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Y. H. Zhang R. S. Qin Y. H. Sun R. W. Barber D. R. Emerson 《Journal of statistical physics》2005,121(1-2):257-267
Gas flow in microchannels can often encounter tangential slip motion at the solid surface even under creeping flow conditions.
To simulate low speed gas flows with Knudsen numbers extending into the transition regime, alternative methods to both the
Navier–Stokes and direct simulation Monte Carlo approaches are needed that balance computational efficiency and simulation
accuracy. The lattice Boltzmann method offers an approach that is particularly suitable for mesoscopic simulation where details
of the molecular motion are not required. In this paper, the lattice Boltzmann method has been applied to gas flows with finite
Knudsen number and the tangential momentum accommodation coefficient has been implemented to describe the gas-surface interactions.
For fully-developed channel flows, the results of the present method are in excellent agreement with the analytical slip-flow
solution of the Navier–Stokes equations, which are valid for Knudsen numbers less than 0.1. The present paper demonstrates
that the lattice Boltzmann approach is a promising alternative simulation tool for the design of microfluidic devices. 相似文献
3.
用格子Boltzmann模型模拟可压缩完全气体流动 总被引:2,自引:0,他引:2
采用一种新的格子Boltzmann模型模拟超音速流动。在这种模型中,粒子的速度不受限制,可以取得很广。而平衡分布函数的支集却相对集中,使模型得以简化。粒子速度的这种自适应特性允许流体以较高的马赫数流动。通过引入粒子的势能使得该模型适用于具有任意比热比的完全气体。利用Chapman-Enskog方法,从BGK型Boltzmann方程推导出Navier-Stokes方程。在六边形网格上模拟了马赫数为3的前台阶绕流,得到了合理的结果。 相似文献
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Development and Comparative Studies of Three Non-Free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows
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This paper at first shows the details of finite volume-based lattice Boltzmann
method (FV-LBM) for simulation of compressible flows with shock waves. In the
FV-LBM, the normal convective flux at the interface of a cell is evaluated by
using one-dimensional compressible lattice Boltzmann model, while the tangential
flux is calculated using the same way as used in the conventional Euler solvers.
The paper then presents a platform to construct one-dimensional compressible
lattice Boltzmann model for its use in FV-LBM. The platform is formed from the
conservation forms of moments. Under the platform, both the equilibrium
distribution functions and lattice velocities can be determined, and
therefore, non-free parameter model can be developed. The paper particularly
presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The
performances of these three models for simulation of compressible flows are
investigated by a brief analysis and their application to solve some
one-dimensional and two-dimensional test problems. Numerical results
showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5
models have the wider application range of Mach number. From the results,
it seems that D1Q4 model could be the best choice for the FV-LBM simulation
of hypersonic flows. 相似文献
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In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic
theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition
(DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of
the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal
developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation
Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis 相似文献
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R. Surmas C. E. Pico Ortiz P. C. Philippi 《The European physical journal. Special topics》2009,171(1):81-90
The formulation of a consistent thermohydrodynamics with a discrete model of the Boltzmann equation requires the representation
of the velocity moments up to the fourth order. Space-filling discrete sets of velocities with increasing accuracy were obtained
using a systematic approach in accordance with a quadrature method based on prescribed abscissas (Philippi et al., Phys. Rev.
E, 73 (5), n. 056702, 2006). These sets of velocities are suitable for collision-propagation schemes, where the discrete velocity
and physical spaces are coupled and the Courant number is unitary. The space-filling requirement leads to sets of discrete
velocities which can be large in thermal models. In this work, although the discrete sets of velocities are also obtained
with a quadrature method based on prescribed abscissas, the lattices are not required to be space-filling. This leads to a
reduced number of discrete velocities for the same approximation order but requires the use of an alternative numerical scheme.
The use of finite difference schemes for the advection term in the continuous Boltzmann equation has shown to have some advantages
with respect to the collision-propagation LBM method by freeing the Courant number from its unitary value and reducing the
discretization error. In this work, a second order Runge-Kutta method was used for the simulation of the Sod's shock tube
problem, the Couette flow and the Lid-driven cavity flow. Boundary conditions without velocity slip and temperature jumps
were written for these discrete Boltzmann equation by splitting the velocity distribution function into an equilibrium and
a non-equilibrium part. The equilibrium part was set using the local velocity and temperature at the wall and the non-equilibrium
part by extrapolating the non-equilibrium moments to the wall sites. 相似文献
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A lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary. 相似文献
8.
In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for
simulation of viscous compressible flows. In the solver, the finite volume method is
applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes
solvers, in this work, the inviscid flux across the cell interface is evaluated by
local reconstruction of solution using one-dimensional lattice Boltzmann model, while
the viscous flux is still approximated by conventional smooth function approximation.
The present work overcomes the two major drawbacks of existing LBFS [28–31], which
is used for simulation of inviscid flows. The first one is its ability to simulate viscous
flows by including evaluation of viscous flux. The second one is its ability to effectively
capture both strong shock waves and thin boundary layers through introduction of a
switch function for evaluation of inviscid flux, which takes a value close to zero in
the boundary layer and one around the strong shock wave. Numerical experiments
demonstrate that the present solver can accurately and effectively simulate hypersonic
viscous flows. 相似文献
9.
Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution-function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, are developed in this paper. The main differences between the two models are discrete equilibrium density and total energy distribution function. One is the D3Q25 model obtained from spherical function, and the other is the D3Q27 standard lattice model obtained from Hermite expansions of the corresponding continuous equilibrium distribution functions. The two models are tested by numerical simulations of some typical compressible flows, and their numerical stability and precision are also analysed. The results indicate that the two models are capable for supersonic flows, while the one from Hermite expansions is not suitable for compressible flows with shock waves. 相似文献
10.
With the discrete method of the hexagonal cell and three different velocities of particle population in each cell, a two-dimensional lattice Boltzmann model is developed in this paper.[1,2] The collision operator in the Boltzmann equation is expanded to fourth order using the Taylor expansion.[3,4] With this model, good results have been obtained from the numerical simulation of the reflection phenomenon of the shock wave on the surface of an obstacle, and the numerical stability is also good. Thus the applicability of the D2Q 19 model is verified. 相似文献
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In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level. 相似文献
12.
Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications 总被引:2,自引:0,他引:2
A version of immersed boundary-lattice Boltzmann method (IB-LBM) is proposed in this work. It is based on the lattice Boltzmann equation with external forcing term proposed by Guo et al. [Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65 (2002) 046308], which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect. In this model, the velocity is contributed by two parts. One is from the density distribution function and can be termed as intermediate velocity, and the other is from the external force and can be considered as velocity correction. In the conventional IB-LBM, the force density (external force) is explicitly computed in advance. As a result, we cannot manipulate the velocity correction to enforce the non-slip boundary condition at the boundary point. In the present work, the velocity corrections (force density) at all boundary points are considered as unknowns which are computed in such a way that the non-slip boundary condition at the boundary points is enforced. The solution procedure of present IB-LBM is exactly the same as the conventional IB-LBM except that the non-slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model. Numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results. This is not the case for the results obtained by the conventional IB-LBM. Another advantage of the present method is its simple calculation of force on the boundary. The force can be directly calculated from the relationship between the velocity correction and the force density. 相似文献
13.
Wolfgang Wagner 《Journal of statistical physics》1995,78(5-6):1555-1570
Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model. 相似文献
14.
Simulation of Combustion Field with Lattice Boltzmann Method 总被引:5,自引:0,他引:5
Turbulent combustion is ubiquitously used in practical combustion devices. However, even chemically non-reacting turbulent flows are complex phenomena, and chemical reactions make the problem even more complicated. Due to the limitation of the computational costs, conventional numerical methods are impractical in carrying out direct 3D numerical simulations at high Reynolds numbers with detailed chemistry. Recently, the lattice Boltzmann method has emerged as an efficient alternative for numerical simulation of complex flows. Compared with conventional methods, the lattice Boltzmann scheme is simple and easy for parallel computing. In this study, we present a lattice Boltzmann model for simulation of combustion, which includes reaction, diffusion, and convection. We assume the chemical reaction does not affect the flow field. Flow, temperature, and concentration fields are decoupled and solved separately. As a preliminary simulation, we study the so-called counter-flow laminar flame. The particular flow geometry has two opposed uniform combustible jets which form a stagnation flow. The results are compared with those obtained from solving Navier–Stokes equations. 相似文献
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Development of a new correlation to calculate permeability for flows with high Knudsen number
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Esmaeil Dehdashti 《中国物理 B》2016,25(2):24702-024702
Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method(LBM) through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition(SRBC). The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes. 相似文献
18.
A non-perturbative algebraic theory of the lattice Boltzmann method is developed based on the symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which imposes restricted extension of higher-order Gaussian moments, (ii) A special quasi-equilibrium distribution function found analytically in closed form on the product-lattice in two and three spatial dimensions, and which proves the factorization of quasi-equilibrium moments, and (iii) An algebraic method of pruning based on a one-into-one relation between groups of discrete velocities and moments. Two routes of constructing lattice Boltzmann equilibria are distinguished. The present theory includes previously known limiting and special cases of lattices, and enables automated derivation of lattice Boltzmann models from two-dimensional tables, by finding the roots of one polynomial and solving a few linear systems. 相似文献
19.
Yu-Dong Zhang Ai-Guo Xu Guang-Cai Zhang Zhi-Hua Chen Pei Wang 《Frontiers of Physics》2018,13(3):135101
A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar–Gross–Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier–Stokes or the Burnett equations. 相似文献
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Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results. 相似文献