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The prediction of hydraulic machines performances is of high interest to manufacturers in today's highly competitive market for new development or refurbishment of hydraulic power plant. An accurate prediction of the machines performances by numerical simulation allows to reduce the time required for the design phase. In order to predict the resulting torque of a Pelton turbine, the physics of the free jet has to be modeled accurately. Indeed, the deviation of the high-speed water jet is the key phenomenon, which produces the wall pressure field on the buckets and defines the trajectories of the water sheets in the casing. The purpose of this Doctoral Thesis is to develop and define the methodology for new numerical simulations, which capture accurately the deviation of high-speed jet flows. The use of particle-based methods is investigated instead of using conventional grid-based methods. The advantage of particle-based methods is their Lagrangian formulation, which avoids the well-known difficulties of the mesh generation for complex geometries with moving interfaces. Finite Particle Method (FPM) and Finite Volume Particle Method (FVPM) are used to improve the overall accuracy of the simulations compared to standard Smoothed Particle Hydrodynamics (SPH). The drawback of particle-based methods is their significant increase of computational costs compared to conventional grid-based methods. To mitigate this drawback, the simulations are performed with the FPM/FVPM solver SPHEROS developed at EPFL for massively parallel simulations on the Lemanicus BG/Q supercomputer. A new adaptive domain decomposition strategy is proposed to perform efficient highly parallelized simulations. The development of the FPM/FVPM solver is validated by comparing its results with experimental data and conventional grid-based simulations for different test cases. First, the impinging jet on a flat plate validates that FPM and FVPM are able to capture accurately the free surface location as well as the pressure profile on the flat plate at different impinging angles. Second, the steady bucket analysis highlights the convergence of the FVPM results according to the spatial discretization. Finally, the rotating buckets analysis shows that the pressure field in the buckets inner wall is in good agreement with the experimental and numerical data and the evolution of the relative flow pattern matches the flow high-speed visualization. Moreover, the FVPM simulation is able to capture the pressure peak during the impingement first stage, which is also highlighted in the measurements.