Many thanks Wolfgang and Daneil.
I think Wolfgang's answer is illuminating.
On Friday, October 28, 2016 at 3:13:56 PM UTC+2, Daniel Arndt wrote:
>
> so the uniform flux from left and right of the rectangle implies periodic
>> boundary condition. But the K ( hydraulic conductivity) is a function of
>> (x,y).
>> If we want to enforce the periodic boundary condition, should we expect
>> to have a condition on K ? should K be periodic as well for example ?
>>
> If you want to use periodic boundary conditions, then you should prescribe
> them and not Neumann boundary conditions. By having something like
> n \cdot \nabla H|_\Gamma_{in} = -n \cdot \nabla H|_\Gamma_{out},
> you are not constraining the tangential direction.
> For periodic boundary conditions, K|_\Gamma{in}=K|_\Gamma{out} makes
> sense. Probably you don't want to have a jump in K across the periodic
> boundary faces.
> You might want to have a look at step-45[1] for how to describe periodic
> boundary conditions in deal.II.
>
>
>> for example, a specific distribution of K field, where we imagine a
>> block of material near the right edge at the exit nodes with much higher
>> hydraulic conductivity, then the flux out of the rectangle can not be
>> uniform. the flow field will be distorted and will become non uniform.
>> enforcing a uniform flow works in an artificial sense in this case.
>> So it seems to me that the limitation on the specification of a fixed
>> head is more essential than just making the system unknown up to a fixed
>> constant.
>>
> I am quite not sure what the question is you want to be answered in the
> end.
>
> Best,
> Daniel
>
> [1] https://www.dealii.org/8.4.1/doxygen/deal.II/step_45.html
>
>
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