Particle methods for ideal fluids, such as smoothed particle hydrodynamics (SPH), lead to finite-dimensional Newtonian equations of motion that are similar in structure to those used in MD simulations. In fact, SPH-type equations are sometimes also considered as mesoscopic models arising from an atomistic descriptions. Whatever point of view is taken, one has to deal with the problem of different time and length-scales associated with fast non-advective vibrational
modes and slow large-scale deformations. Again, these phenomena are common to molecular as well as fluid dynamics. After an introduction to SPH, we will address these issues by looking at the problem of shallow water flows. A few ideas that we will toss around are: averaged fluid equations/large eddy simulations, particle-mesh methods, multiple-time-stepping, geometric integration.