Boundary condition for different permeabilities

General discussions about how to formulate a script for FlexPDE.

Boundary condition for different permeabilities

Postby jabberwocky on Wed Mar 08, 2017 5:16 am

Hi. Which BC should I use for issues such heat flow or seepage, for regions with different permeabilities? Load(u)=0 produces discontinuity such in attachment (more heat or fluid flows through region, than enters it).
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Re: Boundary condition for different permeabilities

Postby moderator on Mon Mar 13, 2017 12:46 pm

As we point out in the documentation of "Natural", the meaning of the Natural (or "load") boundary condition depends on the way you have written your equation.
"Natural" (or "load") defines the value of the surface terms generated by integrating second-order equation terms by parts. This is equivalent to applying the Divergence Theorem.
So in general it is a flux of something as defined by the PDE. For the equation Div(K*grad(u))+S=0, it is the normal component of the flux K*grad(u).
At interior material interfaces, you need to say nothing. The solver will assume that K1*grad(u1)=K2*grad(u2), where 1 and 2 indicate evaluation in materials 1 and 2. That is, flux continuity is assumed, where "flux" is defined by the specific PDE.
See the documentation.
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