Chapter 10 - Isogeometric hierarchical model reduction for advection–diffusion process simulation in microchannels

Microfluidics has proven to be a key technology in various applications, making it possible to reproduce large-scale laboratory settings at a more sustainable small-scale. The current study is focused on enhancing the mixing process of multiple passive species at the microscale, where a laminar flow regime damps turbulence effects. Chaotic advection is often used to improve mixing effects also at very low Reynolds numbers. In particular, we focus on passive micromixers, where chaotic advection is mainly achieved by properly selecting the geometry of microchannels. In such a context, reduced-order modeling can play a role, especially in the design of new geometries. In this chapter, we verify the reliability and the computational benefits lead by a Hierarchical Model (HiMod) reduction when modeling the transport of a passive scalar in an S-shaped microchannel. Such a geometric configuration provides an ideal setting in which to apply a HiMod approximation that exploits the presence of a leading dynamics to commute the original 3D model into a system of 1D coupled problems. It can be proved that HiMod reduction guarantees very good accuracy compared to a high-fidelity model, despite a drastic reduction in terms of the number of unknowns.