I try to simulate, for the moment, a filling domaine with mud, but this mud must stay inside the domaine. The air must go outside by the outlet with porous media, because like you write, this slowing air throught the outlet is important for the model. Eventually, I will filtrate this mud. 


I try for the moment, a wall just before the porous domaine but with air flux and velocity throught this wall and the result seems acceptable. This wall keep the mud inside without restraint air.