Hierarchical Model Reduction for Advection-Diffusion-Reaction Problems

Abstract

Some engineering problems ranging from blood flow to river flow, from internal combustion engines to electronic devices have been recently modelled by coupling problems with different space dimensions (geometrical multiscale method). In this paper we focus on a new approch, where different levels of detail of the problem at hand stem from a different selection of the dimension of a suitable function space. The coarse and fine models are thus identified in a straightforward way. Moreover this approach lends itself to an automatic model adaptive strategy. The approach is addressed on a 2D linear advection-diffusion reaction problem.