[Getdp] ... integral in cylindrical coordinates ...

[Matt Koch]

Hi All,

I am trying to calculate the simple average temperature over a disk,  
in cylindrical coordinates, as follows:

Tave = {int(0 to R) 2*pi*r*T(r)*dr}/{pi*R^2} on Surface Sfc

The question is, what does "Integral" do in a cylindrical geometry?  
Does it automatically account for the 2*pi*r factor in the integral,  
or do I have to explicitly provide that? If I have to provide it, do I  
use XS or X?

So far, I have the following (slightly simplified, with some loss of  
physical consistency):

Function {
   Ftr[Sfc] = 2.0*Pi*$XS/(Pi*Rds^2); // with SurAxi, user provides 2*pi*r
   Ftr[Sfc] = 1.0/(Pi*Rds^2);        // with SurAxi, GetDP provides 2*pi*r
////  Ftr[Sfc] = 1.0/Rds; // with Sur
}

Jacobian {
   {Name Jac;
     Case {
       {Region Sfc; Jacobian SurAxi;}
       {Region Vlm; Jacobian VolAxi;}
////      {Region Sfc; Jacobian Sur;}
////      {Region Vlm; Jacobian Vol;}
     }
   }
}

Formulation {
   {Name Frm; Type FemEquation;
   Quantity {
     {Name Tmp;    Type Local; NameOfSpace Spc;}
     {Name TmpAve; Type Integral; [Ftr[]*Dof{Tmp}]; In Sfc;  
Integration Int; Jacobian Jac;}
   }
   Equation {
     Galerkin { [ TheCon[]*Dof{d Tmp   },{d Tmp} ]; In Vlm;  
Integration Int; Jacobian Jac;}
     Galerkin { [ HTC[]   *Dof{  Tmp   },{  Tmp} ]; In Sfc;  
Integration Int; Jacobian Jac;}
     Galerkin { [-HTC[]   *Dof{  TmpAve},{  Tmp} ]; In Sfc;  
Integration Int; Jacobian Jac;}
   }
}

The reason I am asking is that with Sur and Ftr[Sfc] = 1.0/Rds, I get  
perfectly reasonable results - this obviously simulates a rectangular  
geometry. However, with SurAxi, i.e. cylindrical geometry, and either  
of the other two Ftr[Sfc], nothing makes sense. Is integration in  
cylindrical coordinates implemented properly? Any thoughts on the  
above would be appreciated.

Thanks and Regards,

Matt Koch