Size consistency in smoothed dissipative particle dynamics

Smoothed dissipative particle dynamics (SDPD) is a mesoscopic method that allows one to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a function of the size of the mesoparticles, both at equilibrium and out of equilibrium. We also propose a reformulation of the SDPD equations in terms of energy variables. This increases the similarities with dissipative particle dynamics with energy conservation and opens the way for a coupling between the two methods. Finally, we present a numerical scheme for SDPD that ensures the conservation of the invariants of the dynamics. Numerical simulations illustrate this approach.