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* fichier :  cavitefmm.dgibi
************************************************************************
************************************************************************
*************************************************************************
* CAVITE CARRE A PAROI DEFILANTE                                        *
* Methode implicite sans matrice pour les equations de                  *
* Navier-Stokes (bas Mach)                                              *
*                                                                       *
* BECCANTINI A., SFME/LTMF,  DEC 2003                                   *
*                                                                       *
*************************************************************************
*
* The real file starts after the procedure PNSSM
*
*************************************************************************
*************************************************************************
*********** SOLUTION OF THE NAVIER-STOKES EQUATIONS  ********************
*********** FMM                                      ********************
*************************************************************************
*************************************************************************
*
* RVX . 'RESULTS'         : table containing the results
*
* RVX . 'FREQI'           : frequency of presenting the results
*
* RVX . 'MODEL'           : model object
* RVX . 'RN0'             : density
* RVX . 'GN0'             : qdm
* RVX . 'RET0'            : total energy
*
* RVX . 'PGAS'            : table containing the gas model 
* RVX . 'PGAS' . 'GAMN'   : gamma
* RVX . 'PGAS' . 'MU'     : dynamic viscosity (kg/m^3 x m^2/s)
* RVX . 'PGAS' . 'LAMBDA' : heat diffusion (W/K/m)
* 
*
* RVX . 'GRAVITY'         : gravity
*
* RVX . 'LISTCONS'        : name of the conservative variables
* RVX . 'LISTPRIM'        : name of the primitive variables
*
* RVX . 'LISTERR'         : name of the error variables
*
* RVX . 'METHOD'          : numerical scheme
* RVX . 'CUTOFF'          : cut off speed
*
* RVX . 'SPACEA'          : space accuracy
* RVX . 'LIMITER'         : limiter type
* RVX . 'TIMEA'           : time accuracy
* 
* RVX . 'T0'              : initial time
* RVX . 'TFINAL'          : final time
* RVX . 'DTPS' ('CFL')    : time step or CFL number
*
* RVX . 'DCFL'            : CFL number for dual time
*
*                          Error criteria for dual time loop:
* RVX . 'NDTITER'         : number of iterations
* RVX . 'RELERR'          : Logical (Relative error or absolute error)
* RVX . 'EPSDT'           : error at which dual time iterations are stopped
*
* RVX . 'NJAC'            : Jacobi iterations
*
* RVX . 'PROLIM'          : table called by the procedure PROLIM,
*                           procedure to compute boundary conditions
*
* RVX . 'DIFTIMP'         : boundary condition on temperature
* RVX . 'DIFGTIMP'        : boundary condition on gradient of temperature
* RVX . 'DIFVIMP'         : boundary condition on speed
* RVX . 'DIFGVIMP'        : boundary condition on gradient of speed
* RVX . 'DIFTAUI'         : boundary condition on constraint tensor
* RVX . 'DIFQIMP'         : boundary condition on heat flux
* 
*
 
 'DEBPROC' PNSSM ;
 'ARGUMENT' RVX*TABLE ;
*
*
 'SI' ('EXISTE' RVX 'RESULTS') ;
    'MESS' 'Table RESULTS already exists' ;
 'SINON' ;
    RVX . 'RESULTS' = 'TABLE' ;
    RVX . 'RESULTS' . 'TPS' = RVX . 'T0' ;
    RVX . 'RESULTS' . 'RN'  = 'COPIER' (RVX . 'RN0') ;
    RVX . 'RESULTS' . 'GN'  = 'COPIER' (RVX . 'GN0') ;
    RVX . 'RESULTS' . 'RET' = 'COPIER' (RVX . 'RET0') ;
    RVX . 'RESULTS' . 'LISTLINF' = 'PROG' ;
    RVX . 'RESULTS' . 'LISTITDT' = 'LECT' ;
    RVX . 'RESULTS' . 'LISTITER' = 'LECT' ;
    RVX . 'RESULTS' . 'NITER' = 0 ;
 'FINSI' ;
 
 MDOMINT = RVX . 'MODEL' ;
 NELT = 'NBEL' ('DOMA' MDOMINT 'CENTRE') ;
*
***** Physical properties
*
 GAMN = RVX . 'PGAS' . 'GAMN' ;
 GAMSCA1 = 'MAXIMUM' GAMN ;
 GAMSCA2 = 'MINIMUM' GAMN ;
 'SI' ('EGA' GAMSCA2 GAMSCA1 0.0001) ;
    GAMSCAL = GAMSCA1 ;
 'SINON' ;
    'MESSAGE' ;
    'MESSAGE' 'Gamma is not constant' ;
    'ERREUR' 21 ;
 'FINSI' ;
* 
 MU    = (RVX . 'PGAS' . 'MU') ;
 LAMBDA = (RVX . 'PGAS' . 'LAMBDA') ;
 R     = (RVX . 'PGAS' . 'R') ;
 CV    = R '/' (gamscal '-' 1.) ; 
 
* 
 LISTINCO = RVX . 'LISTCONS' ;
 LISTPRIM = RVX . 'LISTPRIM' ;
 LISTERR  = RVX . 'LISTERR'  ;
* Names of the gradient of temperature
 LMGTEMP = 'MOTS' 'P1DX' 'P1DY' ;
* Names of the gradient of speed
 LMGVIT = 'MOTS' 'P1DX' 'P1DY' 'P2DX' 'P2DY' ;
 
*  
* Upwind scheme
*
 METO = RVX . 'METHOD' ;
 
* Space accuracy (1 or 2) and limiter
* Time accuracy (1 or 2)
 
 ORDESP  = RVX . 'SPACEA' ;
 TYPELIM = RVX . 'LIMITER' ;
 ORDTPS  = RVX . 'TIMEA' ;
 
* Initial/final time
* Deltat or CFL
 TPS     = RVX . 'RESULTS' . 'TPS' ;
 TFINAL  = RVX . 'TFINAL' ;
 'SI' ('EXISTE' RVX 'DTPS') ;
    'SI' ('EXISTE' RVX 'CFL') ;
        'MESSAGE' 'DTPS or CFL ???' ;
        'ERREUR' 21 ;
    'FINSI' ;
    DTPS = RVX . 'DTPS' ;
 'SINON' ;
    CFL = RVX . 'CFL' ;
 'FINSI' ;
 
* Dual time iterations
 NDT = RVX . 'NDTITER' ;
* Relative error 
 EPSDT = RVX . 'EPSDT' ;
* Jacobi iterations
* NJAC = RVX . 'NJAC' ;
* Cut off speed
 ICO = RVX . 'CUTOFF' ;
* To compute the diffusive cut-off
 DELTAX = 'DOMA' MDOMINT 'XXDIEMIN' ;
 USDELTAX = 'INVERSE' DELTAX ;
*
**** Conservative variables
*
*
 MOT1 = 'EXTRAIRE' LISTINCO 1 ;
 'SI' ('EGA' ('VALE' 'DIME') 2) ;
    NOMMOM = 'EXTRAIRE' LISTINCO
       ('LECT' 2 3 ) ;
    NOMVEL = 'MOTS' 'UX' 'UY' ;
    MOT2 = 'EXTRAIRE' LISTINCO 4 ;
 'SINON' ;
    NOMMOM = 'EXTRAIRE' LISTINCO
      ('LECT' 2 3 4) ;
    NOMVEL = 'MOTS' 'UX' 'UY' 'UZ' ;
    MOT2 = 'EXTRAIRE' LISTINCO 5 ;
 'FINSI' ;
 
 RN0   = 'REDU' (RVX . 'RESULTS' . 'RN')  ('DOMA' MDOMINT 'CENTRE') ;
 GN0   = 'REDU' (RVX . 'RESULTS' . 'GN')  ('DOMA' MDOMINT 'CENTRE') ;
 RET0  = 'REDU' (RVX . 'RESULTS' . 'RET') ('DOMA' MDOMINT 'CENTRE') ;
*
**** Primitive variables
*
 VN0 PN0 = 'PRIM' 'PERFMONO' RN0 GN0 RET0 GAMN ;
 TN0 = PN0 '/' (R '*' RN0) ;
 
 MOTRN = 'EXTRAIRE' LISTPRIM 1 ;
 'SI' ('EGA' ('VALE' 'DIME') 2) ;
    MOTVN = 'EXTRAIRE' LISTPRIM
       ('LECT' 2 3 ) ;
    MOTPN = 'EXTRAIRE' LISTPRIM 4 ;
 'SINON' ;
    MOTVN = 'EXTRAIRE' LISTPRIM
       ('LECT' 2 3 4) ;
    MOTPN = 'EXTRAIRE' LISTPRIM 5 ;
 'FINSI' ;
*
**** Coeff to compute gradients for convective term (MCHSCA, MCHVEC)
*    Boundary conditions have to be taken into account
*
 RCHLIM RESLIM = PROLIM (RVX . 'PROLIM') MDOMINT LISTINCO LISTPRIM
    RN0 VN0 PN0 GAMN  ;
 
 MAILLIM = 'EXTRAIRE' RCHLIM 'MAILLAGE' ;
 
 'SI' (MAILLIM 'EGA' 0) ;
    CHPVID PIPI = 'KOPS' 'MATRIK' ;
    MAILLIM = 'DIFF' ('DOMA' MDOMINT 'CENTRE')
                     ('DOMA' MDOMINT 'CENTRE') ;
    GRADRN ALRN MCHSCA = 'PENT' MDOMINT 'CENTRE' 'EULESCAL' 'NOLIMITE'
      ('MOTS' 'SCAL') RN0 ;
    GRADVN ALVN MCHVEC = 'PENT' MDOMINT 'CENTRE' 'EULEVECT' 'NOLIMITE'
      NOMVEL GN0 'CLIM' (RVX . 'DIFVIMP') ;
 'SINON' ;
    SCALBC = 'MANUEL' 'CHPO' MAILLIM 1 'SCAL' 1.0 ;
    'SI' (('VALEUR' 'DIME') 'EGA' 2) ; 
        VECTBC = 'MANUEL' 'CHPO' MAILLIM
            'NATURE' 'DISCRET' 2 'UX' 0.0 'UY' 0.0 ;
*       Same name as NOMVEL            
    'SINON' ;
        VECTBC = 'MANUEL' 'CHPO' MAILLIM
            'NATURE' 'DISCRET' 3 'UX' 0.0 'UY' 0.0 'UZ' ;
    'FINSI' ;
    VECTBC = VECTBC 'ET' (RVX . 'DIFVIMP') ;
* 
    GRADRN ALRN MCHSCA = 'PENT' MDOMINT 'CENTRE' 'EULESCAL' 'NOLIMITE'
      ('MOTS' 'SCAL') RN0 'CLIM' SCALBC ;
 
    GRADVN ALVN MCHVEC = 'PENT' MDOMINT 'CENTRE' 'EULEVECT' 'NOLIMITE'
       NOMVEL VN0 'CLIM' VECTBC ;
 
 'FINSI' ;
 
*
*** Coeff to compute gradient for diffusive flux
*
 
 GRADTN MCHDIT = 'PENT' MDOMINT 'FACE' 'DIAMAN2' ('MOTS' 'SCAL')
          LMGTEMP TN0  (RVX . 'DIFTIMP') (RVX . 'DIFGTIMP') ;
 GRADVN MCHDIV = 'PENT' MDOMINT 'FACE' 'DIAMAN2' NOMVEL LMGVIT 
          VN0 (RVX . 'DIFVIMP') (RVX . 'DIFGVIMP') ;
 NOMVEL = 'MOTS' 'UX' 'UY' ;
*
*
*** After each dual time loop, we could display
*   the evolution of the error in the dual time loop
*   the evolution of the dual time step (the safety factor)
*
 
 LISTLINF = RVX . 'RESULTS' . 'LISTLINF' ;
 LISTITDT = RVX . 'RESULTS' . 'LISTITDT' ; 
 LISTITER = RVX . 'RESULTS' . 'LISTITER' ;
 
*  
 
 'MESSAGE' ;
 'MESSAGE' ('CHAINE' 'Methode = ' METO) ;
 'MESSAGE' ;
 
 'TEMPS' 'ZERO' ;
 
************************************************************************
************************************************************************
**** Temporal loop *****************************************************
************************************************************************
************************************************************************
 
 RN_N1M1  = 'COPIER' RN0 ;
 GN_N1M1  = 'COPIER' GN0 ;
 RET_N1M1 = 'COPIER' RET0 ;
 
 AA = 'DIME' LISTITER ;
 'SI' (AA > 0) ;
    PTITER = 'EXTRAIRE' LISTITER AA ;
 'SINON' ;
    PTITER = 0 ;
 'FINSI' ;
 
 DUSDT = 0.0D0 ;
 
 'REPETER' BLITER -1 ;
 
    PTITER = PTITER '+' 1 ;
*
**** Personal procedure
*
    PROCPT RVX ;
*
*
****  _N1M  = (t^n,\tau^m)
*     _N1M1 = (t^n,\tau^{m+1})
*
*
************************************************************************
****** Loop on dual time***********************************************
************************************************************************
*
*
*** DUSDT0 is the increment of DUSDT in the previous (physical) time
*   iteration.
*
    DUSDT0 = DUSDT ;
    DUSDT = 0.0D0 ;
 
    'REPETER' BLDT NDT ;
 
       RN_N1M  = RN_N1M1 ;
       GN_N1M  = GN_N1M1 ;
       RET_N1M = RET_N1M1 ;
*
**** Primitive variables
*
 
       VN_N1M PN_N1M = 'PRIM' 'PERFMONO' RN_N1M GN_N1M RET_N1M GAMN ;
*
*** Boundary conditions
*
 
       RCHLIM RESLIM = PROLIM (RVX . 'PROLIM') MDOMINT LISTINCO LISTPRIM
           RN_N1M VN_N1M PN_N1M GAMN  ;
 
*    
****** First/second order reconstruction
*
       'SI' (ORDESP 'EGA' 2) ;
*
          NNLIM = 'NBNO' MAILLIM ;
          'SI' (NNLIM 'EGA' 0) ;
             RNLIM = CHPVID ;
             PNLIM = CHPVID ;
             VNLIM = RVX . 'DIFVIMP' ;
          'SINON' ;
             RNLIM = ('EXCO' MOTRN RCHLIM 'SCAL') ;
             PNLIM = ('EXCO' MOTPN RCHLIM 'SCAL') ;
             VNLIM = ('EXCO' MOTVN RCHLIM MOTVN)
                     'ET'  (RVX . 'DIFVIMP') ;
          'FINSI' ;
          GRADRN ALRN0  = 'PENT' MDOMINT 'CENTRE' 'EULESCAL' TYPELIM
              ('MOTS' 'SCAL')  RN_N1M
             'CLIM' RNLIM 'GRADGEO' MCHSCA ;
          GRADPN ALPN0  = 'PENT' MDOMINT 'CENTRE' 'EULESCAL' TYPELIM
              ('MOTS' 'SCAL')  PN_N1M
             'CLIM' PNLIM 'GRADGEO' MCHSCA ;
          GRADVN ALVN0  = 'PENT' MDOMINT 'CENTRE' 'EULEVECT' TYPELIM
              ('MOTS' 'UX' 'UY') VN_N1M
             'CLIM' VNLIM  'GRADGEO' MCHVEC ;
 
*          'SI' (&BLDT < NLCB) ;
*              ALRN0  =  'COPIER' ALRN ;
*              ALPN0  =  'COPIER' ALPN ;
*              ALVN0  =  'COPIER' ALVN ;
*          'SINON' ;
*             'SI' (&BLDT 'EGA' NLCB) ;
*                'MESSAGE' ;
*                'MESSAGE' 'On gele les limiteurs!!!' ;
*                'MESSAGE' ;
*             'FINSI' ;
*          'FINSI' ;
 
          ROF VITF PF GAMF = 'PRET' 'PERFMONO'  2 1 
                              MDOMINT
                              RN_N1M  GRADRN ALRN0 
                              VN_N1M  GRADVN ALVN0  
                              PN_N1M   GRADPN ALPN0  
                              GAMN  ;
       'SINON' ;
          ROF VITF PF GAMF = 'PRET' 'PERFMONO'  1 1 
                              MDOMINT
                              RN_N1M VN_N1M PN_N1M GAMN  ;
       'FINSI' ;
 
       RESIDU DELTAT =  'KONV' 'VF' 'PERFMONO' 'RESI' METO
            MDOMINT LISTINCO  ROF VITF PF GAMF MAILLIM 
            ICO (MU '*' ('INVERSE' RN_N1M) '*' USDELTAX) ;
*            ICO ICO ;
       RESIDU = RESIDU '+' RESLIM ;
 
*
**** La gravite
*
 
       RESGRA = 'FIMP' 'VF' 'GRAVMONO' 'RESI' LISTINCO
                 RN_N1M GN_N1M1 (RVX . 'GRAVITY') ;
 
       RESIDU = RESIDU '+' RESGRA ;
*       
**************************************
**** Diffusive terms *****************
**************************************
*
      TN_N1M = PN_N1M '/' (R '*' RN_N1M) ;
*
      GRADTN = 'PENT' MDOMINT 'FACE' 'DIAMAN2' ('MOTS' 'SCAL')
          LMGTEMP TN_N1M  (RVX . 'DIFTIMP') (RVX . 'DIFGTIMP') 
          'GRADGEO' MCHDIT ;
 
      GRADVN = 'PENT' MDOMINT 'FACE' 'DIAMAN2' NOMVEL LMGVIT 
          VN_N1M (RVX . 'DIFVIMP') (RVX . 'DIFGVIMP') 
          'GRADGEO' MCHDIV ;
      NOMVEL = 'MOTS' 'UX' 'UY' ;
 
*
      ICACCA RESIDI DTCACCA = 'LAPN' 'VF' 'PROPCOST' 'RESI' 'EXPL'
          MDOMINT  MU LAMBDA CV RN_N1M VN_N1M TN_N1M GRADVN  GRADTN
          LISTINCO 'VIMP'  (RVX . 'DIFVIMP')  'TAUI' (RVX . 'DIFTAUI')
         'QIMP' (RVX . 'DIFQIMP')  ;
 
       RESIDU = RESIDU '+' RESIDI ;
       COEFV = (0.0 '*' RN_N1M) '+' 1.0 ;
       COEFV = COEFV '*' (lambda '*' (gamscal '-' 1.)) ;
       COEFV = COEFV '/' (R '*' RN_N1M) ;
*       'MESSAGE' ;
*       'MESSAGE' 'Je fais n importe' ;
*       COEFV = COEFV '*' 0.25 ;
*
****** Residuum for dual tims stepping also involved the
*      variation of the conserved variables with respect
*      to time
 
       'SI' ((&BLITER 'EGA' 1) 'OU' (ORDTPS 'EGA' 1)) ;
           RESIDU = RESIDU '-' DUSDT ;
       'SINON' ;
           RESIDU = RESIDU '-' ((1.5 '*' DUSDT) '-' (0.5 '*' DUSDT0)) ;
       'FINSI' ;
 
*
*** Time step at the first iteration/jacobi iteration
*
 
       'SI' (&BLDT 'EGA' 1) ;
          'SI' ('EXISTE' RVX 'CFL') ;
             DTPS = (RVX . 'CFL') '*' 2.0D0 '*' DELTAT ;
          'SINON' ;
             DTPS = RVX . 'DTPS' ;
          'FINSI' ;
          DTPS = 'MINIMUM' ('PROG' DTPS ((TFINAL '-' TPS) '*' 1.001)) ;
          TPS = TPS '+' DTPS ;
*
          NJAC = 'ENTIER' ('MINIMUM' (RVX . 'NJACITER')) ;
          NJAC0 = NJAC ;
       'SINON' ;
          NJAC = 'IPOL' (('LOG' ERRINF) '/' ('LOG' 10))
                 (RVX . 'NJACLERR') (RVX . 'NJACITER') ;
          NJAC = 'MAXIMUM' ('PROG' NJAC0 NJAC) ;
          NJAC = 'ENTIER' NJAC ;
          NJAC0 = NJAC ;
       'FINSI' ;
 
*
*** JACOBI
*   
 
*
**** CFL dual
*
         'SI' (&BLDT 'EGA' 1) ;
             SAFFACD = ('MINIMUM' (RVX . 'DCFL')) '*' 2 ;
         'SINON' ;
             SAFFACD = ('IPOL' (('LOG' ERRINF) '/' ('LOG' 10))
                 (RVX . 'DCFLERR') (RVX . 'DCFL')) '*' 2 ;
         'FINSI' ;
 
          'SI' ((&BLITER 'EGA' 1) 'OU' (ORDTPS 'EGA' 1)) ;
*              DUN IPRO = 'DETO'  (RVX . 'TYPEJAC')
              DUN IPRO = 'KONV' 'VF' 'PMON1FMM'  (RVX . 'TYPEJAC')
                 LISTINCO MDOMINT  RESIDU RN_N1M GN_N1M RET_N1M GAMN ICO
                 DTPS SAFFACD
                 NJAC 'CLIM' LISTPRIM RCHLIM COEFV ;
          'SINON' ;
*              DUN IPRO = 'DETO'  (RVX . 'TYPEJAC')
              DUN IPRO = 'KONV' 'VF' 'PMON1FMM'  (RVX . 'TYPEJAC') 
                 LISTINCO MDOMINT  RESIDU RN_N1M GN_N1M RET_N1M GAMN ICO
                 (DTPS '/' 1.5)
                 SAFFACD NJAC 'CLIM' LISTPRIM RCHLIM COEFV ;
          'FINSI' ;
*       'FINSI' ;
 
       'SI' (IPRO 'NEG' 0) ;
          'MESSAGE' ;
          'MESSAGE' 'Probleme dans FMM' ;
          'MESSAGE' ;
          'ERREUR' 21 ;
       'FINSI' ;
 
*
**** We compute DUSDT for the future loop
*
 
       DUSDT = DUSDT '+' (DUN '/' DTPS) ;
 
*
**** We evaluate the conservative variables at t^{n+1}, \tau^{m+1}
*
 
       DRN = 'EXCO' MOT1 DUN 'SCAL' ;
       DGN = 'EXCO' NOMMOM DUN NOMVEL ;
       DRET = 'EXCO' MOT2 DUN 'SCAL' ;
 
       RN_N1M1   = RN_N1M '+' DRN ;
       GN_N1M1   = GN_N1M '+' DGN ;
       RET_N1M1  = RET_N1M '+' DRET ;
 
       ERRINF =  'MAXIMUM' DUN 'ABS' LISTERR ;
       LISTLINF = LISTLINF 'ET' ('PROG' ERRINF) ;
       LISTITDT = LISTITDT 'ET' ('LECT'  &BLDT) ;
       LISTITER = LISTITER 'ET' ('LECT' PTITER) ;
 
       'SI' ((&BLDT 'EGA' 1) 'OU'
             (((&BLDT '/' (RVX . 'FREQI')) '*' (RVX . 'FREQI'))
              'EGA' &BLDT)) ;
          'MESSAGE' ;
          'MESSAGE'
          ('CHAINE' 'ITER =' PTITER ' TPS =' TPS
           ' DTITER ='  &BLDT  ' LINF =' ERRINF
           ' DCFL =' SAFFACD ' NJAC =' NJAC) ;
          'MESSAGE' ;
       'FINSI' ;
*
*
*** Update of RVX . 'RESULTS'
*
       RVX . 'RESULTS' . 'RN'   = RN_N1M1 ;
       RVX . 'RESULTS' . 'GN'   = GN_N1M1 ;
       RVX . 'RESULTS' . 'RET'  = RET_N1M1 ;
       RVX . 'RESULTS' . 'LISTLINF' = LISTLINF ;
       RVX . 'RESULTS' . 'LISTITDT' = LISTITDT ;
       RVX . 'RESULTS' . 'LISTITER' = LISTITER ;
*
       'SI' (RVX . 'RELERR') ;
*         Relative error       
          'SI' (&BLDT 'EGA' 1) ;
             ERRINF0 = ERRINF ;
          'SINON' ;
             'SI' (ERRINF < (EPSDT '*' ERRINF0)) ;
                'QUITTER' BLDT ;
             'FINSI' ;
          'FINSI' ;
       'SINON' ;
          'SI' (ERRINF < EPSDT) ;
             'QUITTER' BLDT ;
          'FINSI' ;
       'FINSI' ;
 
 
    'FIN' BLDT ;
 
************************************************************************
****** End of the loop on dual time*************************************
************************************************************************
*
*** Update of RVX . 'RESULTS'
*
    RVX . 'RESULTS' . 'TPS' = TPS ;
    RVX . 'RESULTS' . 'NITER' = (RVX . 'RESULTS' . 'NITER') '+' 1 ;
*
    'SI' (TPS '>EG' TFINAL) ;
       'QUITTER' BLITER ;
    'FINSI' ;
 
 'FIN' BLITER ;
 
 TCPU = 'TEMPS' 'NOEC' ;
 RVX . 'RESULTS' . 'TCPU' = TCPU ;
 
 'FINPROC' ;
 
*************************************************************************
*************************************************************************
*************************************************************************
*************************************************************************
 
 'OPTION'  'DIME' 2
           'ELEM' 'QUA4'
           'ISOV' 'LIGN'
           'TRAC' 'PSC'
           'ECHO' 1
           ;
 
 LOGTRI = VRAI ;
* GRAPH = VRAI ;
  GRAPH = FAUX ;
 
*******************************
**** MESH     *****************
******************************* 
 
 RAF = 8 ;
 
 L = 1 ;
 H = L ;
 
 DENINI = (L '/' (8. '*' RAF)) ;
 DENCEN = 8 '*' DENINI ;
 
 A1 = 0.0 0.0 ;
 A12 = (L '/' 2.) 0.0 ;
 A2 = L 0.0 ;
 A23 = L  (H '/' 2.0) ;
 A3 = L H ;
 A34 = (L '/' 2.0)  H ;
 A4 = 0.0 H ;
 A41 = 0.0  (H '/' 2.0) ;
 
 A1A2 = (A1 'DROIT' A12 'DINI' DENINI 'DFIN' DENCEN) 'ET'
        (A12 'DROIT' A2 'DINI' DENCEN 'DFIN' DENINI);
 A2A3 = (A2 'DROIT' A23 'DINI' DENINI 'DFIN' DENCEN) 'ET'
        (A23 'DROIT' A3 'DINI' DENCEN 'DFIN' DENINI);
 A3A4 = (A3 'DROIT' A34 'DINI' DENINI 'DFIN' DENCEN) 'ET'
        (A34 'DROIT' A4 'DINI' DENCEN 'DFIN' DENINI);
 A4A1 = (A4 'DROIT' A41 'DINI' DENINI 'DFIN' DENCEN) 'ET'
        (A41 'DROIT' A1 'DINI' DENCEN 'DFIN' DENINI);
 
 DOMINT = 'DALLER' A1A2 A2A3 A3A4 A4A1 'PLAN' ;
 
 'SI' LOGTRI ;
    'OPTION' 'ELEM' 'TRI3' ;
    DOMINT = 'SURFACE' ( A1A2 'ET' A2A3 'ET' A3A4 'ET' A4A1 ) 'PLAN' ;
 'FINSI' ;
 
 MDOMINT = 'MODELISER' DOMINT 'EULER' ;
 MA1A2   = 'MODELISER' A1A2 'EULER' ;
 MA2A3   = 'MODELISER' A2A3 'EULER' ;
 MA3A4   = 'MODELISER' A3A4 'EULER' ;
 MA4A1   = 'MODELISER' A4A1 'EULER' ;
 
 $DOMINT = 'DOMA' MDOMINT 'VF' ;
 $A1A2 = 'DOMA' MA1A2 'VF' ;
 $A2A3 = 'DOMA' MA2A3 'VF' ;
 $A3A4 = 'DOMA' MA3A4 'VF' ;
 $A4A1 = 'DOMA' MA4A1 'VF' ;
 
 QDOMINT = 'DOMA' MDOMINT 'QUAF' ;
 QA1A2 = 'DOMA' MA1A2 'QUAF' ;
 QA2A3 = 'DOMA' MA2A3 'QUAF' ;
 QA3A4 = 'DOMA' MA3A4 'QUAF' ;
 QA4A1 = 'DOMA' MA4A1 'QUAF' ;
 
 'ELIMINATION' QDOMINT (DENINI '/' 100) QA1A2 ;
 'ELIMINATION' QDOMINT (DENINI '/' 100) QA2A3 ;
 'ELIMINATION' QDOMINT (DENINI '/' 100) QA3A4 ;
 'ELIMINATION' QDOMINT (DENINI '/' 100) QA4A1 ;
 
 'SI' GRAPH ;
    'TRACER' DOMINT 'TITRE' ('CHAINE' 'NBEL =' ('NBEL' DOMINT)) ;
 'FINSI' ;
 
***************************************
******** PHYSICAL PARAMETERS  *********
***************************************
 
 gamscal = 1.4 ;
 RAIR = 288. ;
*
 ro_0 = 1.0 ;
 p_0 = 1.0D5 ;
 ret_0 = (1. '/' (gamscal '-' 1.)) '*' p_0 ;
 CSON = (gamscal * p_0 '/' ro_0) '**' 0.5 ;
*
 VParois = 0.01 '*' cson ;
*
 Rey = 1000 ;
 mu = (ro_0 '*' L '*' VParois) '/' Rey ;  
*
 Pr = 0.72 ;
* lambda = mu * cp '/' pr ;
 lambda = mu '*' (gamscal '*' RAIR '/' (gamscal '-' 1.0))
   '/' Pr ;
 
***************************************
**** INITIAL CONDITIONS ***************
***************************************
 
*
*  A4     ->     A3
*
*  
*               
*
*  A1            A2
*
 
 GAMN =  'KCHT'  $DOMINT 'SCAL' 'CENTRE' gamscal ;
 
 
 RN0  = 'KCHT'  $DOMINT 'SCAL' 'CENTRE' ro_0 ;
 GN0  = 'KCHT'  $DOMINT 'VECT' 'CENTRE' ((ro_0 '*' 0) 0.0) ;
 RETN0 = 'KCHT'  $DOMINT 'SCAL' 'CENTRE' (ret_0) ;
 
 VN0 PN0 =   'PRIM' 'PERFMONO'
           RN0 GN0 RETN0 GAMN  ;
 
 TN0 = PN0 '/' (Rair '*' RN0) ;
 
 CHPVID CACCA = 'KOPS' MATRIK ;
* Conditions aux bords
 
 VLIM =  ('MANUEL' 'CHPO' ($A3A4 . 'CENTRE') 2 'UX' Vparois 'UY' 0.0
          'NATU' 'DISCRET' ) 'ET'
         ('MANUEL' 'CHPO' (($A4A1 . 'CENTRE') 'ET'
          ($A1A2 . 'CENTRE') 'ET' ($A2A3 . 'CENTRE'))
          2 'UX' 0.0 'UY' 0.0 'NATU' 'DISCRET') ;
 GRADVLIM = CHPVID ;
 TAULIM = 'COPIER' CHPVID ;
* 
 TLIM =  CHPVID ;
 GRADTLIM = 'MANUEL' 'CHPO' (($A3A4 . 'CENTRE') 'ET' ($A4A1 . 'CENTRE')
        'ET' ($A1A2 . 'CENTRE') 'ET' ($A2A3 . 'CENTRE'))
        2 'P1DX' 0.0 'P1DY' 0.0 'NATU' 'DISCRET' ;
 
 QLIM =  'MANUEL' 'CHPO' (($A3A4 . 'CENTRE') 'ET' ($A4A1 . 'CENTRE')
        'ET' ($A1A2 . 'CENTRE') 'ET' ($A2A3 . 'CENTRE'))
      2 'UX' 0.0 'UY' 0.0 'NATU' 'DISCRET' ;
 
*
***** Pictures of the initial conditions
*
 MOD1     =  'MODELISER'  ($DOMINT . 'MAILLAGE') 'THERMIQUE' ;
 'SI' GRAPH ;
    CELL = 'VALEUR' 'ISOV' ;
    'OPTION' 'ISOV' 'SULI' ; 
*
    CHM_RN   =  'KCHA' MDOMINT 'CHAM' RN0 ;
    CHM_PN   =  'KCHA' MDOMINT 'CHAM' PN0 ;
    CHM_TN   =  'KCHA' MDOMINT 'CHAM' TN0 ;
    CHM_VN   =  'KCHA' MDOMINT 'CHAM' VN0 ;
    TRAC CHM_RN  MOD1 'TITR'  ('CHAINE'  'RO at t=' 0.0);
    TRAC CHM_PN  MOD1 'TITR'  ('CHAINE'  'P at t=' 0.0);
    TRAC CHM_TN  MOD1 'TITR'  ('CHAINE'  'T at t=' 0.0);
    TRAC CHM_VN  MOD1 'TITR'  ('CHAINE'  'VN at t=' 0.0);
*
    'OPTION' 'ISOV' CELL ;
 'FINSI' ;
 
* Names of conserved variables
 
 NOMDEN = 'MOTS' 'RN' ;
 NOMMOM = 'MOTS' 'RUX' 'RUY' ;
 NOMRET = 'MOTS' 'RETN' ;
 NOMVEL = 'MOTS' 'UX' 'UY' ;
 NOMPRE = 'MOTS' 'NOMPRE' ;
 LISTCONS = NOMDEN 'ET' NOMMOM 'ET' NOMRET ;
 LISTP    = NOMDEN 'ET' NOMVEL 'ET' NOMPRE ;
 
 UNCONS = ('NOMC' ('MOTS' 'SCAL') NOMDEN  RN0 'NATU' 'DISCRET') 'ET'
    ('NOMC' NOMVEL GN0 NOMMOM 'NATU' 'DISCRET') 'ET'
    ('NOMC' ('MOTS' 'SCAL')  RETN0 NOMRET 'NATU' 'DISCRET') ; 
 
*************************************************************************
*************************************************************************
*************************************************************************
*************************************************************************
************   COMPUTATION OF THE SOLUTION  *****************************
*************************************************************************
*************************************************************************
*************************************************************************
*************************************************************************
 
*************************************************************************
******PROCEDURE PROCPT **************************************************
*************************************************************************
*
*
 'DEBPROC' PROCPT ;
 'FINPROC' ;
*
 
*************************************************************************
******PROCEDURE PROLIM **************************************************
*************************************************************************
*
 'DEBPROC' PROLIM ;
 'ARGUMENT' RVX*'TABLE' MDOMINT*'MMODEL' LISTINCO*'LISTMOTS'
            LISTPRIM*'LISTMOTS'
            RN*'CHPOINT' VN*'CHPOINT' PN*'CHPOINT' GAMN*'CHPOINT' ;
*
*** Boundary conditions
*    
 CHPVID PIPI = 'KOPS' MATRIK ;
* 'RESPRO' RCHLIM RESLIM ;
 'RESPRO' CHPVID CHPVID ;
 'FINPROC' ;
 
*************************************************************************
****** FIN PROCEDURE PROLIM *********************************************
*************************************************************************
*
 RV = 'TABLE' ;
 RV . 'FREQI' = 1 ;
 RV . 'MODEL' = MDOMINT ;
*
**** Conservative variables / primitive variables
*
*
 RV . 'LISTCONS' = LISTCONS ;
 RV . 'LISTPRIM' = LISTP ;
*
 RV . 'RN0' = RN0 ;
 RV . 'GN0' = GN0 ;
 RV . 'RET0' = RETN0 ;
*
**** Gas property/gravity
*
 RV . 'PGAS' = 'TABLE' ;
 RV . 'PGAS' . 'GAMN' = GAMN ;
 RV . 'PGAS' . 'MU'   = mu ;
 RV . 'PGAS' . 'R'    =  Rair ;
 RV . 'PGAS' . 'LAMBDA' = lambda ;
*                        
 RV . 'GRAVITY' = 'MANUEL' 'CHPO' ('DOMA' MDOMINT 'CENTRE') 2 'UX' 0.0
                  'UY' 0.0 ;
*
* Table for BC (convective flux)
*
 RV . 'PROLIM' = 'TABLE' ;
*
* BC (diffusive flux)
*
* RVX . 'DIFTIMP'         : boundary condition on temperature
* RVX . 'DIFGTIMP'        : boundary condition on gradient of temperature
* RVX . 'DIFVIMP'         : boundary condition on speed
* RVX . 'DIFGVIMP'        : boundary condition on gradient of speed
* RVX . 'DIFTAUI'         : boundary condition on constraint tensor
* RVX . 'DIFQIMP'         : boundary condition on heat flux
*
* 
 RV . 'DIFTIMP'  = TLIM  ;
 RV . 'DIFGTIMP' = GRADTLIM ;
 RV . 'DIFQIMP' = QLIM ;
 RV . 'DIFVIMP' = VLIM ;
 RV . 'DIFGVIMP' = GRADVLIM ;
 RV . 'DIFTAUI' = TAULIM ;
 
* GRADTF MCHTNF = 'PENT' MDOMINT 'FACE' 'DIAMAN2' ('MOTS' 'SCAL')
*    ('MOTS' 'P1DX' 'P1DY') TN0  TLIM GRADTLIM ;
* GRADVF MCHVNF = 'PENT' MDOMINT 'FACE' 'DIAMAN2'  ('MOTS' 'UX' 'UY')
*   ('MOTS' 'P1DX' 'P1DY' 'P2DX' 'P2DY') VN0 VLIM TAULIM ;
* 
* ICACCA RESIDI DTCACCA = 'LAPN' 'VF' 'PROPCOST' 'RESI' 'EXPL'
*     MDOMINT  MU LAMBDA CV RN0 VN0 TN0 GRADVF  GRADTF
*     (RV . 'LISTCONS') 'VIMP'  (RV . 'DIFVIMP')  'TAUI' (RV . 'DIFTAUI')
*    'QIMP' (RV . 'DIFQIMP')  ;
 
 
*
**** Numerical parameters
*
*
* Variable to compute Linf error
*
 RV . 'LISTERR' = NOMMOM  ;
* RV . 'LISTERR' = NOMDEN ;
* RV . 'LISTERR' = NOMRET ;
*  
* Upwind scheme
*
 RV . 'METHOD' = 'RUSANOLM' ;
* RV . 'METHOD' = 'AUSMPLM' ;
 
*
**** Cut off
* We take a constant cutoff
*
  RV . 'CUTOFF' = 'MANUEL' 'CHPO' ('DOMA' MDOMINT 'CENTRE') 1
    'SCAL' Vparois ;
 
* Reconstruction/limiter
* Time accuracy (1 or 2)
* Iterations
* Final time
 RV . 'SPACEA' = 2 ;
 RV . 'LIMITER' = 'NOLIMITE' ;
* RV . 'LIMITER' = 'LIMITEUR' ;
 RV . 'TIMEA' = 1 ;
*
**** Phisical time
*
 RV . 'T0' = 0 ;
 RV . 'TFINAL' = 1.0D6 ;
 RV . 'CFL' = 1.0D16 ;
* RV . 'DTPS' = 1.0D16 ;  
*
**** Dual time
* 
*    Safety factor for the dual time step
*    Max. Dual time iterations
*    Absolute/relative error 
*
 RV . 'DCFLERR' = 'PROG' 16. -32. ;
 RV . 'DCFL'    = 'PROG' 1.0D1 1.0D1 ;
 RV . 'NDTITER' = 1000 ;
 RV . 'RELERR' = FAUX ;
 RV . 'EPSDT' = 1.0D-5 ;
**** Jacobi iterations
 RV . 'TYPEJAC' = 'PJACO' ;
* RV . 'TYPEJAC' = 'LJACOF' ;
* RV . 'TYPEJAC' = 'LJACOB' ;
* RV . 'TYPEJAC' = 'LJACOFB' ;
 RV . 'NJACITER' = 'PROG' 15    15 ;
 RV . 'NJACLERR' = 'PROG' 16.  -16 ;
*
**** Parameters for PROCPT
*
 'TEMPS' 'ZERO' ;
 PNSSM RV ;
* 'TEMPS' 'IMPR' ;
 
**********************************************************
**********************************************************
**********************************************************
************** PLOTS *************************************
**********************************************************
**********************************************************
**********************************************************
**********************************************************
 
 RN  = RV . 'RESULTS' . 'RN'  ;
 GN  = RV . 'RESULTS' . 'GN'  ;
 RET = RV . 'RESULTS' . 'RET' ;
 
 LISTITER = RV . 'RESULTS' . 'LISTITER' ;
 LISTITDT = RV . 'RESULTS' . 'LISTITDT' ;
 LISTLINF = RV . 'RESULTS' . 'LISTLINF' ;
 
*
*** Convergence evolution inside of each iteration
*
 
    NITERE = 'DIME' LISTITER ;
    I1 = 1 ;
    AA = 'PROG' ;
    BB = 'PROG' ;
    CC = 'PROG' ;
    'REPETER' BLITER NITERE ;
       I0 = I1 ;
       I1 = 'EXTRAIRE' LISTITER &BLITER ;
       'SI' (I1 'EGA' I0) ;
          AA = AA 'ET' ('PROG' ('EXTRAIRE' LISTITDT &BLITER)) ;
          BB = BB 'ET' ('PROG' ('EXTRAIRE' LISTLINF &BLITER)) ;
       'SINON' ;
          everr = 'EVOL' 'MANU' 'niter' AA 'Log(Linf)'
            (('LOG' (BB '+' ('PROG' ('DIME' BB) '*' 1.0D-20))) '/'
             ('LOG' 10.)) ;
          'SI' GRAPH ;
             'DESSIN' everr 'TITRE' ('CHAINE' 'Convergence at iter '
              (I1 '-' 1)) ;
          'FINSI' ;
          AA = 'PROG' ;
          BB = 'PROG' ;
       'FINSI' ;
    'FIN' BLITER ;
    everr = 'EVOL' 'MANU' 'niter' AA 'Log(Linf)'
            (('LOG' (BB '+' ('PROG' ('DIME' BB) '*' 1.0D-20))) '/'
             ('LOG' 10.)) ;
    'SI' GRAPH ;
       'DESSIN' everr 'TITRE' ('CHAINE' 'Convergence at iter '
          (I1)) ;
    'FINSI' ;
  'FINSI' ;
 
 
 
  VN PN = 'PRIM' 'PERFMONO' RN GN RET GAMN 'TRICHE' ;
  CN2 = GAMN '*' (PN '/' RN) ;
  VN2 = 'PSCAL' VN VN NOMVEL NOMVEL ;
  MACHN2 = VN2 '/' CN2 ;
  MACHN = MACHN2 '**' 0.5 ;
 
  HTN = (GAMN '/' (GAMN '-' 1.0)) '*' (PN '/' RN) ;
  ECIN = 0.5 '*' ('PSCAL' VN VN  NOMVEL NOMVEL) ;
  HTN = HTN '+' ECIN ;
 
  SN = PN '/' (RN '**' GAMSCAL) ;
 
  tps = RV . 'RESULTS' . 'TPS' ;
 
 'SI' GRAPH ;
 
    'OPTION' 'ISOV' 'SURF' ;
 
    CHM_RN  =  'KCHA'  MDOMINT  'CHAM'  RN  ;
    CHM_VN  =  'KCHA'  MDOMINT  'CHAM'  VN  ;
    CHM_PN  =  'KCHA'  MDOMINT  'CHAM'  PN  ;
    CHM_MN  =  'KCHA'  MDOMINT  'CHAM'  MACHN  ;
    CHM_HTN =  'KCHA'  MDOMINT  'CHAM'  HTN  ;
    CHM_SN  =  'KCHA'  MDOMINT  'CHAM'  SN  ;
 
    'TRAC' CHM_RN  MDOMINT ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'rho at t=' TPS)   ;
    'TRAC' CHM_VN  MDOMINT  ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'v at t= '  TPS)   ;
    'TRAC' CHM_PN  MDOMINT ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'p at t= '  TPS)   ;
    'TRAC' CHM_MN  MDOMINT ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'Mach at t= '  TPS)   ;
    'TRAC' CHM_HTN  MDOMINT ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'ht at t= '  TPS ' hl =' HTL) ;
    'TRAC' CHM_SN  MDOMINT ('CONTOUR' DOMINT)
       'TITR' ('CHAINE' 'sn at t= '  TPS ' hl =' SL) ;
 
*    'OPTION' 'ISOV' 'LIGN' ;
*    RNV = 'ELNO' $DOMINT ('KCHT' $DOMINT 'SCAL' 'CENTRE' RN) ;
*    'TRACER' DOMINT RNV ('CONTOUR' DOMINT) 15 'TITRE' 'ro';
*    PNV = 'ELNO' $DOMINT ('KCHT' $DOMINT 'SCAL' 'CENTRE' PN) ;
*    'TRACER' DOMINT PNV ('CONTOUR' DOMINT) 15 'TITRE' 'p' ;
*    MNV = 'ELNO' $DOMINT ('KCHT' $DOMINT 'SCAL' 'CENTRE' MACHN) ;
*    'TRACER' DOMINT MNV ('CONTOUR' DOMINT) 15 'TITRE' 'Mach' ;
*    RUX = 'EXCO' GN 'UX' ;
*    RUXV   =  'ELNO' $DOMINT ('REDU' RUX $DOMINT . 'CENTRE') ;
*    'TRACER' DOMINT RUXV ('CONTOUR' DOMINT) 15
*    'TITRE' 'rux' ;
 
    VECN = 'VECTEUR' VN ;
    'TRACER' VECN DOMINT ;
 
    MODVN = 'PSCAL' VN VN NOMVEL NOMVEL ;
    MODVN = MODVN '**' 0.5 ;
    MODVN = MODVN '+' (('MAXIMUM' MODVN) '*' 0.000001) ;
    VN1 = VN '/' MODVN ;
    VECN1 = 'VECTEUR' 0.01 VN1 'JAUNE' ;     
    'TRACER' DOMINT VECN1 ('CONTOUR' DOMINT)
       'TITRE' ('CHAINE' 'Normalized VN : ' TITOLO) ;
 'FINSI' ;
 
*
**** Evolution objects
*
 TAB1 = 'TABLE' ;
 TAB1 . 'TITRE'= 'TABLE' ;
 TAB1 . 1 = 'MARQ CROI NOLI';
 TAB1 . 'TITRE' . 1  = 'Reference (Su)' ;
 TAB1 . 2 = 'REGU' ;
 TAB1 . 'TITRE' . 2  = 'Numerical res.' ;
 
 LXSU = 'PROG' 0   0.0625  0.0703   0.0781  0.0938  0.1563  0.2266  
     0.2344   0.5  0.8047  0.8594   0.9063  0.9453  0.9531  0.9609  
     0.9688   1 ;
 LUY_X_SU = 'PROG' 0   0.2763  0.2918   0.3053  0.3282  0.3711  0.3279 
      0.3193   0.0243 -0.317 -0.4245 -0.5182 -0.3972 -0.3421 -0.2816 
      -0.2175   0 ;
 EV_UYX = 'EVOL' 'MANU' 'x' LXSU 'uy' LUY_X_SU ;
 
 LYSU = 'PROG' 0. 0.0547 0.0625 0.0703 0.1016 0.1719 0.2812 0.4531
     0.5  0.6172  0.7344  0.8516  0.9531  0.9609  0.9688  0.9766  1 ;
 LUX_Y_SU = 'PROG' 0 -0.1788 -0.1999 -0.2204 -0.2972 -0.3834  -0.2759   
    -0.1058 -0.0605 0.0564 0.1857 0.3316 0.466 0.5109 0.5743 0.6582 1 ;
 EV_UXY = 'EVOL' 'MANU' 'ux' LUX_Y_SU 'y' LYSU ;
 
 'OPTION' 'ELEM' 'QUA4' ;
 LISTX = 'PROG' 0.5 ;
 'REPETER' BL1 ('DIME' LISTX) ;
    XL  = 'EXTRAIRE' LISTX &BL1 ;
    YMIN = 'MINIMUM' ('COORDONNEE' 2 DOMINT) ;
    YMAX = 'MAXIMUM' ('COORDONNEE' 2 DOMINT) ;
    DELTAY = YMAX '-' YMIN ;
    PL1 = XL (YMIN '+' (1.0D-10 '*' DELTAY)) ;
    PL2 = XL 0.0 ;
    PL3 = XL (YMAX '-' (1.0D-10 '*' DELTAY)) ;
    LIG1 = (PL1 'DROIT' PL2 'DINI' DENINI 'DFIN' DENCEN)
      'ET' (PL2 'DROIT' PL3 'DINI' DENCEN 'DFIN' DENINI)  ;
    'SI' GRAPH ;
       'TRACER' (DOMINT 'ET' (LIG1 'COULEUR' 'ROUG')) 'TITR' 'lig1' ;
    'FINSI' ;
    UX = ('EXCO' 'UX' VN) '/' Vparois;
    UXV = 'ELNO' UX $DOMINT ;
    CH_UX = 'CHANGER' 'CHAM' UXV ('DOMA' MDOMINT 'MAILLAGE') ;
    UXLIG1 =  'PROI' CH_UX LIG1 ;
    EVUX  = 'EVOL' 'CHPO' UXLIG1  LIG1 ;
    EVUX1 = 'EVOL' 'MANU' 'ux' ('EXTRAIRE' EVUX 'ORDO') 'y'
         ('EXTRAIRE' EVUX 'ABSC') ;
    'SI' GRAPH ;
       'DESSIN' (EV_UXY 'ET' EVUX1) 'TITRE'
          ('CHAINE' 'Nondimensional ux at x = ' XL) 'LEGE' 
          TAB1 ;
    'FINSI' ;
 'FIN' BL1 ;
 
 'OPTION' 'ELEM' 'QUA4' ;
 LISTY = 'PROG' 0.5 ;
 'REPETER' BL1 ('DIME' LISTY) ;
    YL  = 'EXTRAIRE' LISTY &BL1 ;
    XMIN = 'MINIMUM' ('COORDONNEE' 2 DOMINT) ;
    XMAX = 'MAXIMUM' ('COORDONNEE' 2 DOMINT) ;
    DELTAX = XMAX '-' XMIN ;
    PL1 = (XMIN '+' (1.0D-10 '*' DELTAX)) YL;
    PL2 = 0.0 YL ;
    PL3 = (XMAX '-' (1.0D-10 '*' DELTAX)) YL ;
    LIG1 = (PL1 'DROIT' PL2 'DINI' DENINI 'DFIN' DENCEN)
      'ET' (PL2 'DROIT' PL3 'DINI' DENCEN 'DFIN' DENINI)  ;
    'SI' GRAPH ;
       'TRACER' (DOMINT 'ET' (LIG1 'COULEUR' 'ROUG')) 'TITR' 'lig1' ;
    'FINSI' ;
    UY = ('EXCO' 'UY' VN) '/' Vparois;
    UYV = 'ELNO' UY $DOMINT ;
    CH_UY = 'CHANGER' 'CHAM' UYV ('DOMA' MDOMINT 'MAILLAGE') ;
    UYLIG1 =  'PROI' CH_UY LIG1 ;
    EVUY  = 'EVOL' 'CHPO' UYLIG1  LIG1 ;
    'SI' GRAPH ;
       'DESSIN' (EV_UYX 'ET' EVUY)
       'TITRE' ('CHAINE' 'Nondimensional uy at y = ' YL)
       'LEGE' TAB1  ;
    'FINSI' ;
 'FIN' BL1 ;
 
* TEST
 
  LERR = 'EXTRAIRE' EVERR 'ORDO' ;
  AA = 10. '**' ('EXTRAIRE' LERR 1) ;
  BB = 10. '**' ('EXTRAIRE' LERR ('DIME' LERR)) ;
  'SI' ((BB '/' AA) '>' 1.0D-5) ;
      'ERREUR' 'Probleme de convergence' ;
  'FINSI' ;
  'FIN' ;
 
 
 
 
 
 
 
 

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