Hydropower has been identified as a key technology to mitigate climate change due to its very low lifecycle greenhouse gas emission intensity and its capacity to integrate intermittent renewable energy sources such as wind and solar into the electrical grid. One of the problems that limits a wider adoption of hydropower is the erosive wear that hydraulic turbines are subject to when operated under sediment-laden water. The technical capacity to predict the erosion process of prototype-scale machines is instrumental to the optimization of the runner designs and the operation strategies of hydroelectric plants. However, this technical capacity is lacking: neither laboratory experiments nor traditional numerical simulations are capable of delivering quantitative predictions. The difficulty of simulating the erosion process is explained by its multiscale character: it is a very gradual modification of large surfaces, yet it is the consequence of trillions of ephemeral impacts by microscopic sediments. This thesis presents a novel multiscale model of erosion that bypasses the need for erosion correlations by explicitly simulating the sediment impacts, without sacrificing the scope to simulate the long-term erosion process of an industrial-scale component. The proposed model is composed of two sequentially coupled submodels: the microscale model describes the particle impacts with all the detail required to accurately capture the high strain rate thermomechanical process involved; the macroscale model describes the turbulent sediment transport and the accumulation of erosion on the domain of interest. A projective integration scheme is used together with the multiscale model to simulate the long-term transformation of the surface and its effects on the hydrodynamics and subsequently on the erosion rate. After introducing the model formulation, a detailed discussion of the simplifications inherent to the multiscale approach and the modeling assumptions is presented. The finite volume particle method used to discretize the governing equations is introduced next, followed by the experimental characterization of the runner material. Four case studies are used to assess, verify and validate the proposed multiscale model. The first case study deals with the erosion of a flat plate by an impinging jet; convergence, parametric and sensitivity analyses of the microscale and macroscale models are presented, as well as a first satisfactory validation. The second case study demonstrates the use of projective integration to predict the long-term surface transformation of a 2D bucket and its effects on the outlet angle and reaction force; a feedback whereby the surface alteration increases the erosion rate is evidenced. The third case study deals with the erosion of a static prototype-scale Pelton bucket whereas the fourth case study involves a rotating prototype-scale Pelton runner; satisfactory validations of the erosion distribution results are presented for both cases. The results obtained, namely quantitative predictions of the erosion of industrial-scale components, have no precedent in the literature. Furthermore, the model is shown to provide physically sound descriptions of the underlying impact condition distributions that explain the erosion distributions obtained. Overall, it can be said that the multiscale model is a significant improvement over the state-of-the-art models in regard to accuracy and transferability.