Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06238 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913193145663488 |
|---|---|
| author | Conni, Giovanni Piccardo, Stefano Perotto, Simona Porta, Giovanni Michele Icardi, Matteo |
| author_facet | Conni, Giovanni Piccardo, Stefano Perotto, Simona Porta, Giovanni Michele Icardi, Matteo |
| contents | 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 HiPhom$\varepsilon$ (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 HiPhom$\varepsilon$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06238 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | HiPhom$\varepsilon$ -: HIgh order Projection-based HOMogenisation for advection diffusion reaction problems Conni, Giovanni Piccardo, Stefano Perotto, Simona Porta, Giovanni Michele Icardi, Matteo Numerical Analysis 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 HiPhom$\varepsilon$ (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 HiPhom$\varepsilon$, 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. |
| title | HiPhom$\varepsilon$ -: HIgh order Projection-based HOMogenisation for advection diffusion reaction problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.06238 |