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

Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

The discrete unified gas kinetic scheme (DUGKS) was originally developed for single-species flows covering all the regimes, whereas the gas mixtures are more frequently encountered in engineering applications. Recently, the DUGKS has been extended to binary gas mixtures of Maxwell molecules on the basis of the Andries–Aoki–Perthame kinetic (AAP) model [P. Andries et al., “A consistent BGK-type model for gas mixtures,” J. Stat. Phys. 106, 993–1018 (2002)]. However, the AAP model cannot recover a correct Prandtl number. In this work, we extend the DUGKS to gas mixture flows based on the McCormack model [F. J. McCormack, “Construction of linearized kinetic models for gaseous mixtures and molecular gases,” Phys. Fluids 16, 2095–2105 (1973)], which can give all the transport coefficients correctly. The proposed method is validated by several standard tests, including the plane Couette flow, the Fourier flow, and the lid-driven cavity flow under different mass ratios and molar concentrations. Good agreement between results of the DUGKS and the other well-established numerical methods shows that the proposed DUGKS is effective and reliable for binary gas mixtures in all flow regimes. In addition, the DUGKS is about two orders of magnitude faster than the direct simulation Monte Carlo for low-speed flows in terms of the wall time and convergent iteration steps

Overview of the entropy production of incompressible and compressible fluid dynamics

In this paper, we present an overview of the entropy production in fluid dynamics in a systematic way. First of all, we clarify a rigorous derivation of the incompressible limit for the Navier–Stokes–Fourier system of equations based on the asymptotic analysis, which is a very well known mathematical technique used to derive macroscopic limits of kinetic equations (Chapman–Enskog expansion and Hilbert expansion are popular methodologies). This allows to overcome the theoretical limits of assuming that the material derivative of the density simply vanishes. Moreover, we show that the fundamental Gibbs relation in classical thermodynamics can be applied to non-equilibrium flows for generalizing the entropy and for expressing the second law of thermodynamics in case of both incompressible and compressible flows. This is consistent with the thermodynamics of irreversible processes and it is an essential condition for the design and optimization of fluid flow devices. Summarizing a theoretical framework valid at different regimes (both incompressible and compressible) sheds light on entropy production in fluid mechanics, with broad implications in applied mechanics

Lattice Boltzmann method for miscible gases: A forcing-term approach

A lattice Boltzmann method for miscible gases is presented. In this model, the standard lattice Boltzmann method is employed for each species composing the mixture. Diffusion interaction among species is taken into account by means of a force derived from kinetic theory of gases. Transport coefficients expressions are recovered from the kinetic theory. Species with dissimilar molar masses are simulated by also introducing a force. Finally, mixing dynamics is recovered as shown in different applications: an equimolar counterdiffusion case, Loschmidt's tube experiment, and an opposed jets flow simulation. Since collision is not altered, the present method can easily be introduced in any other lattice Boltzmann algorithms.Thèse CNAM

A kinetic perspective on k-epsilon turbulence model and corresponding entropy production

In this paper, we present an alternative derivation of the entropy production in turbulent flows, based on a formal analogy with the kinetic theory of rarefied gas. This analogy allows proving that the celebrated k-epsilon model for turbulent flows is nothing more than a set of coupled BGK-like equations with a proper forcing. This opens a novel perspective on this model, which may help in sorting out the heuristic assumptions essential for its derivation, such as the balance between turbulent kinetic energy production and dissipation. The entropy production is an essential condition for the design and optimization of devices where turbulent flows are involved