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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2018-03-01
|
| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1177/1687814017726953 |
| _version_ | 1828838428462022656 |
|---|---|
| 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. |
| first_indexed | 2024-12-12T19:02:13Z |
| format | Article |
| id | doaj.art-eccd4230bf4d4a91b51b79f29a6df868 |
| institution | Directory Open Access Journal |
| issn | 1687-8140 |
| language | English |
| last_indexed | 2024-12-12T19:02:13Z |
| publishDate | 2018-03-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| 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 |