We present 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 satisfies the first and second laws of thermodynamics. This is done by casting the model into the GENERIC structure. The GENERIC structure ensures thermodynamic consistency and allows for the introduction of correct thermal fluctuations in simple terms. In this way, we obtain a consistent discrete model for Lagrangian fluctuating hydrodynamics. Simulation results are presented that show the validity of the model for simulating hydrodynamic problems at mesoscopic scales.

• Received 13 November 2000

DOI:https://doi.org/10.1103/PhysRevE.64.046115