Multiscale coupling in heterogeneous diffusion processes: a port-based approach

In this paper, we discuss the geometric structure of the dynamics of a multiscale diffusion process. The fiber bundle structure of the spatial domain allow us to exhibit a Stokes-Dirac structure associated with the diffusion equation. Furthermore, the model of diffusion in a biphasic heterogeneous medium being based on a multiscale approach, we prove that the 2-scale interconnection is a Dirac structure. We then illustrate these results with the example of a 2-level mathematical model of a pressure swing adsorption (PSA) process.