Development of POD-based Reduced Order Models applied to shallow water Riemann solvers

Reduced-order models (ROMs) based on the proper orthogonal decomposition have been proposed to reduce the computational resources required by the full-order models (FOMs) to approximate partial differential equations. In this paper a Roe-based ROM is developed to solve the shallow water equations in presence of source terms more efficiently than the Roe-based FOM. The well-balanced property and other numerical corrections such as the entropy fix and the wet-dry treatment are taken into account using augmented Riemann solvers to build the Roe-based FOM. In addition to this, a time averaging approach is necessary to develop the Roe-based ROM. This approach is validated by solving some cases and the computed solutions are compared with those ones of Lax-Friedrichs-based ROMs. It is also studied whether the ROM preserves or not the well-balancing, the entropy fix and the wet-dry treatment. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

In this study, a Roe-based reduced-order model is developed to efficiently solve the shallow water equations with source terms, compared to the Roe-based full-order model. The augmented Riemann solvers are used to consider the well-balanced property, entropy fix, and wet-dry treatment in constructing the Roe-based full-order model. Additionally, a time averaging approach is necessary for developing the Roe-based reduced-order model. The approach is validated through solving test cases and comparing the computed solutions with those of Lax-Friedrichs-based reduced-order models.