Interface width and bulk stability: Requirements for the simulation of deeply quenched liquid-gas systems

Simulations of liquid-gas systems with interface terms evaluated by central difference discretizations 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. We derived the minimum interface width required for the accurate simulation of liquid-gas systems with a diffuse interface. This criterion is demonstrated for lattice Boltzmann simulations of a van der Waals gas. Combining this criterion with predictions for the bulk stability defines the parameter range for stable and accurate simulation results even for high density ratios of over 1000.