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.

翻译：使用双曲浅水瞬间方程式进行地球物理流模拟,需要将潜在的大型PDE系统,即所谓的瞬间系统,有效地分解,这就需要量身定制的减少命令模型技术,以便进行高效和准确的模拟,同时保证质量保护等物理特性。在本文中,我们为双曲浅水瞬间方程式开发了第一个减少模型,并实现了大规模保护。这是通过将模型分解成大型(保守)部分和微型(非保守)部分来完成的,以及随后使用POD-Galerkin或动态低级近距离的模型进行减少。数字实验展示了新模型减少方法的性能,包括高精度和快速计算时间以及有保障的保护和一致性特性。