Neste trabalho, apresenta-se um estudo a respeito de problemas de interação Fluido-Partícula e dos métodos e formulações usados para resolvê-los. Além disso, propõe-se um novo método para resolver problemas acoplados de mecânica dos fluidos e mecânica das partículas. A ideia é baseada em trabalhos anteriores de (Gomes e Pimenta 2015) e (Campello 2016), e o objetivo é desenvolver um modelo computacional adequado e eficiente para simular problemas envolvendo fluidos carregados com partículas sólidas. O problema de fluido é resolvido por uma abordagem Euleriana de elementos finitos, usando elementos mistos locais de velocidade-pressão, os quais satisfazem a condição de compatibilidade LBB. O sistema de equações não linear obtido é resolvido iterativamente pelo método de Newton-Raphson. Uma característica importante é que a malha de fluidos permanece fixa durante a passagem do fluxo, assim como nas abordagens Eulerianas clássicas. O problema das partículas, por sua vez, é resolvido com uma abordagem Lagrangiana de elementos discretos, em que os contatos de partícula com partícula e partícula com paredes (limites fixos) são livremente permitidos e resolvidos. A influência do fluido no movimento das partículas é representada por meio de forças e momentos, que são calculados a partir do escoamento e impostos às partículas de maneira acoplada, iterativa e explícita. As interfaces entre o fluido e as partículas são tratadas por meio da técnica de fronteiras imersas, onde as condições de contorno do fluido nos contatos com partículas são impostas através da interpolação de funções descontínuas e constantes de multiplicadores de Lagrange ao longo das interfaces. É adotado um método explícito, interativo e escalonado para conseguir a convergência dentro de cada passo de tempo do problema. Para ilustrar o potencial do método proposto, são apresentadas simulações de escoamentos carregados de partículas. / In this work, a study is presented on Fluid-Particle interaction problems and the methods and formulations used to solve them. In addition, is proposed a new method for solving coupled problems of fluid mechanics and particle mechanics. The idea is based on previous works by (Gomes e Pimenta 2015) and (Campello 2016), and the goal is to develop an efficient computational model suited to simulate problems involving flowing fluid media laden with solid particles. The fluid problem is resolved by an Eulerian finite element approach using local element velocity-pressure pairs satisfying the LBB compatibility condition, with the resulting nonlinear system of equations being iteratively solved by the Newton-Raphson method. As an important feature, the fluid mesh remains fixed during the flow, just as in classical Eulerian approaches. The particles´ problem, in turn, is resolved in a Lagrangian discrete element approach, wherein both particle-to-particle and particle-to-wall (fixed boundaries) contacts are freely permitted and resolved. The influence of the fluid on the motion of the particles is represented by means of forces and moments, which are computed from the fluid flow and imposed on the particles in a coupled, iterative and explicit way. The fluid-particles´ interfaces are treated by means of immersed boundary technique, in which the fluid interface conditions with the (nonmatching) particles´ boundaries are imposed through discontinuous piecewise constant Lagrange multipliers interpolating functions along the interfaces. An explicit, staggered and interactive scheme is adopted to achieve convergence within each time step of the problem. In order to illustrate the potentialities of the proposed scheme, particle-laden fluid flow simulations are presented.

Ce travail de thèse a pour objet l’étude numérique et expérimentale de la déstabilisation de milieux granulaires immergés par fluidisation. Cette instabilité hydromécanique est un mécanisme précurseur de l’érosion régressive, processus de dégradation au coeur de la problématique de l’érosion interne des ouvrages hydrauliques en terre. La compréhension de ces mécanismes d’érosion nécessite une description rigoureuse du couplage et de l’interaction entre le fluide et les particules de sol. A cette fin, un modèle 2D a été utilisé en couplant deux méthodes particulaires, la méthode des éléments discrets (DEM) pour modéliser le comportement mécanique de la phase solide et la méthode Lattice Boltzmann (LBM) pour la phase fluide. Des expériences servant de validation à cette simulation numérique 2D ont également été réalisées en s’appuyant sur une technique de visualisation interne d’un empilement granulaire combinant l’ajustement d’indice de réfraction des deux phases et la fluorescence induite par plan laser. / The subject of this thesis is the numerical analysis and experimental investigation of the destabilization of submerged granular media caused by fluidization. This hydromechanical instability is one of the mechanisms that may trigger the regressive erosion, which is one of the main degradation phenomena driving the internal erosion of earthen hydraulic constructions. Such erosion mechanisms can only be understood through a rigorous description of the coupling and interaction between the eroding fluid and the soil particles. For this purpose, a 2D model has been used coupling two different numerical techniques, namely the discrete element method (DEM) for modelling the mechanical behaviour of the solid phase and the Lattice Boltzmann method (LBM) for the fluid phase. The experimental validation of this numerical 2D simulation has been carried out using two optical techniques for the internal visualization of a granular sample, namely the adjustment of the refraction index of the two phases and the laser-induced fluorescence.