Interface Width and Bulk Stability: requirements for the simulation of Deeply Quenched Liquid-Gas Systems

TL;DR

This paper derives criteria for the minimum interface width in lattice Boltzmann simulations of liquid-gas systems to ensure accuracy and stability, enabling high density ratio simulations previously thought infeasible.

Contribution

It introduces a minimum interface width criterion and combines it with bulk stability predictions to identify stable, accurate simulation parameters for high density ratios.

Findings

Derived minimum interface width for accurate simulations

Predicted stable parameter ranges for high density ratios

Enabled simulations of density ratios over 1000

Abstract

Simulations of liquid-gas systems with extended interfaces are observed to fail to give accurate results for two reasons: the interface can get ``stuck'' on the lattice or a density overshoot develops around the interface. In the first case the bulk densities can take a range of values, dependent on the initial conditions. In the second case inaccurate bulk densities are found. In this communication we derive the minimum interface width required for the accurate simulation of liquid gas systems with a diffuse interface. We demonstrate this criterion for lattice Boltzmann simulations of a van der Waals gas. When combining this criterion with predictions for the bulk stability we can predict the parameter range that leads to stable and accurate simulation results. This allows us to identify parameter ranges leading to high density ratios of over 1000. This is despite the fact that lattice Boltzmann simulations of liquid-gas systems were believed to be restricted to modest density ratios of less than 20.