On the well-posed coupling between free fluid and porous viscous flows

Philippe Angot (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We present a well-posed model for the Stokes/Brinkman problem with {\em jump embedded boundary conditions (J.E.B.C.)} on an immersed interface. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface $\S$ separating the fluid and porous domains. These conditions are well chosen to get the coercivity of the operator. Then, the general framework allows to prove the global solvability of some models with physically relevant stress or velocity jump boundary conditions for the momentum transport at a fluid-porous interface. The Stokes/Brinkman problem with {\em Ochoa-Tapia \& Whitaker (1995)} interface conditions and the Stokes/Darcy problem with {\em Beavers \& Joseph (1967)} conditions are both proved to be well-posed by an asymptotic analysis. Up to now, only the Stokes/Darcy problem with {\em Saffman (1971)} approximate interface conditions was known to be well-posed.

Mots clés: Jump embedded boundary conditions; Stokes/Brinkman problem; Stokes/Darcy problem; Fluid/porous coupled flows; Well-posedness analysis; Asymptotic analysis; Vanishing viscosity

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Philippe Angot. On the well-posed coupling between free fluid and porous viscous flows. 2009. ⟨hal-00476386v1⟩