Calculations of fluvial flows are strongly influenced by geometry complexity and large overall uncertainty on every single measurable property, such as velocity and shear. Moreover, a considerable portion of the data obtained from computational simulations arose from two-dimensional, steady-state models. The present work states a different approach to perform computer-based simulations and analyze fluvial flows. For the first part, the suitability of OpenFOAM to be used as the main CFD solver to analyze fluvial flows is studied. Initially, two well documented channel configurations are computationally studied using OpenFOAM. Finally, these results are compared to the output obtained from one of the widely used quasi-3D CFD solvers used to perform studies about environmental hydraulics.

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Yes / The flow in the main channel of a meandering compound channel does not occur in the ridge direction because of the effect of the upstream floodplain flows. This study proposes a model for estimating the flow direction in the depth-averaged two-dimensional domain (depth-averaged flow angles) between the entrance and the apex sections. Detailed velocity measurements were performed in the region between the meander entrance section and apex section in a large-scale meandering compound channel. The vertical size of the secondary current cell is highly related to the depth-averaged flow angle; thus, the means of the local flow angles above the secondary current cell and within the cell are separately discussed. The experimental measurements indicate that the mean local flow angle above the cell is equal to the section angle, whereas the mean local flow angle within the cell is equal to zero. The proposed model is validated using published data from five sources. Good agreement is obtained between the predictions and measurements, indicating that the proposed model can accurately estimate the depth-averaged flow direction in the meandering compound channels. Finally, the limitations and application ranges of the model are discussed. / National Key Research and Development Program of China (No. 2016YFC0402302), the National Natural Science Foundation of China (Nos. 51539007 and 51609160)

A numerical solution algorithm based on finite volume method is developed for unsteady, two-dimensional, depth-averaged shallow water flow equations. The model is verified using test cases from the literature and free surface data obtained from measurements in a laboratory flume. Experiments are carried out in a horizontal, rectangular channel with vertical solid boxes attached on the sidewalls to obtain freesurface data set in flows where three-dimensionality is significant. Experimental data contain both subcritical and supercritical states. The shallow water equations are solved on a structured, rectangular grid system. Godunov type solution procedure evaluates the interface fluxes using an upwind method with an exact Riemann solver. The numerical solution reproduces analytical solutions for the test cases successfully. Comparison of the numerical results with the experimental two-dimensional free surface data is used to illustrate the limitations of the shallow water equations and improvements necessary for better simulation of such cases.

Yes / For overbank flows in meandering channels, the flow direction along a meander varies and is affected by floodplain vegetation. This study proposes a model for predicting the depth-averaged two-dimensional flow direction (depth-averaged flow angle) along a meander in smooth and vegetated meandering compound channels. Laboratory experiments were performed in smooth and vegetated channels. Measurements show that the height of the secondary current cell in the main channel is increased by dense floodplain vegetation comparing with that in a non-vegetated channel. A method of determining the height of the cell is proposed. At the middle section between the apex and exit sections, where the secondary current cell is absent, the depth-averaged flow angle is independent of the height of the cell. Beyond the middle section, a new secondary current cell is formed, and the flow angle is highly dependent on the height of the cell. The proposed model is thoroughly verified using the flume experimental and field observed data. Good agreement is obtained between predictions and measurements, indicating that the proposed model is capable of accurately predicting the depth-averaged flow angle along a meander in smooth and vegetated meandering compound channels. / National Key Research and Development Program of China (No. 2016YFC0402302), and the National Natural Science Foundation of China (Nos. 51709022, 51609160 and 51539007)

Yes / In this paper, an improved Shiono-Knight model (SKM) has been proposed to calculate the rectangular compound open channel flows by considering a Multi-Zonal (MZ) approach in modelling turbulence and secondary flows across lateral flow direction. This is an effort to represent natural flows with compound shape more closely. The proposed model improves the estimation of secondary flow by original SKM model to increase the accuracy of depthaveraged velocity profile solution formed within the transitional region between different sections (i.e. between main-channel and floodplain) of compound channel. This proposed MZ model works by sectioning intermediate zones between floodplain and main-channel for running computation in order to improve the modelling accuracy. The modelling results have been validated using the experimental data by national UK Flood Channel Facility (FCF). It has been proven to work reasonably well to model secondary flows within the investigated compound channel flow cases and hence produce better representation to their flow lateral velocity profile.

Dans cette thèse, on s’intéresse à l’approximation numérique d’un modèle d’écoulement dispersif en eau peu profonde. Les applications visées par ce type de modélisation sont nombreuses (écoulement dans les océans, les rivières, etc) et cette thèse est motivée en particulier par les risques naturels et la production d’énergie renouvelable. Le modèle étudié a été dérivé par moyenne selon la verticale des équations d’Euler et prend en compte la pression non-hydrostatique. Il est alors nécessaire de résoudre un système de type incompressible; ce qui nous amène à résoudre une équation elliptique en pression. Nous proposons une méthode numérique pour résoudre le système dispersif avec topographie pour les modèles 1D et 2D. L’approche développée est basée sur un schéma de type prediction-correction, initialement introduit par Chorin-Temam pour les équations de Navier-Stokes. Nous définissons un cadre générique qui permet de concevoir un schéma valable en 1D et 2D et aussi de pouvoir augmenter l’ordre de précision. Ainsi, nous proposons une formulation variationnelle qui nous permet d’appliquer la méthode des éléments finis avec des choix d’espaces compatibles. Le travail effectué étant destiné à simuler des processus géophysiques réels, la méthode a été conçue pour pouvoir traiter les transitions de sol sec/mouillé et cette propriété a été confirmée par plusieurs tests numériques. Afin de valider la méthode, nous présentons la comparaison entre certaines solutions analytiques et leurs simulations numériques. / In this PhD thesis we are interested in the numerical approximation of a dispersive shallow water system, aimed at modeling the free surface flows (e.g. ocean and rivers) and motivated by applications for natural hazards and sustainable energy resources. This model is a depth-averaged Euler system and takes into account a non-hydrostatic pressure which brings crucial information for understanding the behavior of the flow, particularly when dispersion occur. We develop a numerical method for the one- and the two-dimensional dispersive shallow water system with a topography. The approach is based on a prediction-correction method initially introduced by Chorin-Temam, and we establish a global framework in order to easily increase the order of accuracy of the method. The prediction part leads to solving a shallow water system for which we use finite volume methods, while the correction part leads to solving a mixed problem in velocity and pressure. We propose a variational formulation of the mixed problem which allows us to apply a finite element method with compatible spaces. In this framework we establish compatible boundary conditions between the prediction part and the correction part. The method is performed for the one-dimensional model and for the two-dimensional problem on unstructured grids. In order to make the method practical for real geophysical cases, we have derived a scheme able to treat wet/dry interfaces and to this end we give many examples to test its performance. Moreover, we provide a comparison of simulated solutions with data from laboratory experiments.