Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: a study using POD-Galerkin and dynamical low-rank approximation

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaran...

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Bibliographic Details
Published in:Advances in computational mathematics 2024-08, Vol.50 (4), Article 76
Main Authors: Koellermeier, Julian, Krah, Philipp, Kusch, Jonas
Format: Article
Language:English
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Decomposition
Flow simulation
Galerkin method
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Model reduction
Physical properties
Shallow water
Visualization
Water conservation
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Summary:Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction for the hyperbolic shallow water moment equations and achieve mass conservation. This is accomplished using a macro-micro decomposition of the model into a macroscopic (conservative) part and a microscopic (non-conservative) part with subsequent model reduction using either POD-Galerkin or dynamical low-rank approximation only on the microscopic (non-conservative) part. Numerical experiments showcase the performance of the new model reduction methods including high accuracy and fast computation times together with guaranteed conservation and consistency properties.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10175-y