
| 481 | do 12 j=n-1,1,-1 |
|---|
| 482 | u(j)=u(j)-gam(j+1)*u(j+1) |
|---|
| 483 | 12 continue |
|---|
| 484 | return |
|---|
| 485 | end |
|---|
| 486 | |
|---|
| 487 | c ******************************************************************** |
|---|
| 488 | c ******************************************************************** |
|---|
| 489 | c ******************************************************************** |
|---|
| 490 | |
|---|
| 491 | SUBROUTINE LUBKSB(A,N,NP,INDX,B) |
|---|
| 492 | |
|---|
| 493 | implicit none |
|---|
| 494 | |
|---|
| 495 | integer i,j,n,np,ii,ll |
|---|
| 496 | real sum |
|---|
| 497 | real a(np,np),indx(np),b(np) |
|---|
| 498 | |
|---|
| 499 | c DIMENSION A(NP,NP),INDX(N),B(N) |
|---|
| 500 | II=0 |
|---|
| 501 | DO 12 I=1,N |
|---|
| 502 | LL=INDX(I) |
|---|
| 503 | SUM=B(LL) |
|---|
| 504 | B(LL)=B(I) |
|---|
| 505 | IF (II.NE.0)THEN |
|---|
| 506 | DO 11 J=II,I-1 |
|---|
| 507 | SUM=SUM-A(I,J)*B(J) |
|---|
| 508 | 11 CONTINUE |
|---|
| 509 | ELSE IF (SUM.NE.0.) THEN |
|---|
| 510 | II=I |
|---|
| 511 | ENDIF |
|---|
| 512 | B(I)=SUM |
|---|
| 513 | 12 CONTINUE |
|---|
| 514 | DO 14 I=N,1,-1 |
|---|
| 515 | SUM=B(I) |
|---|
| 516 | IF(I.LT.N)THEN |
|---|
| 517 | DO 13 J=I+1,N |
|---|
| 518 | SUM=SUM-A(I,J)*B(J) |
|---|
| 519 | 13 CONTINUE |
|---|
| 520 | ENDIF |
|---|
| 521 | B(I)=SUM/A(I,I) |
|---|
| 522 | 14 CONTINUE |
|---|
| 523 | RETURN |
|---|
| 524 | END |
|---|
| 525 | |
|---|
| 526 | c ******************************************************************** |
|---|
| 527 | c ******************************************************************** |
|---|
| 528 | c ******************************************************************** |
|---|
| 529 | |
|---|
| 530 | SUBROUTINE LUDCMP(A,N,NP,INDX,D,ierr) |
|---|
| 531 | |
|---|
| 532 | implicit none |
|---|
| 533 | |
|---|
| 534 | integer n,np,nmax,i,j,k,imax |
|---|
| 535 | real d,tiny,aamax |
|---|
| 536 | real a(np,np),indx(np) |
|---|
| 537 | integer ierr ! error =0 if OK, =1 if problem |
|---|
| 538 | |
|---|
| 539 | PARAMETER (NMAX=100,TINY=1.0E-20) |
|---|
| 540 | c DIMENSION A(NP,NP),INDX(N),VV(NMAX) |
|---|
| 541 | real sum,vv(nmax),dum |
|---|
| 542 | |
|---|
| 543 | D=1. |
|---|
| 544 | DO 12 I=1,N |
|---|
| 545 | AAMAX=0. |
|---|
| 546 | DO 11 J=1,N |
|---|
| 547 | IF (ABS(A(I,J)).GT.AAMAX) AAMAX=ABS(A(I,J)) |
|---|
| 548 | 11 CONTINUE |
|---|
| 549 | IF (AAMAX.EQ.0.) then |
|---|
| 550 | write(*,*) 'In moldiff: Problem in LUDCMP with matrix A' |
|---|
| 551 | write(*,*) 'Singular matrix ?' |
|---|
| 552 | c write(*,*) 'Matrix A = ', A |
|---|
| 553 | c TO DEBUG : |
|---|
| 554 | ierr =1 |
|---|
| 555 | return |
|---|
| 556 | c stop |
|---|
| 557 | END IF |
|---|
| 558 | |
|---|
| 559 | VV(I)=1./AAMAX |
|---|
| 560 | 12 CONTINUE |
|---|
| 561 | DO 19 J=1,N |
|---|
| 562 | IF (J.GT.1) THEN |
|---|
| 563 | DO 14 I=1,J-1 |
|---|
| 564 | SUM=A(I,J) |
|---|
| 565 | IF (I.GT.1)THEN |
|---|
| 566 | DO 13 K=1,I-1 |
|---|
| 567 | SUM=SUM-A(I,K)*A(K,J) |
|---|
| 568 | 13 CONTINUE |
|---|
| 569 | A(I,J)=SUM |
|---|
| 570 | ENDIF |
|---|
| 571 | 14 CONTINUE |
|---|
| 572 | ENDIF |
|---|
| 573 | AAMAX=0. |
|---|
| 574 | DO 16 I=J,N |
|---|
| 575 | SUM=A(I,J) |
|---|
| 576 | IF (J.GT.1)THEN |
|---|
| 577 | DO 15 K=1,J-1 |
|---|
| 578 | SUM=SUM-A(I,K)*A(K,J) |
|---|
| 579 | 15 CONTINUE |
|---|
| 580 | A(I,J)=SUM |
|---|
| 581 | ENDIF |
|---|
| 582 | DUM=VV(I)*ABS(SUM) |
|---|
| 583 | IF (DUM.GE.AAMAX) THEN |
|---|
| 584 | IMAX=I |
|---|
| 585 | AAMAX=DUM |
|---|
| 586 | ENDIF |
|---|
| 587 | 16 CONTINUE |
|---|
| 588 | IF (J.NE.IMAX)THEN |
|---|
| 589 | DO 17 K=1,N |
|---|
| 590 | DUM=A(IMAX,K) |
|---|
| 591 | A(IMAX,K)=A(J,K) |
|---|
| 592 | A(J,K)=DUM |
|---|
| 593 | 17 CONTINUE |
|---|
| 594 | D=-D |
|---|
| 595 | VV(IMAX)=VV(J) |
|---|
| 596 | ENDIF |
|---|
| 597 | INDX(J)=IMAX |
|---|
| 598 | IF(J.NE.N)THEN |
|---|
| 599 | IF(A(J,J).EQ.0.)A(J,J)=TINY |
|---|
| 600 | DUM=1./A(J,J) |
|---|
| 601 | DO 18 I=J+1,N |
|---|
| 602 | A(I,J)=A(I,J)*DUM |
|---|
| 603 | 18 CONTINUE |
|---|
| 604 | ENDIF |
|---|
| 605 | 19 CONTINUE |
|---|
| 606 | IF(A(N,N).EQ.0.)A(N,N)=TINY |
|---|
| 607 | ierr =0 |
|---|
| 608 | RETURN |
|---|
| 609 | END |
|---|
| 610 | |
|---|
