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$$$$ ECHI     NOTICE  CHAT      11/09/12    21:15:59     7124           
                                             DATE     11/09/12
$X ECHI (Operateur de discretisation)

  Operateur ECHI                          Voir aussi :

     Syntaxe EQEX (cf EQEX) :

     ... 'EQEX' ... 'OPTI' MOT1 MOT2
                    'ZONE' MOD2
                    'OPER' 'ECHI' OBJ1 OBJ2
                    'INCO' MOT3 (MOT4)




     Description :
     _____________

     ECHI operator treat volumic or surfacic mass or energy (or any
other scalar quantity) exchange between the meshed domain and the
outside domain.

     For a scalar equation dealing with the evolution of an unknown
named T, the exchange term is of the form h(T-To) where h is the
exchange coefficient (per unit time and per unit surface or volume),
T the unknown on which the exchange acts (primal unknown), To the
outside data.

     For a system the exchange term is of the generalised form h(T-U)
in a scalar equation dealing with the evolution of an unknown named V.
T is the unknown on which the exchange acts (primal unknown), U the
outside data and V the dual unknown.

     Sign convention is the following: when the flux is greater than
zero (h>0 and T>To (resp T>U)) the quantity T (resp. V) in the meshed
domain decreases.

     Transient procedures EXEC and EXIC use this operator with data
constructed with EQEX operator with the syntax done.


     Contents :
     __________
                                                                                
    'OPTI' : Key word introducing numerical options
     MOT1  : Discretization in space ('EF', 'VF' or 'EFM1')
     MOT2  : Discretization in time ('EXPL' or 'IMPL')
     By default, EFM1 and EXPL are assumed.

    'ZONE' : Key word introducing geometric informations
     MOD2  : MODEL of subtype 'NAVIER_STOKES' associated to the
             region where ECHI works.

    'OPER' : Key word introducing operator's name and physical data
    'ECHI' : Operator's name treated by EQEX
     OBJ1  : Exchange coefficient h (CHPOINT SCAL CENTRE or FLOTTANT
             or MOT)
     OBJ2  : Outside data U (CHPOINT SCAL CENTRE or CHPOINT SCAL
             SOMMET or FLOTTANT or MOT)

    'INCO' : Key word introducing primal and dual unknowns' name
     MOT3  : Primal unknown's name (T)
     MOT4  : Dual unknown's name (V)

     When primal and dual names are the same, only one is mandatory.
     Note that dual and primal unknowns are always the same when
     explicit formulation is used.

     When explicit formulation is used, mass matrix is lumped and
     so treated implicitely. With this treatment, no new constraint
     is set on the time step.


     Remarks :
     ___________
                                                                                
     1) When OBJ1 or OBJ2 are of type MOT, we look for data in INCO
table at the index OBJ1 or OBJ2.

     2) Geometric support (spg) of CHPOINT is one of those contained
in the table of subtype DOMAINE. Some compatibilities are verified :
   - For EF or EFM1 formulation, dual unknown's spg is SOMMET
   - For VF formulation, dual unknown's spg is CENTRE
   - In implicit formulation, when primal and dual unknowns are not
     the same, primal unknown's spg is CENTRE or SOMMET
   - Exchange coefficient spg is CENTRE or SOMMET for EF or EFM1
     formulation and only CENTRE for VF formulation

     3) EF, EFM1 et VF formulations are available in explicit and
implicit. In explicit, EF is treated as EFM1 ; in implicit EFM1 as EF.

     4) The kind of element present in the mesh (index MAILLAGE of
DOMAINE table) indicates if the exchange is volumic or surfacic :
   - Surface exchange if
        in 2D, element type is SEG2 or SEG3,
        in 3D, element type is TRI3, QUA4, TRI6, TRI7 or QUA9. 
   - Volume exchange if
        in 2D, element type is TRI3, QUA4, TRI6, TRI7 or QUA9. 
        in 3D, element type is  CUB8, PRI6, TET4,
                                CU27, PR21, TE15,
                                PR18 or TE10.
   - SEG2 or SEG3 type element are not authorized in 3D
   - In 3D, PYR5 element are not available

     5) When surface exchange is considered, faces will be at the
boundary of the meshed domain.

     6) Graduate user who develops his own transient procedure calls
the ECHI operator with the following syntax :
  B A =  ECHI TAB1 ;
with TAB1 : Table of subtype EQEX ; contains physical and numerical
            informations ; created by the EQEX operator.
     A    : the mass matrix (diagonal if EXPL), stored in a MATRIK
     B    : the tight hand side, stored in a CHPO. CHPO component's 
            name of the dual unknown contribution is MOT4.