| In hemodynamics, local
phenomena, such as the perturbation of flow pattern in a specific vascular region, are
strictly related to the global features of the whole circulation (see e.g. cite{FNQV}).
In cite{QRV1} we have proposed a heterogeneous model where a
local, accurate, 3D description of blood flow by means of the Navier-Stokes equations
in a specific artery is coupled with a
systemic, 0D, lumped model of the remainder of circulation. This is a geometrical multiscale strategy,
which couples an initial-boundary value problem to be used in a specific vascular region with
an initial-value-problem in the rest of the circulatory system. It has been
succesfully adopted to predict the outcome of a surgical operation (see cite{Biorheo,eccom}).
However, its interest goes beyond the context of blood flow simulations,
as we point out in the Introduction.
In this paper we provide a well posedness analysis
of this multiscale model, by proving a local-in-time existence result
based on a fixed-point technique.
Moreover, we investigate the role of matching conditions between the two submodels for the numerical simulation. |
