Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation (Communications in Computational Physics, 2012)
We present a systematic derivation of a model based on the central momentlattice Boltzmann equation that rigorously maintains Galilean invariance of forces tosimulate 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 latticeBoltzmann equation are obtained by matching those of the continuous full Boltzmannequation of various orders. This results in an exact hierarchical identity between thecentral moments of the source terms of a given order and the components of the centralmoments of the distribution functions and sources of lower orders. The correspondingsource terms in velocity space are then obtained from an exact inverse transformationdue 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 andsimulation 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 onthe above formulation, a new approach in lattice Boltzmann framework to incorporateturbulence models for simulation of Galilean invariant statistical averaged or filteredturbulent fluid motion is discussed.