Work

HiPhom\({\varepsilon }\): High-Order Projection-Based Homogenization for Advection-Diffusion-Reaction Problems

Year: 2025

Type: article

Abstract: . We propose a new model reduction technique for multiscale scalar transport problems that exhibit dominant axial dynamics. Toward this aim, we rely on the separation of variables to combine a hierarchical model (HiMod) reduction with a two-scale asymptotic expansion. We extend the two-scale asymptotic expansion to an arbitrary order and exploit the high-order correctors to define the HiMod modal basis which approximates the transverse dynamics of the flow, while we adopt a finite element discretization to model the leading stream. The resulting method, which is named HiPhom[Formula: see text] (high-order projection-based homogenization), is successfully assessed both in steady and unsteady advection-diffusion-reaction settings. The numerical results confirm the very good performance of HiPhom[Formula: see text], which improves the accuracy and the convergence rate of HiMod and extends the reliability of the standard homogenized solution to transient and preasymptotic regimes.

Source: Multiscale Modeling and Simulation

DOI: 10.1137/23m1604989

Authors: Giovanni Conni, Stefano Piccardo, Simona Perotto, Giovanni Michele Porta, Matteo Icardi