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)|
|Journal||Advances in Mechanical Engineering|
|State||Published - Mar 27 2018|
Bibliographical noteKAUST 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).