Coarse-graining of a fluid and its relation with dissipative particle dynamics and smoothed particle dynamics

We propose a coarse-graining procedure for a fluid system that allows us to discuss from a conceptual point of view different ''mesoscopic'' approaches to hydrodynamic problems. Dissipative Particle Dynamics (DPD) and Smoothed Particle Dynamics (SPS) are discussed simultaneously within this framework. In particular, we give physical meaning to the weight function used in SPD. The close analogy between DPD and SPD suggests a synthesis of both approaches that overcomes the conceptual shortcomings of both.