The hydroabrasive erosion of hydraulic machine components, especially Pelton buckets and needles, is a widespread problem that entails significant costs. The multiscale nature of the process renders its simulation very computationally demanding unless specific strategies are used to approach it. A previously validated multiscale model of erosion that tackles the problem of spatial scale separation is presented. It involves two coupled submodels that describe the microscopic sediment impacts and the macroscopic turbulent sediment transport, respectively, without introducing the uncertainty inherent to empirical erosion correlations. As a further step and in order to circumvent the temporal scale separation, a novel projective integration scheme is introduced. It allows simulating the erosion process for long time periods, including the eroded surface evolution and its effect on the flow field. The proposed model is tested on a 2D case involving a bucket being eroded by a slurry jet. The results are compared qualitatively with experimental data on Pelton buckets. The main features of the erosion distribution, the surface transformation and its effect on the flow are captured correctly.