A new lattice Boltzmann (LB) model is introduced, based on a regularization of the pre-collision distribution functions in terms of the local density, velocity, and momentum flux tensor. The model dramatically improves the precision and numerical stability for the simulation of fluid flows by LB methods. This claim is supported by simulation results of some 2D and 3D flows.
We present a regularized version of the color gradient lattice Boltzmann (LB) scheme for the simulation of droplet formation in microfluidic devices of experimental relevance. The regularized version is shown to provide computationally efficient access to Capillary number regimes relevant to droplet generation via microfluidic devices, such as flow-focusers and the more recent microfluidic step emulsifier devices.
The present work is dedicated to a better understanding of the stability properties of regularized lattice Boltzmann (LB) schemes. To this extent, linear stability analyses of two-dimensional models are proposed: the standard Bhatnagar-Gross-Krook (BGK) collision model, the original pre-collision regularization and the recursive regularized model, where off-equilibrium distributions are partially computed thanks to a recursive formula. A systematic identification of the physical content carried by each LB mode is done by analyzing the eigenvectors of the linear systems. Stability results are t…
We investigate the applicability of the Method of Regularized Stokeslets (MRS) in the simulation of micro-swimmers at low Reynolds number. The chosen model for the study is the well-known three linked spheres swimmer. We compare our results with the lattice Boltzmann method, multiparticle collision dynamics, a numerical solution of the Oseen tensor equation and an analytical solution, all taken from Earl $\textit{et al.}$ [J. Chem. Phys. 126, 064703 (2007)]. The MRS is studied in detail, and our results show an excellent agreement with the lattice Boltzmann method, and with the analytical solu…
This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical prob…
With the aim of better understanding the numerical properties of the lattice Boltzmann method (LBM), a general methodology is proposed to derive its hydrodynamic limits in the discrete setting. It relies on a Taylor expansion in the limit of low Knudsen numbers. With a single asymptotic analysis, two kinds of deviations with the Navier-Stokes (NS) equations are explicitly evidenced: consistency errors, inherited from the kinetic description of the LBM, and numerical errors attributed to its space and time discretization. The methodology is applied to the Bhatnagar-Gross-Krook (BGK), the regula…
The Boltzmann equation becomes invalid as the size of gas molecules is comparable with the average intermolecular distance. A better description is provided by the Enskog collision operator, which takes into account the finite size of gas molecules. This extension implies non-local collisions as well as an increase in collision frequency, making it computationally expensive to solve. An approximation of the Enskog collision operator, denoted the simplified Enskog collision operator, is used in this work to develop a quadrature-based Lattice Boltzmann model for non-ideal monatomic dense gases. …
A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on an extended equilibrium state that is constructed to reproduce the first 13 moments of the Maxwell-Boltzmann distribution exactly. This extends the validity of the standard 5-constraint (mass, momentum and energy) approach and leads to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times t…
A non-local quasi-equilibrium state in the Bhatnagar-Gross-Krook Boltzmann equation for thermo-hydrodynamics: Conservation laws, the Boltzmann H-theorem, and the fluctuation-dissipation theorem
本研究利用动量生成子解析技术，在 BGK 玻尔兹曼方程中提出一种包含长程相互作用的非局部准平衡态表述，导出可灵活选择输运系数和状态方程的热流体动力学方程，并验证了其与守恒定律、玻尔兹曼 H 定理及涨落耗散定理的一致性。
A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the weight defined by the equilibrium distribution function itself. The D-dimensional Hermite polynomials is a sub-case of the present ones, associated to the particular weight of a gaussian function. The proposed lattice Boltzmann method allows for the treatment of semi-classical fluids, such as electrons in metals under the Drude-Sommerfeld model, which is a part…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of the resulting solver has been the topic of discussions in the literature. Here we present a rigorous analysis of the hydrodynamics and numerics of the entropic. In doing so we demonstrate that the entropic equilibrium features unconditional linear stability, in contrast to the conventional polynomial equilibrium. We reveal the mechanisms through which uncond…
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding…
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, …
The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expa…
A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic moments of discrete equilibrium distribution function. Such a model possesses both an adjustable specific heat ratio and Prandtl number, and can be applied to a wide range of flow regimes including continuous, slip, and transition flows. To recover results for actual situations, the nondimensionalization process is demonstrated. To verify and validate the ne…
We present a series of three-dimensional discrete Boltzmann (DB) models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely solving the kinetic moment relations that it satisfies. The crucial physical requirement is that all the used kinetic moment relations must be consistent with the non-equilibrium statistical mechanics. The necessity of such a kinetic model is that, with increasing the complexity of flows, the dynamical characterization of non-equilibrium state and the understand…
A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing detailed inspection of various non-equilibrium observables. Based on the TNE features, we define a TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a c…
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-…
In this article, we propose a generalized non-equilibrium chemical kinetics model from \textit{ab initio} simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross-section model for dissociation that captures recent \textit{ab initio} data accurately. The cross-section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorpo…
Istituto per le Applicazioni del Calcolo CNR（意大利国家研究委员会计算应用研究所）；Roma Tre University（罗马第三大学）；INFN ”Tor Vergata”（意大利国家核物理研究所托尔维尔加塔分部）；Department of Physics, Harvard University（哈佛大学物理系）
In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchm…
In this paper we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, separating entropy fluxes and production rates properly, and determining a dissipation matrix. Our approach takes the advantage of both EIT and GENERIC formalisms, and shows a direct correspondence with Levermore's moment closure hierarchies for the Boltzmann…
Numerical simulation results of basic exactly solvable fluid flows using the previously proposed Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear …
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the governing equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as a discrete velocity Boltzmann system. As a result of this interpretation, the local equilibrium distribution functions are simple algebraic functions of the conserved variables and the fluxes, without the low Mach number expansion present in the equilibrium distribution of the traditional Lattice Boltzmann Method (LBM). This new Lattice Boltzmann Relaxation S…
