Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model

This study presents the integration of isotropic color gradient discretization into a lattice Boltzmann Rothman–Keller (RK) model designed for two-phase flow simulation. The proposed model removes one limitation of the RK model, which concerns the handling of O(1000) large density ratios between the fluids for a wide range of parameters. Taylor’s series expansions are used to characterize the difference between an isotropic gradient discretization and the commonly used anisotropic gradient. The proposed color gradient discretization can reduce, by one order of magnitude, the spurious current problem that affects the interface between the phases. A set of numerical tests is conducted to show that a rotationally invariant discretization enables widening of the parameter range for the surface tension. Surface tensions from O(10−2) to O(10−8), depending on the density ratio, are accurately simulated. An extreme density ratio of O(10,000) is successfully tested for a steady bubble with an error of 0.5% for Laplace’s law across a sharp interface, with a thickness of about 5–6 lattice units.