A structurally compatible forcing scheme for three-dimensional cumulant lattice Boltzmann method

Abstract

This study introduces a structurally compatible forcing scheme for the three-dimensional cumulant lattice Boltzmann method (LBM) based on the D3Q27 velocity set, and successfully integrates the pseudopotential model into the three-dimensional cumulant LBM framework. Asymptotic analysis confirms the scheme’s capability to recover the macroscopic Navier–Stokes equations, demonstrating its compatibility with the cumulant LBM structure. Numerical experiments reveal that under constant external force fields, the proposed scheme reduces the relative errors from 2.44$\times 10^{-5}$ (the conventional scheme) to 4.09$\times 10^{-8}$ by accounting for high-order cumulants in the force coupling. Notably, the integration of the pseudopotential model via this scheme effectively suppresses anisotropic distortions observed in the traditional scheme, reducing the maximum dimensionless radial deviation of the droplet from 7.21% to 0.11%. Furthermore, wettability simulations confirm the reliability of the scheme, showing a strong linear correlation ($R^2>0.99$) between the contact angle and the adhesive parameter $G_w$. Additionally, droplet collision tests validate its robustness in dynamic scenarios. This work develops a structurally compatible forcing scheme for the three-dimensional cumulant LBM, which modifies the force effects on high-order cumulants. The proposed scheme maintains the cumulant-based LBM structure while enabling robust simulations across diverse flow regimes, from single-phase flow to dynamic droplet collision.