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

TL;DR

This paper introduces a novel model reduction technique for hyperbolic shallow water moment equations that preserves mass conservation by decomposing the model into macro and micro parts, enabling efficient and accurate simulations.

Contribution

It develops the first mass-conserving model reduction method for hyperbolic shallow water moment equations using macro-micro decomposition with POD-Galerkin and low-rank approximation.

Findings

High accuracy in numerical experiments

Fast computation times achieved

Guaranteed conservation and consistency

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.