Thermodynamically admissible form for discrete hydrodynamics

TL;DR

This paper develops a discrete fluid model based on the GENERIC formalism that conserves key physical quantities, incorporates thermal fluctuations, and reproduces thermodynamic behavior accurately, unifying SPH and DPD approaches.

Contribution

It introduces a thermodynamically consistent discrete hydrodynamics model that combines features of SPH and DPD with correct fluctuation and entropy properties.

Findings

Model conserves mass, momentum, and energy.

Entropy is non-decreasing over time.

Thermal fluctuations match the Einstein distribution at equilibrium.

Abstract

We construct a discrete model of fluid particles according to the GENERIC formalism. The model has the form of Smoothed Particle Hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the Dissipative Particle Dynamics model with any desired thermodynamic behavior. The resulting algorithm has the following properties: mass, momentum and energy are conserved, entropy is a non-decreasing function of time and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.