@Article{CiCP-12-732,
author = {Kannan N. Premnath and Sanjoy Banerjee},
title = {Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation},
journal = {Communications in Computational Physics},
year = {2012},
volume = {12},
number = {3},
pages = {732--766},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.181210.090911a},
url = {http://global-sci.org/intro/article_detail/cicp/7312.html}
}