Abstarct: Interactions and collision among suspended particles in a fluid such as polymers, colloids, nanoparticles and others because of their wide range of practical applications in applied physics and theoretical fields are of interests among researchers. This phenomenon is widely used in the drug delivery systems, filtration, fuel and combustion and also enhanced oil recovery. Although experimental studies due to their reliable results are cherished, but they suffer from some shortcomings. Recently, as a result of advances in computational programming numerical methods have been such good substitutes. Out of many the hybrid immersed boundary-lattice Boltzmann method (IB-LBM) which is an Eulerian-Lagrangian approach has been a powerful tool to simulate systems containing particles. Using this robust method, researchers are able to simulate various problems with different geometry, size and particle numbers. Most of the previous studies related to moving boundaries are limited to circular particles with identical size. Different factors govern the sedimentation manners of the moving particles. Among them outline and size of the immersed body have a considerable role. Also, in practice and industrial usages most of the particles have an outline beside the circular shape. Among non-circular particles, ellipse due to its physical appearance and distinguished application has gained much more attention. In this thesis we aimed at developing the IB-LBM to simulate and study the sedimentation behavior of elliptical particle in the laminar state. Thus, a new and robust method to handle the collision among solid surfaces has been proposed. To do so, a review study has been conducted on the existed methods in this subject which are mostly restricted to circular bodies. This subject is important because numerical methods are in need of an explicit method to calculate forces stem from collision among solid surfaces, numerical methods fail to act adequately while particles are in close contact with each other or the wall. Consequently, an explicit method is absolutely in need. Utilizing the proposed complementary algorithm, sedimentation of circular particles in an enclosure is carried out to validate the code and method. The effect of particle size on the Drafting Kissing Tumbling (DKT) phenomena has been investigated. Then, freefalling of a single ellipse in a narrow box including the impact of wall on the sedimentation manner is revealed. Sedimentation manner of two elliptical particles at different configurations is also examined. The problem of a hybrid system of particles with various sizes and shapes in an enclosure containing Newtonian fluid is done to show the reliability of the suggested repulsive force model. Most of the multiphase flows are happening under the influence of thermal aspect on the particles freefalling. Using the IB-LBM and applying the recommended collision method, effects of heat transfer on circular and elliptical particles sedimentation is inspected. Moreover, using the obtained results from numerical modeling, the impact of some parameters such as, size, shape, density ratio, Grashof number, aspect ratio on the particles freefalling and DKT phenomena is explored. The new repulsive force model in the IB-LBM frxame can be used to properly simulate biologic problems and injecting particles in a microfluidic device.