[Getdp] coupled electrical field - particle densities
Reinhold Ingo
ingo.reinhold at s2001.tu-chemnitz.de
Tue Nov 14 18:27:37 CET 2006
Dear all,
I'm not too familiar with GetDP and hope to get some answers by
posting my problem here.
I'm trying to compute a problem with coupled electrical field and
particle densities. From the literature it is suggested that for
example electron densities in partial discharges are computed by
something like
dt(ne)=div(D grad(ne))-div( ve*ne)+C*ne
The electrical field is then
div( epsr grad(phi))-e/eps0*ne=0
However what confuses me now is, that when I'm trying to compute the
problem in GetDP I run into a lot of problems. Maybe I'm doing
something wrong in the formulation.
If I'm right the second equation gives a weak formulation of
Galerkin { [ epsr[] * Dof{d v} , {d v} ]; In Volume; Jacobian Vol;
Integration Int; }
GlobalTerm { [ -elemc*Dof{NE}/(eps0) , {V} ]; In Boundary;}
Since NE is defined as a GlobalQuantity my problem of understanding
is now how to arrange the first equation in such a way, that both
work together in a non-linear algorithm, even though the density is
in the plane, while NE in the above given formula is only at the
boundary and set up in a function space like this
FunctionSpace {
{ Name Elec; Type Form0;
BasisFunction {
{ Name sn ; NameOfCoef vn ; Function BF_Node ; Support Region
[{Volume}] ; Entity NodesOf[ All,Not Boundary] ; }
{ Name sf ; NameOfCoef vfu ; Function BF_GroupOfNodes ; Support
Volume ; Entity GroupsOfNodesOf[Boundary] ; }
}
GlobalQuantity {
{ Name GlobalElectricPotential ; Type AliasOf ; NameOfCoef
vfu ; }
{ Name GlobalElectronDensity ; Type AssociatedWith ; NameOfCoef
vfu; }
}
Constraint {
{ NameOfCoef GlobalElectronDensity ; EntityType
GroupsOfNodesOf ; NameOfConstraint ElectronDensity; }
{ NameOfCoef GlobalElectricPotential ; EntityType
GroupsOfNodesOf ; NameOfConstraint ElectricScalarPotential ; } }
}
}
My guess was that the electron density is then calculated using
Galerkin { Dt[ Dof{NE} , {NE} ]; In Volume; Jacobian Vol;
Integration Int; }
Galerkin { [ Dof{NE}*we , {d ne} ]; In Volume; Jacobian Vol;
Integration Int; }
Galerkin { [ -De*Dof{d ne} , {d ne} ]; In Volume; Jacobian Vol;
Integration Int; }
Galerkin { [ -C*Dof{NE} , {NE} ]; In Volume; Jacobian Vol;
Integration Int; }
but didn't succeed.
It would be really great if someone could give me hint how to
formulate it.
Thanks in advance and nice greetings from Chemnitz,
Ingo
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