Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

Zeng, Xianyi; Stabile, Giovanni; Karatzas, Efthymios N.; Scovazzi, Guglielmo; Rozza, Gianluigi

doi:10.1016/j.cma.2022.115143

Cited by 7 publications

(2 citation statements)

References 40 publications

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“…As possible future work, it would be interesting to apply these augmented Riemann solvers-based ROMs to problems with Dirichlet BCs following [65], to perform parametric sensitivity analysis as done in [52,53], and also extend them to 2D shallow water problems following works as [39]. In the field of boundary condition problems, the shifted boundary method applied in recent work such as [66,67] could be very useful. It would also be worth extending the study of consistency through the use of higher order schemes and analyse how they respond and whether they maintain the order of convergence or not.…”

Section: Declaration Of Competing Interestmentioning

confidence: 99%

Development of Pod-Based Reduced Order Models Applied to Shallow Water Equations Using Augmented Riemann Solvers

Solán-Fustero

Gracia

Navas-Montilla

et al. 2023

Preprint

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Section: Declaration Of Competing Interestmentioning

confidence: 99%

Development of Pod-Based Reduced Order Models Applied to Shallow Water Equations Using Augmented Riemann Solvers

Solán-Fustero

Gracia

Navas-Montilla

et al. 2023

Preprint

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“…Cheng et al [2] applied the new second-order moving-water equilibria preserving central-upwind method for the 1D Saint-Venant system of shallow water model. Zeng et al [3] implemented fully discrete embedded finite element approximations for the shallow water equations and its reduced-order form. Huang et al [4] developed the high-order well-balanced AP scheme for the shallow water equations via source terms.…”

Section: Introductionmentioning

confidence: 99%

Some recent finite volume schemes for one and two layers shallow water equations with variable density

Mohamed

Sahmim

Benkhaldoun

et al. 2023

Math Methods in App Sciences

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We propose a class of finite volume algorithms that are both simple and efficient for solving numerically the shallow water equations with varying densities; shallow water flows in single and two layers are considered. In these flow regimes, variable horizontal or vertical density is taken into account. The shallow water equations for the hydraulic variables are coupled with a suspended sediment transport equation for the concentration variable to construct the model. To approximate the numerical solution of the models under consideration, a generalized Rusanov method is proposed; this method avoids solving Riemann problems during the time integration process, and it is simple and accurate.The proposed method is divided into two stages: predictor and corrector; the presented finite volume approach is well balanced, conservative, and simple.Non-oscillatory and suitable for shallow water equations when Riemann problems are challenging to solve. Several test problems for single-layer and two-layer shallow water flows are applied to the proposed method. The numerical resultsshow that the proposed finite volume approach has high resolution and that it is capable of simulating shallow water equations with variable density in flow regimes with strong shocks accurately. KEYWORDS one and two layers shallow water equations, Riemann invariant, well-balanced finite volume scheme MSC CLASSIFICATION 76S99, 35L65, 65M08

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A localized reduced basis approach for unfitted domain methods on parameterized geometries

Chasapi

Antolín

Buffa

2023

Computer Methods in Applied Mechanics and Engineering

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Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

Cited by 7 publications

References 40 publications

Development of Pod-Based Reduced Order Models Applied to Shallow Water Equations Using Augmented Riemann Solvers

Development of Pod-Based Reduced Order Models Applied to Shallow Water Equations Using Augmented Riemann Solvers

Some recent finite volume schemes for one and two layers shallow water equations with variable density

A localized reduced basis approach for unfitted domain methods on parameterized geometries

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