On the Three-dimensional Central Moment Lattice Boltzmann Method

TL;DR

This paper introduces a 3D central moment lattice Boltzmann method that enhances accuracy and Galilean invariance in simulating fluid flows with forces, through novel attractors and semi-implicit source term treatments.

Contribution

It develops a new 3D central moment LBM with improved force handling, frame invariance, and reduced aliasing, based on factorized moments and semi-implicit source terms.

Findings

Accurate simulation of 3D fluid flows with external forces.

Frame-invariant and Galilean invariant dynamics achieved.

Validated with benchmark problems showing high accuracy.

Abstract

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.