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arXiv · 2201.09546

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

Xianyi Zeng·Giovanni Stabile·Efthymios N. Karatzas·Guglielmo Scovazzi·Gianluigi Rozza
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Abstract

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial discretization is combined with an explicit predictor/multi-corrector time integration to integrate in time the numerical solutions to the shallow water equations, both for the full and reduced-order model. In order to improve the approximation of the solution manifold also for geometries that are untested during the offline stage, the snapshots have been pre-processed by means of an interpolation procedure that precedes the reduced basis computation. The methodology is tested on geometrically parametrized shapes with varying size and position.

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Xianyi Zeng, Giovanni Stabile, Efthymios N. Karatzas, Guglielmo Scovazzi, Gianluigi Rozza. 2022-01-24. Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method. https://doi.org/10.1016/j.cma.2022.115143

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