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We present a formulation for accommodating defective boundary conditions for the incompressible Navier--Stokes equations where only averaged values are prescribed on measurable portions of the boundary. In particular we consider the case where the flow rate is imposed on several domain sections. This methodology has an interesting application in the numerical simulation of flow in blood vessels, when only a reduced set of boundary data are generally available for the upstream and downstream sections.
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Formaggia et al. (2002) studied this question.
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