Nonorthogonal central-moments-based lattice Boltzmann scheme in three dimensions

Abstract

We present an alternative three-dimensional lattice Boltzmann collision operator consisting of a nonorthogonal basis of central moments. Our formulation is characterized by an intelligible derivation with a relatively simple and quite general implementation. It is successfully validated against several established, well-consolidated, well-defined benchmark problems, showing excellent properties in terms of accuracy and convergence. If compared to the adoption of the classical Bhatnagar-Gross-Krook operator, our model possesses superior stability.

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

“…Compared with the method in Ref. [40], where the computational cost overhead ratio is about 7.0, the present implementation shows significant reduction in the computational cost.…”

“…It is known that the most computationally demanding part in 3D CLBM is the reconstruction step of the postcollision DFs [22,29,40]. In the present work, the computational cost can be reduced significantly due to the facts that: first, the reconstruction step is divided into two substeps; second, the simplified central moment set is used such that the elements in M −1 and N −1 are much simplified (see Appendix B).…”

“…We consider the same problem under different mesh sizes, i.e., 5 × 101 × 5, 5 × 201 × 5, and 5 × 401 × 5, and measure the CPU time required for 10 000 iterations by SRT-LBM, the present CLBM and the previous CLBM in Ref. [40]. For each case, the CPU time is the average value after removing the minimum and maximum in nine runs.…”

Alternative formulation to incorporate forcing terms in a lattice Boltzmann scheme with central moments

“…[29,30]. In this case, the central moments are Here, we have derived the scheme for the D2Q9 and D3Q27 models.…”

“…Again, the binomial theorem has been adopted to construct such a forcing operator. Despite its effectiveness and excellent numerical properties, it may lead to cumbersome practical implementations that are particularly evident in three dimensions [29,30]. This paper proposes a different strategy to model external forces in a CM-based collision kernel.…”