  The GENERIC structure allows for a unified treatment of different discrete
models of hydrodynamics. We first propose a finite volume Lagrangian
discretization of the continuum equations of hydrodynamics through the Voronoi
tessellation. We then show that a slight modification of these discrete
equations has the GENERIC structure. The GENERIC structure ensures
thermodynamic consistency and allows for the introduction of correct thermal
noise. In this way, we obtain a consistent discrete model for Lagrangian
fluctuating hydrodynamics. For completeness, we also present the GENERIC
versions of the Smoothed Particle Dynamics model and of the Dissipative
Particle Dynamics model. The thermodynamic consistency endorsed by the GENERIC
framework allows for a coherent discussion of the gas-liquid phase coexistence
of a van der Waals fluid.
