Analysis of singular perturbations on the brinkman problem for fictitious domain models of viscous flows

We show the justification of a formulation by fictitious domain to study in compressible viscous flows inside fluid-porous-solid systems by using the B rinkman model in a heterogeneous fictitious porous medium covering the whol e auxiliary domain. The singular perturbations of this problem are analysed when the permeability of the medium tends to infinity in the fluid domain and/or to zero in the solid domain. In addition, the viscosity inside the s olid body may possibly tend to infinity. The strong convergence of the solu tions is established. Some error estimates on the solution are derived as a function of the penalty parameter. The error bound on the resulting applie d force for the flow around a bluff obstacle is also given. Copyright (C) 1 999 John Wiley & Sons, Ltd.