Three-dimensional central-moments-based lattice Boltzmann method with external forcing: A consistent, concise and universal formulation

The cascaded or central-moments-based lattice Boltzmann method (CM-LBM) is a robust alternative to the more conventional BGK-LBM for the simulation of high-Reynolds number flows. Unfortunately, its original formulation makes its extension to a broader range of physics quite difficult. To tackle this issue, a recent work [A. De Rosis, Phys. Rev. E 95, 013310 (2017)] proposed a more generic way to derive concise and efficient three-dimensional CM-LBMs. Knowing the original model also relies on central moments that are derived in an adhoc manner, i.e., by mimicking those of the Maxwell-Boltzmann distribution to ensure their Galilean invariance a posteriori, a very recent effort [A. De Rosis and K. H. Luo, Phys. Rev. E 99, 013301 (2019)] was proposed to further generalize their derivation. The latter has shown that one could derive Galilean invariant CMs in a systematic and a priori manner by taking into account high-order Hermite polynomials in the derivation of the discrete equilibrium state. Combining these two approaches, a compact and mathematically sound formulation of the CM-LBM with external forcing is proposed. More specifically, the proposed formalism fully takes advantage of the D3Q27 discretization by relying on the corresponding set of 27 Hermite polynomials (up to the sixth order) for the derivation of both the discrete equilibrium state and the forcing term. The present methodology is more consistent than previous approaches, as it properly explains how to derive Galilean invariant CMs of the forcing term in an a priori manner. Furthermore, while keeping the numerical properties of the original CM-LBM, the present work leads to a compact and simple algorithm, representing a universal methodology based on CMs and external forcing within the lattice Boltzmann framework.Comment: Published in Phys. Fluids as Editor's Pic

Double-distribution-function discrete Boltzmann model for combustion

A 2-dimensional discrete Boltzmann model for combustion is presented. Mathematically, the model is composed of two coupled discrete Boltzmann equations for two species and a phenomenological equation for chemical reaction process. Physically, the model is equivalent to a reactive Navier-Stokes model supplemented by a coarse-grained model for the thermodynamic nonequilibrium behaviours. This model adopts 16 discrete velocities. It works for both subsonic and supersonic combustion phenomena with flexible specific heat ratio. To discuss the physical accuracy of the coarse-grained model for nonequilibrium behaviours, three other discrete velocity models are used for comparisons. Numerical results are compared with analytical solutions based on both the first-order and second-order truncations of the distribution function. It is confirmed that the physical accuracy increases with the increasing moment relations needed by nonequlibrium manifestations. Furthermore, compared with the single distribution function model, this model can simulate more details of combustion.Comment: Accepted for publication in Combustion and Flam

Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions

We present a mathematical formulation of kinetic boundary conditions for Lattice Boltzmann schemes in terms of reflection, slip, and accommodation coefficients. It is analytically and numerically shown that, in the presence of a non-zero slip coefficient, the Lattice Boltzmann flow develops a physical slip flow component at the wall. Moreover, it is shown that the slip coefficient can be tuned in such a way to recover quantitative agreement with analytical and experimental results up to second order in the Knudsen number.Comment: 27 pages, 4 figure

Lattice Boltzmann Methods for thermal flows: continuum limit and applications to compressible Rayleigh-Taylor systems

We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible Fourier- Navier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-B\'enard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx \times Lz = 1664 \times 4400 and with Rayleigh numbers up to Ra ~ 2 \times 10^10.Comment: 26 pages, 13 figure

Lattice Boltzmann Method for mixtures at variable Schmidt number

When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook (BGK) evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.Comment: 18 pages, 6 figure