On the effect of force isotropy in a multiphase cascaded lattice Boltzmann scheme with entropic stabilization

The study of multiphase flows is a pivotal topic in natural sciences and engineering. A modeling approach to depict such phenomena combines the Lattice Boltzmann Method (LBM), a mesoscopic Navier-Stokes solver, and the Shan-Chen (SC) pseudopotential method, the latter postulating an interparticle interaction force inducing a spontaneous phase separation within a diffuse interface. To handle the inaccuracy and instability of the naive SC-LBM at high density ratio (DR) and dynamic viscosity ratio (VR), a twofold approach is proposed in recent literature: enhancing the collision process by a Cascaded Lattice Boltzmann Method (CLBM) constrained by a post-collision entropy minimization (KBC), and extending the formulation while tuning parameters of the interaction force to aid thermodynamic consistency, thus damping parasitic discretization effects and enabling surface tension tuning. In our work, we investigate how the interplay between the interparticle force isotropy order and key modeling parameters affects the KBC-CLBM discretization artifacts and stability. The nontrivial results achieved in terms of isotropy effectiveness hierarchy would guide future applied research in the adoption of suitable force stencils, complying with the required physical parameters (DR and VR), while limiting the computational burden. Static tests yield thermodynamically consistent results with the spurious currents magnitude lower than ${10}^{-3}$ lattice units at DR ≈3000 and VR ≈600 in the E8 isotropy order case. The compliance with the Laplace law has been proven, even at tuned surface tension. Droplet oscillation test results show consistency with transient analytical models, especially at E8 and even at higher DR and VR, also with surface tension modulation. Given the model's capabilities, we consider the outcome of our work as a step towards gaining a deeper understanding of natural phenomena and solving engineering problems.