We propose a two-population lattice Boltzmann model on standard lattices for the simulation of compressible flows. The model is fully on-lattice and uses the single relaxation time Bhatnagar-Gross-Krook kinetic equations along with appropriate correction terms to recover the Navier-Stokes-Fourier equations. The accuracy and performance of the model are analyzed through simulations of compressible benchmark cases including Sod shock tube, sound generation in shock-vortex interaction and compressible decaying turbulence in a box with eddy shocklets. It is demonstrated that the present model provides an accurate representation of compressible flows, even in the presence of turbulence and shock waves.
Rooted from the gas kinetics, the lattice Boltzmann method is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate the rarefied gas flow beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (i.e. D2Q36), is accurate up to the early transition flow regime, the latter method, with the same discrete velocities as that used in simulating hydrodynamics (i.e. D2Q9), is ac…
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational effi…
This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature. In that context, elements of kinetic theory of ideal gases are presented and discussed at length. Then a detailed discussion of the lattice Boltzmann method for ideal gases from discretization to Galilean invariance issues and different collision models along with their effect on stability and consistency at the hydrodynamic level is presented. Extension to non-ideal …
In this paper, we present the algorithm for the simulation of a single bubble rising in a stagnant liquid using Euler-Lagrangian (EL) approach. The continuous liquid phase is modeled using BGK approximation of lattice Boltzmann method (LBM), and a Lagrangian particle tracking (LPT) approach has been used to model the dispersed gas (bubble) phase. A two-way coupling scheme is implemented for the interface interaction between two phases. The simulation results are compared with the theoretical and experimental data reported in the literature and it was found that the presented modeling technique…
We present a systematic procedure for the construction of relativistic lattice Boltzmann models (R-SLB) appropriate for the simulation of flows of massless particles. Quadrature rules are used for the discretization of the momentum space in spherical coordinates. The models are optimized for one-dimensional flows. The applications considered in this paper are the Sod shock tube and the one-dimensional boost invariant expansion (Bjorken flow). Our models are tested against exact solutions in the inviscid and ballistic limits. At intermediate relaxation times (finite viscosity), we compare with …
Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nanopores ranging in size from a few to hundreds of nanometers. In addition to the noncontinuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation-Maxi…
A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales
Huazhong University of Science and Technology（华中科技大学）；Hong Kong University of Science and Technology（香港科技大学）；Shanghai Suochen Information Technology Co., Ltd（上海速晨信息技术有限公司）
Many catalyst devices employ flow through porous structures, which leads to a complex macroscopic mass and heat transport. To unravel the detailed dynamics of the reactive gas flow, we present an all-encompassing model, consisting of thermal lattice Boltzmann model by Kang et al., used to solve the heat and mass transport in the gas domain, coupled to a finite differences solver for the heat equation in the solid via thermal reactive boundary conditions for a consistent treatment of the reaction enthalpy. The chemical surface reactions are incorporated in a flexible fashion through flux bounda…
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. …
Gas separation of a binary gaseous mixture is one of characteristic phenomena in the micro-scale flows that differ from the conventional size flows. In this work, the separation in a binary gas mixture flows through a microchannel is investigated by the lattice Boltzmann method with a diffuse-bounce-back (DBB) boundary condition. The separation degree and rate are measured in the He--Ar and Ne--Ar systems for different mole fractions, pressure ratios, and Knudsen numbers. The results show that the separation phenomenon in the He--Ar mixture is more obvious than that in the Ne--Ar mixture at th…
Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations
我们分析了Adhikari格子玻尔兹曼方法[Europhys. Lett. 71，473（2005）]，并发现只要考虑稳定系统，即使对于小波长，它也显示出与理论的极好的一致性。这与其他有限差分和旧的格子玻尔兹曼实现相反，这些实现仅在大波长的限制下显示收敛。特别是交叉关联函数消失到小于0.5%。然而，对于较大的平均速度，伽利略不变性的违反表现出自己通过类似于那些早期的实现的幅度的错误。
In the CLB method, a Bosanquet-type effective viscosity is employed to account for the rarefaction effect on the gas viscosity. To gain accurate simulations and to match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection boundary scheme with a modified second-order slip boundary condition is adopted in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel (the ratio of the length to the height L/H=100) with pressure boundary condition over a wide range of Knudsen n…
In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to account for the wall-induced discontinuity in the distribution function. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $δ$, where the temperature of the plates varies from $1\ {\rm…
Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing e…
For a massless gas with constant cross section in a homogeneous, isotropically expanding spacetime we reformulate the relativistic Boltzmann equation as a set of non-linear coupled moment equations. For a particular initial condition this set can be solved exactly, yielding the first analytical solution of the Boltzmann equation for an expanding system. The non-equilibrium behavior of this relativistic gas can be mapped onto that of a homogeneous, static non-relativistic gas of Maxwell molecules.
Direct numerical simulation of liquid-gas-solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary -- in particular if the bubble-particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble-particle interaction at a size ratio of 1-2 orders of magnitude that makes simulations feasible on currently available super-c…
We study a two phase flow with interactions of liquid and rarefied gas inside the gas phase. The gas phase is modeled by the BGK model of the Boltzmann equation. The liquid phase is modeled by the incompressible Navier-Stokes equations. In this paper we have excluded the heat transfer between two phases. The interface boundary conditions for the liquid and gas phases is presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction since the droplet moves inside the gas phase and its interface deforms with respect to time and space. Therefore, the similar meshfre…
