| Summary: | Isothermal flows of viscous (Newtonian) fluids without body forces are considered in this thesis. A two-dimensional numerical method based on the vorticity transport equation is used to simulate flows for three different model geometries. Specifically, the Random Vortex method is combined with the Vortex-In-Cell algorithm. In this mixed Eulerian-Lagrangian method, the main discretization is performed on the vorticity field, which is represented by a number of singular Lagrangian vortex elements. These vortex elements are generated on solid walls to verify the no-slip condition and are subsequently transported in time according to the vorticity transport equation. The laminar starting flow down a step is a well defined flow. Considering this flow model, instantaneous numerical simulations have been carried out and the results are compared to experimental results in the literature. Good agreement is obtained. Analysis of the numerical results and comparisons to experimental results show that for low Reynolds number flows (Re = 97), the recirculation zone is composed of one vorticity region throughout the simulations. For higher Reynolds number flows (Re = 153 and 303), the recirculation zone is respectively composed of three and four distinct vorticity regions at intermediate stages of its development, while for later times the structures inside the recirculation zone are not clearly defined. During intermediate stages of the flow development, and for the range of Reynolds numbers investigated, the distance from the step to the reattachment point of the main vorticity region increases quasi-linearly with the dimensionless time. Again, good agreement is obtained between experimental data and computed solutions. Using the same flow model, we present a numerical convergence proof by successively refining the numerical parameters. It is shown that the refinement of the vorticity generation parameters seems to primarily affect the smoothness of the solution rather than the overall structure of the flow. On the other hand, it is shown that for a given time step, higher order convection schemes improve the overall flow structure. Steady state numerical simulations were performed. Numerical streamwise velocity profiles are compared to their experimental counterparts for four Reynolds number flows (Re = 73, 125, 191 and 229). The computed length of the recirculation zone is also compared to various results. In all steady step flows, excellent agreement was obtained. Finally, both steady and unsteady flow simulations were performed on a model representing the cavities that result from the shingle-like arrangement of the scales on the upper surface of a butterfly wing. In gliding flight, the lifting force was experimentally proven to be stronger on a wing with scales. Excellent agreement is obtained in comparing results of our numerical simulations to experimental results in the literature. In particular, for low and very low Reynolds number flows (Re = 0.62, 1.00, 3.30 and 100), the recirculation zone is composed of one primary vorticity region. For higher Reynolds number flows (Re = 624), the recirculation zone area exhibits strong dynamics where coherent structures are shed at regular intervals from the vertical wall and eventually coalesce during intermediate stages of the developing flow"--Résumé abrégé par UMI
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