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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2018-03-01
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| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1177/1687814017726953 |
| Summary: | 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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| ISSN: | 1687-8140 |