Constructing thermodynamically consistent models with a non-ideal equation of state

TL;DR

This paper develops a particle-based fluid model incorporating non-ideal effects with a focus on thermodynamic consistency, using biased collisions to accurately reproduce the equation of state and address density fluctuation issues.

Contribution

It introduces a generalized particle-based model with biased stochastic collisions that ensure thermodynamic consistency for fluids with excluded volume effects.

Findings

Derived the equation of state for the model

Identified criteria for collision probabilities to ensure consistency

Highlighted issues with naive implementations leading to fluctuations

Abstract

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which depend on local velocities and densities and conserve momentum and kinetic energy. The equation of state is derived and criteria for the correct choice of collision probabilities are discussed. In particular, it is shown how a naive implementation can lead to inconsistent density fluctuations.