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

Solán-Fustero, P. (Universidad de Zaragoza) ; Gracia, J.L. (Universidad de Zaragoza) ; Navas-Montilla, A. (Universidad de Zaragoza) ; García-Navarro, P. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.cma.2023.116038

Año: 2023

Publicado en: Computer Methods in Applied Mechanics and Engineering 410 (2023), 116038 [27 pp.]
ISSN: 0045-7825

Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/DGA-FEDER/T32-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-FEDER/PGC2018-094341-B-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)
Área (Departamento): Área Mecánica de Fluidos (Dpto. Ciencia Tecnol.Mater.Fl.)