I am sorry I can not formulate my problem more clearly. This is another try.

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 ?

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.



On Wednesday, October 26, 2016 at 2:57:36 PM UTC+2, Wolfgang Bangerth wrote:
>
> On 10/25/2016 01:36 PM, Retired Replicant. wrote: 
> > It seems to me that the specification of the flux out is not correct. In 
> > principle, instead of the Qout, one should specifiy a fixed head or 
> > temperature and the flux should adjust itself acoordingly. 
>
> You are asking a modeling question: how do I properly describe a 
> particular 
> situation? But it is not clear to me (or Daniel, judging from his answers) 
> what this situation is supposed to be. What he is saying is that there is 
> no 
> problem *mathematically* with what you are trying to do (with the 
> exception of 
> the fact that the solution is only determined up to a constant). What you 
> are 
> asking is whether the prescribed boundary condition makes sense 
> *physically*, 
> but that is a separate question. 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 [email protected] 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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