A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform

Long, Tobias; Barnett, Robert; Jefferson-Loveday, Richard; Stabile, Giovanni; Icardi, Matteo

Abstract

Problems with dominant advection, discontinuities, travelling features, or shape variations are widespread in computational mechanics. However, classical linear model reduction and interpolation methods typically fail to reproduce even relatively small parameter variations, making the reduced models inefficient and inaccurate. This work proposes a model order reduction approach based on the Radon Cumulative Distribution Transform (RCDT). We demonstrate numerically that this non-linear transformation can overcome some limitations of standard proper orthogonal decomposition (POD) reconstructions and is capable of interpolating accurately some advection-dominated phenomena, although it may introduce artefacts due to the discrete forward and inverse transform. The method is tested on various test cases coming from both manufactured examples and fluid dynamics problems.

Citation

Long, T., Barnett, R., Jefferson-Loveday, R., Stabile, G., & Icardi, M. (2025). A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform. Advances in Computational Mathematics, 51(1), https://doi.org/10.1007/s10444-024-10209-5

• Journal Article Type: Article
• Acceptance Date: Nov 6, 2024
• Online Publication Date: Jan 3, 2025
• Publication Date: Jan 3, 2025
• Deposit Date: Jan 6, 2025
• Publicly Available Date: Jan 4, 2026
• Journal: Advances in Computational Mathematics
• Print ISSN: 1019-7168
• Electronic ISSN: 1572-9044
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 1
• DOI: https://doi.org/10.1007/s10444-024-10209-5
• Keywords: Reduced order model · Non-linear transformations · Advection-dominated problems · Radon transform · Cumulative distribution · Proper orthogonal decomposition
• Public URL: https://nottingham-repository.worktribe.com/output/43948309
• Publisher URL: https://link.springer.com/article/10.1007/s10444-024-10209-5
• Additional Information: Received: 3 May 2023; Accepted: 6 November 2024; First Online: 3 January 2025; : ; : The authors declare no competing interests.