NUMERICAL SIMULATION OF SHALLOW WATER EQUATIONS AND RELATED MODELS
This thesis is devoted to the numerical approximation of the shallow water equations and of some related models. In the first part, we analyze the mathematical properties and the applications of the staggered grid scheme. The robustness of this scheme is validated on various applications such as...
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| Format: | Dissertations |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/33526 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This thesis is devoted to the numerical approximation of the shallow water equations
and of some related models.
In the first part, we analyze the mathematical properties and the applications
of the staggered grid scheme. The robustness of this scheme is validated on various
applications such as the rotating shallow water equations for geostrophic flows model
and viscous shallow water equations.
In the second part, we consider some related models. Firstly focusing on the
coupling between the Exner equation and the shallow water equations, modelling
bedload sediment transport, we observe in a particular case the numerical convergence
of the scheme to the exact solution, as well as a good agreement with
the experimental data in the dam-break with erodible bottom test. Secondly, we
present a numerical scheme based on the finite volume collocated scheme (HLLC)
in order to approximate the Richard-Gavrilyuk model. This model is an extension
of the shallow water model, fit for modelling the shear shallow water flows. Some
numerical tests provide a validation of the scheme. |
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