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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| Published in | Advances in computational mathematics Vol. 50; no. 4 |
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| Language | English |
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01.08.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 76 |
| Author | Koellermeier, Julian Krah, Philipp Kusch, Jonas |
| Author_xml | – sequence: 1 givenname: Julian orcidid: 0000-0002-8822-461X surname: Koellermeier fullname: Koellermeier, Julian email: j.koellermeier@rug.nl organization: Bernoulli Institute, University of Groningen, Groningen Cognitive Systems and Materials Center, University of Groningen – sequence: 2 givenname: Philipp orcidid: 0000-0001-8982-4230 surname: Krah fullname: Krah, Philipp organization: Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université – sequence: 3 givenname: Jonas orcidid: 0000-0002-2061-2114 surname: Kusch fullname: Kusch, Jonas organization: Institut für Mathematik, Universität Innsbruck |
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| Keywords | Dynamical low-rank approximation Shallow water moment equations 65M08 65F55 76B15 POD-Galerkin Model order reduction 65M60 |
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| SubjectTerms | 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 |
| Title | 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 |
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