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| Author(s): |
Thiago Felipe Castro Carrenho
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2024-02-29 |
| Examining board members: |
Maicon Ribeiro Correa;
José Mario Martínez Pérez;
Márcio Rentes Borges
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| Advisor: | Maicon Ribeiro Correa |
| Abstract | |
The Saint-Venant equations consist of a system of Partial Differential Equations of hyperbolic nature widely applied for determining the hydrodynamic regime of flows in natural channels, such as rivers, representing an one-dimensional form of the shallow waters equations. For the cases where erosion effects are considered, this system is coupled to the Exner Equation, that models the transport and deposition of sediments, resulting in the Saint-Venant-Exner system. In the present work, we present the modeling of the flow of an incompressible newtonian fluid by the Saint-Venant-Exner equations for shallow waters rectangular channels. Firstly, we describe the Saint-Venant equations and present a well-balanced and conservative finite volume method, Upwind type, of two steps to solve the Saint-Venant equations. A wide set of simulations is shown, comproving the good balance of the method and its stability and robustness in the face of different boundary conditions and bathymetries. Then we add to this modeling the sediment transport by the Exner equation, making the model bathymetry also vary in time. We then adequate the presented model for solving the Saint-Venant-Exner system, in a decoupled form, where the Saint-Venant equations and the Exner equation are solved separately. Lastly, the proposed methodology is utilized to simulate the problem of hydrodynamic coupled to sediment transport in different scenarios of interest (AU) | |
| FAPESP's process: | 22/13007-2 - Numerical methods for the shallow-water system |
| Grantee: | Thiago Felipe Castro Carrenho |
| Support Opportunities: | Scholarships in Brazil - Master |