On 10/28/2016 06:18 AM, Retired Replicant. wrote:
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.
It's still not entirely clear to me what exact situation you *want* to model.
As I mentioned in the previous email, the question is a *modeling* question,
i.e., what is correct and what is wrong depends on *what situation you want to
describe*. You can't ask questions such as "should K be periodic as well".
Whether K *is* periodic or not is something that is part of the situation you
try to model. If it is, then that may lead to you to one set of equations; if
it isn't, then you will get another set of equations.
But let me try to guess:
* Let's say, you do want to describe periodic flow in a domain [0,1]^2,
then clearly you assume that K is periodic as well, and you can impose
boundary conditions
H(0,y) = H(1,y)
or
n * K(0,y) grad H(0,y) = N * K(1,y) grad H(1,y)
where the assumed periodicity implies that K(0,y)=K(1,y)
* Let's say you have boundary conditions of the form
n * K(0,y) grad H(0,y) = 1
n * K(1,y) grad H(1,y) = 1
given, does this correspond to periodic flow? The answer is that if
K(0,y)=K(1,y), then yes, the solution is periodic. Otherwise, it is
not periodic.
Best
Wolfgang
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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