HiPhom𝜺: HIgh order Projection-based HOMogenisation for advection diffusion reaction problems

Conni, Giovanni; Piccardo, Stefano; Michele Porta, Giovanni; Icardi, Matteo

Abstract

We propose a new model reduction technique for multiscale scalar transport problems that exhibit dominant axial dynamics. To 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 discretisation to model the leading stream. The resulting method, which is named HiPhomε (HIgh-order Projection-based HOMogEnisation), is successfully assessed both in steady and unsteady advection-diffusion-reaction settings. The numerical results confirm the very good performance of HiPhomε which improves the accuracy and the convergence rate of HiMod and extends the reliability of the standard homogenised solution to transient and pre-asymptotic regimes.

Citation

Conni, G., Piccardo, S., Michele Porta, G., & Icardi, M. (in press). HiPhom𝜺: HIgh order Projection-based HOMogenisation for advection diffusion reaction problems. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal,

• Journal Article Type: Article
• Acceptance Date: Oct 1, 2024
• Deposit Date: Jan 9, 2025
• Publicly Available Date: Jan 9, 2025
• Journal: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
• Print ISSN: 1540-3459
• Electronic ISSN: 1540-3467
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Keywords: multiscale; homogenisation; hierarchical model reduction; finite elements
• Public URL: https://nottingham-repository.worktribe.com/output/43953046