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Cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in[Geier \textit{et al.}, Phys. Rev. E \textbf{63}, 066705 (2006)] possesses verygood numerical stability. However, two constraints exist in three-dimensional(3D) CLBM simulations. Firstly, the conventional implementation for 3D CLBMinvolves cumbersome operations and requires much higher computational costcompared to the single-relaxation-time (SRT) LBM. Secondly, it is a challengeto accurately incorporate a general force field into the 3D CLBM. In thispaper, we present an improved method to implement CLBM in 3D. The main strategyis to adopt a simplified central moment set, and carry out thecentral-moment-based collision operator based on a generalmulti-relaxation-time (GMRT) framework. Next, the recently proposed consistentforcing scheme in CLBM [L. Fei and K. H. Luo, Phys. Rev. E \textbf{96}, 053307(2017)] is extended to incorporate a general force field into 3D CLBM. Comparedwith the recently developed non-orthogonal CLBM [A. D. Rosis, Phys. Rev. E\textbf{95}, 013310 (2017)], our implementation is proved to reduce thecomputational cost significantly. The inconsistency of adopting the discreteequilibrium distribution functions (EDFs) in the non-orthogonal CLBM isrevealed and discussed. The 3D CLBM developed here in conjunction with theconsistent forcing scheme is verified through numerical simulations of severalcanonical force-driven flows, highlighting very good properties in terms ofaccuracy, convergence and consistency with the nonslip rule. Finally, thetechniques developed here for 3D CLBM can be applied to make the implementationand execution of 3D MRT-LBM much more efficient.

Three-dimensional cascaded lattice Boltzmann method: improved implementation and consistent forcing scheme