On the coupling of 1D and 3D diffusion-reaction equations. Applications to tissue perfusion problems
Wednesday 10th December 2008
D'Angelo, Carlo; Quarteroni, Alfio
In this paper we consider the coupling between two diffusion-reaction problems, one taking place in a three-dimensional domain, the other in a one-dimensional subdomain. This coupled problem is the simplest model of fluid flow in a three-dimensional porous medium featuring fractures that can be described by one-dimensional manifolds. In particular this model can provide the basis for a multiscale analysis of blood flow through tissues, in which the capillary network is represented as a porous matrix, while the major blood vessels are described by thin tubular structures embedded into it: in this case, the model allows the computation of the 3D and 1D blood pressures respectively in the tissue and in the vessels.