[Getdp] How to calculate a numerical quantity with GetDP ?

[Olivier Castany]

Hello,

after I have solved a problem with GetDP, I would like to compute some 
numerical quantities with GetDP

1) is it possible ?

For example, if I've got a field {T}, how can I do the following :

2) calculate the flux "- lambda[] * {d T}" throught a surface S of 
   the mesh

3) calculate the same flux, but through a surface of the _dual_ mesh,
   close to a surface S of the mesh (how can one define such a 
   surface in GetDP ?)

4) calculate the average temperature on a surface S

Following is a sample file for which I would like to compute the 
above-mentioned quantities. The surfaces of interest could be 
surfaces SA and SV.

And a last question (not related to the former) :

5) In the problem I solved, I need to write "Support Region [{D,SA}]" in 
the FunctionSpace. Simply writing "Support D" yields irrelevant results.
However, all the nodes of SA are nodes of D. 
Could somebody explain why I need to do that ? What exaclty is this 
"Support group-def" ? Isn't it the set of nodes in the "group-def" ?

Have a nice day,

Olivier C.

-------------------
barre.geo :

/*
Metal rod
*/

lc_ext = 0.03;

rayon = 0.05;
longueur = 0.5;

Point(1) = {0,0,0,1};// longueur caractéristique du centre sans utilité
Point(2) = {rayon,0,0,lc_ext};
Point(3) = {-rayon,0,0,lc_ext};
Point(4) = {0,-rayon,0,lc_ext};
Point(5) = {0,rayon,0,lc_ext};

Circle(1) = {2,1,5};
Circle(2) = {5,1,3};
Circle(3) = {3,1,4};
Circle(4) = {4,1,2};

Line Loop(5) = {1,2,3,4};
Plane Surface(6) = {5};

Extrude {0,0,longueur} {
  Surface{6}; Layers{ 30,1 }; Recombine;
}

Physical Surface(31) = {6};
Physical Surface(32) = {27,15,19,23,28};
Physical Volume(33) = {1};

/* Remark : gmsh statistics show :

Geometry : 24 lines... it should be : 12 
Mesh : 296 nodes on lines...   it should be : 132
       400 nodes on surfaces... it should be : 260
*/

-------------
barre.pro :

/*
Temperature in a metal rod : 

- the temperature is imposed at one end (surface SV) 
- convection happens on all other surfaces (surface SA) (j.n = h(T - 
T_ext))
- conduction of heat in the material (volume D) (j = - lambda Grad(T))
- equilibrium situation (Div(j)=0) 
*/

Group{
D = Region[33];// Entire volume 
SV = Region[31];// Surface with imposed temperature
SA = Region[32];// Other surfaces with air convection
}


Function {
h[] = 30.;// Wm-2K-1 (strong natural air convection)
lambda[] = 20.;// Wm-1K-1 (some highly allied steel)
T_ext[] = 30.;// °C      (air temperature)
}


// Temperature imposed on surface SV :200°C
Constraint {
{ Name temperature_sur_SV ; Type Assign;
  Case {
    { Region SV ; Value 200. ; }
  }
  }
}

FunctionSpace {
{ Name temperature_dans_barre ; Type Form0 ;
  BasisFunction {
  { Name w_n ; NameOfCoef T_n ; Function BF_Node ;
  Support Region [{D,SA}] ; Entity NodesOf[ All ] ; }
  }
  Constraint {
  { NameOfCoef T_n ; EntityType NodesOf ; 
  NameOfConstraint temperature_sur_SV ; }
  }
}
}

Jacobian {
  { Name JVol ;
    Case { 
      { Region All ; Jacobian Vol ; }
    }
  }
  { Name JSur ;
    Case { 
      { Region All ; Jacobian Sur ; }
    }
  }
}

Integration {
  { Name I ;
    Case { 
      { Type Gauss ;
        Case { 
  { GeoElement Point       ; NumberOfPoints  1 ; }
          { GeoElement Line        ; NumberOfPoints  3 ; }
          { GeoElement Triangle    ; NumberOfPoints  4 ; }
          { GeoElement Quadrangle  ; NumberOfPoints  4 ; }
          { GeoElement Tetrahedron ; NumberOfPoints  4 ; }
          { GeoElement Hexahedron  ; NumberOfPoints  6 ; }
          { GeoElement Prism       ; NumberOfPoints  6 ; } 
        }
      }
    }
  }
}

/****************** Integral formulation to solve :
find T such that :

\int_D lambda Grad(T).Grad(T') + \int_SA h (T - T_ext) T' = 0
holds for all T' with T' = 0 on SV
******************************************/

Formulation {
  { Name formulation_du_probleme ; Type FemEquation ;
    Quantity { 
      { Name T ; Type Local ; NameOfSpace temperature_dans_barre ; }
    }
    Equation {
      Galerkin { [ lambda[] * Dof{d T} , {d T} ] ;  
                 In D ; Jacobian JVol ; Integration I ; }

      Galerkin { [ h[] *  Dof{T} , {T} ] ;
                 In SA ; Jacobian JSur ; Integration I ; }

      Galerkin { [ -h[] * T_ext[] , {T} ] ;
                 In SA ; Jacobian JSur ; Integration I ; }
 
    }
  }
}

Resolution {
  { Name resolution_du_probleme ;
    System {
      { Name A ; NameOfFormulation formulation_du_probleme ; }
    }
    Operation { 
      Generate[A] ; Solve[A] ; SaveSolution[A] ; 
    }
  }
}

PostProcessing {
  { Name post_processing ; NameOfFormulation formulation_du_probleme ;
    Quantity {
      { Name T; Value { Local { [ {T} ] ; In SA ; Jacobian JSur ; }}}
    }
  }
}

PostOperation {
  { Name post_operations ; NameOfPostProcessing post_processing;
    Operation {
      Print[ T, OnElementsOf SA, File "T.pos"] ;
    }
  }
}

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