Abstract
We show the justification of a formulation by fictitious domain to study incompressible viscous flows inside fluid–porous–solid systems by using the Brinkman model in a heterogeneous fictitious porous medium covering the whole 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 solid body may possibly tend to infinity. The strong convergence of the solutions is established. Some error estimates on the solution are derived as a function of the penalty parameter. The error bound on the resulting applied force for the flow around a bluff obstacle is also given. Copyright © 1999 John Wiley & Sons, Ltd.
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