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

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.Comment: 37 pages, 1 figur

Simulation of immiscible two-phase flows based on a kinetic diffuse interface approach

International audienceA direct numerical simulation (DNS) code is developed to simulate immiscible two-phase flows based on the recently developed discrete unified gas-kinetic scheme (DUGKS). This scheme simulates hydrodynamic equations of the quasi-incompressible Cahn-Hilliard-Navier-Stokes system by the use of two mesoscopic distributions and the proper design of their equilibrium distributions and source terms. Several immiscible two-phase flows are used to validate the scheme in both 2D and 3D, including a stationary droplet in 2D and 3D, the Rayleigh-Taylor flows, and two-phase homogeneous isotropic decaying turbulence. The results obtained by DUGKS are compared carefully to these from the literature and the ARCHER code, i.e., a Coupled Level Set-Volume of Fluid (CLSVOF) method. The comparisons indicate that DUGKS is a promising scheme for direct numerical simulations of immiscible two-phase flows