The most common condition I have seen is vanishing of normal component of fluid velocity at the wall. It makes sense, because Darcy's law describes pore-averaged flow, and the fluid moves even within pores contacting the wall. But, I have found a series of publications where the adhesion condition is set as if it is a pure fluid flow. Is this a possible/correct method? Will the difference cause rapid changes of flow characteristics?
N.B. The articles use a Darcy-Brinkman flow model.
If I remember well, the Darcy-Brinkman is a second order PDE, right?. In that case you may prescribe Dirichlet BC's. The usual Darcy's equation is first order, so you only can prescribe the normal component. I don't know if this helps you.
G.S. Beavers, etc. Boundary condtions at a naturally permeable wall.
Try this paper.
On the boundary you should provide a correctness of mass conservation law, I guess.
Thank you for answers.
Yes, it is obvious the Brinkman model is a second order PDE and it needs the extra boundary condition. But It is unclear why the velocity equal zero at the solid impermeable wall. If the velocity is pore-averaged it will be non-zero within pores. And the velocity can be zero only at pore-scale level where the motion is chaotic. So, we need to make some assumptions about the viscous stress (probably, some effective viscous stress) or pressure?
Dear Kirill, though I don't know much in this area, but if velocity is zero at the solid boundary, then it should be as a result of no-slip condition, which I suppose makes physical sense. This is so since the velocity of fluid adjacent to the solid has to be zero.
I have found a some new paper touches the topic question. It shows the no-slip conditions may be incorrect for the models with Brinkman terms, and the no-flux condition should be applied.
http://link.springer.com/article/10.1134/S0015462814020112
Dear I think it depend on the problem you have, generally people take the normal velocity component zero.
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