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Simulation numérique multidimensionnelle d'écoulements estuariens

Abstract : In this work, we are interested by the hydrodynamical multidimensional modeling and simulation of estuarian river flows. The physical model to be employed is a 3D one, but due to the huge computational cost, it cannot be used on the whole length of the river. Therefore, it is interesting to use different lower-dimensional models on adequate regions of the river, according to its topography and its bathymetry. Therefore, new hydrodynamical models are proposed in 1D, 2D and 2.5D. We start from the 3D problem based on the instationary and incompressible Navier-Stokes equations, which is written in a weak form. Then simpler models are derived by means of a projection method. A 1D model is derived on the median curve of the river, as well as two 2D models called 2D-horizontal and 2D-vertical models, either they are written on the free surface or on the median longitudinal surface of the river. The 2.5D model is obtained by adding the 2D-vertical and 2D-horizontal discrete spaces. All these models take into account the geometry of the river and provide a 3D velocity and a 3D pressure. The pressure is an unknown of the problem and it is not supposed to be hydrostatic. Moreover, model estimators between the 3D model and any of its lower-dimensional approximations in 1D, 2D or 2.5D, are defined and justified. These model estimators compute the error between the 3D model and the simpler models, and then also indicate the validity domain of these simpler hydrodynamical models, from a qualitative point of view. All these new hydrodynamical models are implemented in finite element codes written in C++, and coupled numerically with the model estimators.
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https://tel.archives-ouvertes.fr/tel-00453696
Contributor : Agnès Pétrau <>
Submitted on : Friday, February 5, 2010 - 2:17:19 PM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Thursday, October 18, 2012 - 2:40:18 PM

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  • HAL Id : tel-00453696, version 1

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Agnès Pétrau. Simulation numérique multidimensionnelle d'écoulements estuariens. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2009. Français. ⟨tel-00453696v1⟩

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