Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE S and PDE S for Blood Flow Simulations

MOX 4

Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE S and PDE S for Blood Flow Simulations

Wednesday 1st May 2002

Quarteroni, Alfio; Veneziani, Alessandro

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.