Development of POD-based reduced order models applied to shallow water equations using augmented Riemann solvers. (English) Zbl 1539.76136
Summary: 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.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
Keywords:
reduced-order modelling; POD methods; Lax-Friedrichs method; Roe method; computational resources; shallow water equationsReferences:
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