# [Getdp] Neumann boundary condition

Bernhard Kubicek bernhard.kubicek at arsenal.ac.at
Tue Mar 25 11:24:38 CET 2008

Honestly, I am kind of in a hurry at the moment, and could not catch the
complete nature of the problem. But in the ThermalProblem Wiki-Example,
http://geuz.org/getdp/wiki/ThermalProblem
there are Galerkin Terms for the Heatflow boundary condition (a constant
flow of heat on a physical surface).
This kind of helped me with my potential calculations that have a total
current as boundary condition.

Equation {
//Diffusion
Galerkin { [ k[] * Dof{d T} , {d T} ];
In Vol_The; Integration I1; Jacobian JVol;  }

//Time dependence
Galerkin { Dt [ rhoc[] * Dof{T} , {T} ];
In Vol_The; Integration I1; Jacobian JVol;  }
//Volumetric heat source
Galerkin { [ -qVol[] , {T} ];
In Vol_The; Integration I1; Jacobian JVol;  }

//constant Flow from a surface
Galerkin { [ -Flux[] , {T} ]; // - sign for incoming flux
In Sur_The; Integration I1; Jacobian JSur;  }

//cooling at a surface to an constant temperature outside wall
Galerkin { [ h[] * Dof{T} , {T} ] ;
In SurConv_The ; Integration I1; Jacobian JSur;  }

Galerkin { [ -h[] * TConv[] , {T} ] ;
In SurConv_The ; Integration I1; Jacobian JSur;  }

//Radiation cooling on a surface, but forces multiple solves, due to the non-possible Dof and nonlinearities.
Galerkin { [ hr[{T}] * (({T}+273.)^4-(TConv[]+273.)^4) , {T} ] ;
In SurRad_The ; Integration I1; Jacobian JSur;  }

Maybe this helps somehow,
very nice greetings,
bernhard,

On Thu, 2008-03-20 at 17:10 -0700, Tammo.Heeren at AlconLabs.com wrote:
> Hi Luis,
>
> Thank you for your response and the code. I am working my way through it
> to understand it.
> Here is what I understand so far, please correct me if I am wrong.
>
> ---
> 1. Galerkin { [ Dof{d u} , {d u} ] ; In OMEGA ; Jacobian Vol ;
> Integration Int ; }
> 2. Galerkin { [ -f[] , {u} ] ; In OMEGA ; Jacobian Vol ; Integration Int
> ; }
> 3. Galerkin { [ -g[] , {u} ] ; In GAMMA ; Jacobian Sur ; Integration Int
> ; }
> 4. Galerkin { [ Dof{u} , {uo} ] ; In OMEGA ; Jacobian Vol ; Integration
> Int ; }
> 5. Galerkin { [ Dof{uo} , {uo} ] ; In OMEGA ; Jacobian Vol ; Integration
> Int ; }
> ---
>
> - GAMMA is a line surrounding surface OMEGA. Both are in domain DOMAIN.
> - I assume that GAMMA and OMEGA share nodes
> - div( grad(u) ) - f = 0 in OMEGA
> - f is defined in DOMAIN, though I suppose you only have to define it in
> OMEGA
> - u is defined in DOMAIN as a Form0 FunctionSpace
> - grad(u) comes for the Form0 FunctionSpace and the {d u} in the second
> part of the Galerkin
> - div(...) stems from the {d u} in the first part of the Galerkin
> - the -f comes from the second Galerkin term
>
> I don't understand where
> > \frac{\partial u}{\partial n} = g in \Gamma
> comes from.
>
> - if GAMMA and OMEGA share nodes, than the Galerkin terms 1 and 2 are
> also valid in GAMMA
> - then have div( grad(u) ) - f - g = 0 in GAMMA
>
> I am also a little fuzzy about Galerkin terms 4 and 5.
> - I assume that Galerkin 4. simply copies the function space u onto uo
> - u is defined as Form0 and uo is defined as Scalar (where is the
> difference?)
> - does Galerkin 5. then simply copy uo onto itself?
>
> If anybody else can contribute some inside, I would be happy to hear it.
>
> Gruesse,
>
> Tammo
>
> ---
> FunctionSpace {
>     { Name FSU ; Type Form0 ;
>         BasisFunction {
>             { Name sn ; NameOfCoef un ; Function BF_Node ;
>             Support DOMAIN ; Entity NodesOf[ All ] ; }
>         }
>         Constraint {
>         }
>     }
>     { Name FSU0 ; Type Scalar ;
>         BasisFunction {
>             { Name so ; NameOfCoef uo ; Function BF_Region ;
>             Support OMEGA ; Entity OMEGA ; }
>         }
>         Constraint {
>         }
>     }
> }
>
> Formulation {
>     { Name Uform ; Type FemEquation ;
>         Quantity {
>             { Name u; Type Local;  NameOfSpace FSU; }
>             { Name uo; Type Local;  NameOfSpace FSU0; }
>         }
>         Equation {
>                 // div( grad( u ) ) = f in Omega (Surface)
>                 Galerkin { [ Dof{d u} , {d u} ] ; In OMEGA ; Jacobian
> Vol ; Integration Int ; }
>                 Galerkin { [ -f[] , {u} ] ; In OMEGA ; Jacobian Vol ;
> Integration Int ; }
>                 Galerkin { [ -g[] , {u} ] ; In GAMMA ; Jacobian Sur ;
> Integration Int ; }
>                 Galerkin { [ Dof{u} , {uo} ] ; In OMEGA ; Jacobian Vol ;
> Integration Int ; }
>                 Galerkin { [ Dof{uo} , {uo} ] ; In OMEGA ; Jacobian Vol
> ; Integration Int ; }
>         }
>     }
> }
> ---
>
>
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