Comparative analysis and computational optimization of potential-based multiphase lattice Boltzmann models

Abstract

The potential-based multiphase lattice Boltzmann models are widely used because they root in thermodynamics and evade the interface tracking or integrating. This paper investigates several potential-based models with the common equations of state (EOS) by the theoretical analyses and numerical computations of the thermodynamic consistency and spurious currents. Surprisingly, the Shan–Chen model presents a superior accuracy compared to the Zhang–Chen models, although they are mathematically equivalent. We find that the great improvement is attributed to the square root form of the pseudopotential model, which significantly lessens the error of numerical gradient calculation. Inspired by the improvement, a general formula φ′=n−1φ1−n∂x(φn) is introduced for calculating the gradient, and the coefficient n=0.1 yields better results than n=0.5, which is equal to the pseudopotential model. This scheme is further applied to optimize the evaluation of the chemical potential model. The improved chemical potential model displays lower numerical errors in the liquid–gas transition region and smaller spurious currents near the curved phase interface than the pseudopotential model. Additionally, the improved model is confirmed to meet the Young–Laplace law and Galilean invariance.