Re: bim package symmetry boundary condition at reactor outlet

[Carlo De Falco]

Hi,

On 15 Feb 2016, at 15:54, bim7 <address@hidden> wrote:

> Hi to all, 
> 
> I am using the latest bim-package to model a species transport problem in
> cylindrical coordinates. 
> It is a classical tube reactor, with an inlet, an impermeabel wall, a
> symmetry line in the center and an outlet. 
> 
> Applying a Dirichlet boundary conditions for the inlet works quite fine and
> a Neumann boundary with no flux at all through the wall works as well. 
> 
> I am having quite some trouble to get the right outlet boundary condition.
> Naturally I would apply a symmetric boundary condition stating that there is
> no concentration change in the axial direction over the boundary in normal
> direction. 
> 
> I tried using a Neumann BC but this looks like setting the overall flux to
> zero and not only the diffusive part of it.

Indeed that is the case, in BIM the problem is expressed in conservative form, 
i.e.:

div ( F(u) ) = f     in Omega

where 

F(u) = - a ( grad (u) - b u)

given the test function v, and denoting the boundary of Omega by Gamma, 
the weak formulation of the problem is expressed as

< - F(u), grad (v) >_{Omega} + < F(u) * n, v>_{Gamma} = <f, v>_{Omega}

so the homogeneous natural boundary condition corresponds in this case to 
setting

F(u) * n  = 0


> Counter-balancing that by the
> redirected convective flux did not work for me so far.  

I'm not sure what you mean here, can you provide more detail?

> Robin does not work either, despite it seems to be the right choice.

what Robin condition are you imposing exactly?

> Any ideas on how I could solve that issue? 

A simple solution is to use the function "bim2a_advection_upwind"
function and impose a dirichlet boundary condition on the outlet,
the nodal values on the outlet will be incorrect but the solution
on any other nodes will not be affected. 

If you don't like to see the spurious steep layer at the end of the domain
you could define your mesh with a thin layer of "ghost" elements beyond
the end of your geometry and then postprocess the solution to remove this layer.

A more rigorous solution is also possible but requires more complex explanation.

> Best regards, 
> Sebastian 

HTH,
c.