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

• Published in: Advances in computational mathematics Vol. 50; no. 4
• Main Authors: Koellermeier, Julian, Krah, Philipp, Kusch, Jonas
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer Nature B.V
• 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; Dynamical low-rank approximation; Shallow water moment equations; 65M08; 65F55; 76B15; POD-Galerkin; Model order reduction; 65M60
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-024-10175-y

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.