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

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...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 51; no. 1
Main Authors Long, Tobias, Barnett, Robert, Jefferson-Loveday, Richard, Stabile, Giovanni, Icardi, Matteo
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.02.2025
Subjects
Advection
Computational mechanics
Fluid dynamics
Linear transformations
Mathematics
Model reduction
Proper Orthogonal Decomposition
Radon
Reduced order models
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Summary: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.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10209-5