Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation

TL;DR

This paper develops a Galilean invariant lattice Boltzmann model using central moments to accurately simulate inertial frame independent turbulent flows, incorporating turbulence models for filtered turbulence simulations.

Contribution

It introduces a systematic derivation of a central moment-based lattice Boltzmann model that maintains Galilean invariance and extends to turbulence modeling for filtered turbulent flows.

Findings

Achieved Galilean invariance in force modeling for lattice Boltzmann methods.

Extended the model to include reduced compressibility for incompressible flows.

Proposed a new approach for turbulence simulation within the lattice Boltzmann framework.

Abstract

We present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.