Stabilizing local boundary conditions for two-dimensional shallow water equations

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...

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Váldodahkkit: Ben Mansour Dia, Jesper Oppelstrup
Materiálatiipa: Artihkal
Giella:English
Almmustuhtton: SAGE Publishing 2018-03-01
Ráidu:Advances in Mechanical Engineering
Liŋkkat:https://doi.org/10.1177/1687814017726953
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author Ben Mansour Dia
Jesper Oppelstrup
author_facet Ben Mansour Dia
Jesper Oppelstrup
author_sort Ben Mansour Dia
collection DOAJ
description 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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spelling doaj.art-eccd4230bf4d4a91b51b79f29a6df8682022-12-22T00:15:04ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402018-03-011010.1177/1687814017726953Stabilizing local boundary conditions for two-dimensional shallow water equationsBen Mansour Dia0Jesper Oppelstrup1Computer, Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi ArabiaDepartment of Mathematics, KTH Royal Institute of Technology, Stockholm, SwedenIn 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.https://doi.org/10.1177/1687814017726953
spellingShingle Ben Mansour Dia
Jesper Oppelstrup
Stabilizing local boundary conditions for two-dimensional shallow water equations
Advances in Mechanical Engineering
title Stabilizing local boundary conditions for two-dimensional shallow water equations
title_full Stabilizing local boundary conditions for two-dimensional shallow water equations
title_fullStr Stabilizing local boundary conditions for two-dimensional shallow water equations
title_full_unstemmed Stabilizing local boundary conditions for two-dimensional shallow water equations
title_short Stabilizing local boundary conditions for two-dimensional shallow water equations
title_sort stabilizing local boundary conditions for two dimensional shallow water equations
url https://doi.org/10.1177/1687814017726953
work_keys_str_mv AT benmansourdia stabilizinglocalboundaryconditionsfortwodimensionalshallowwaterequations
AT jesperoppelstrup stabilizinglocalboundaryconditionsfortwodimensionalshallowwaterequations