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Implementing the boundary equations in Stokes-Darcy Interface

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Hi everyone, Working on Stokes-Darcy coupling of two simple rectanglar 2D domains, the fluid flows in the Stokes domain first then penetrates into Darcy's, there are three simple equations that must be applied in the interface between the two physics : 1/ Continuity of the normal flux/velocity, 2/ Continuity of normal Stress and finally 3/ Beaver-Joseph-Saffman (BJS) ... the attached image shows the simpliest forms of these equations. My question is, what is the most efficient way to implement these three equations ? Thanks in advance.


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