Usually I see that the flow in the modeled by Darcy Law and the matching condition at the interface is the well-known Beavers-Joseph Condition. But, practically, this is not correct as the wall thiciness is very small compared to the radius of the lumen. Has anyone come across a better model? How to model the slip at the interface? Is it OK to neglect the elastic nature of the wall and treat it as a rigid wall while computing Wall Shear Stress to ultimately analyze atherosclerosis or aneurysm?