In the absence of viscosity, fluid dynamics can be derived from a Hamiltonian principle which implies conservation of energy and other symmetry invariants [1]. Under those circumstances, it appears as desirable to obtain spatial truncations that are conservative and satisfy a discrete Hamiltonian principle. In my talk, I will discuss one particular approach for the rotating shallow-water equations which is based on a combination of Lagrangian particles and an Eulerian grid. The resulting method is similar to classical particle-in-cell (PIC) methods. However, contrary to standard PIC methods, the new Hamiltonian particle-mesh (HPM) method [3] conserves circulation, mass, and energy. For a discussion of these conservation properties in the context of smoothed particle hydrodynamics (SPH) see [2]. The HPM method (and the related method [4]) should allow for a more rigorous study of the statistical mechanics of shallow water flows similar to what has been achieved for the point vortex model of incompressible flows.