Stabilizing local boundary conditions for two-dimensional shallow water equations

Ben Mansour Dia; Jesper Oppelstrup

doi:10.1177/1687814017726953

Stabilizing local boundary conditions for two-dimensional shallow water equations

Ben Mansour Dia, Jesper Oppelstrup

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

Original language	English (US)
Pages (from-to)	168781401772695
Journal	Advances in Mechanical Engineering
Volume	10
Issue number	3
DOIs	https://doi.org/10.1177/1687814017726953
State	Published - Mar 27 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper is funded by King Fahd University of Petroleum and Minerals (KFUPM).

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10.1177/1687814017726953

https://repository.kaust.edu.sa/bitstream/10754/627540/1/1687814017726953.pdf

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title = "Stabilizing local boundary conditions for two-dimensional shallow water equations",

abstract = "In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.",

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N2 - In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.

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Stabilizing local boundary conditions for two-dimensional shallow water equations

Abstract

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