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Stabilizing local boundary conditions for two-dimensional shallow water equations
King Fahd Univ Petr & Minerals, Coll Petr Engn & Geosci, CIPR, Dhahran 31261, Saudi Arabia.;King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn Div CEMSE, Thuwal, Saudi Arabia..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Advances in Mechanical Engineering, ISSN 1687-8132, E-ISSN 1687-8140, Vol. 10, no 3, article id 1687814017726953Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Sage Publications, 2018. Vol. 10, no 3, article id 1687814017726953
Keywords [en]
Shallow water flow, boundary control, Riemann invariants
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-226791DOI: 10.1177/1687814017726953ISI: 000429747300001Scopus ID: 2-s2.0-85044740828OAI: oai:DiVA.org:kth-226791DiVA, id: diva2:1203656
Available from: 2018-05-04 Created: 2018-05-04 Last updated: 2018-05-29Bibliographically approved

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Oppelstrup, Jesper

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