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1.
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
2.
A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows
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Yu Sun Shu Chang Liming Yang & C. J. Teo 《advances in applied mathematics and mechanics.》2016,8(5):703-721
In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented
for the simulation of inviscid and viscous compressible flows. With the finite
volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS
is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by
the conventional smooth function approximation. Unlike the traditional gas-kinetic
scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS),
the numerical dissipation is controlled with a switch function in the present scheme.
That is, the numerical dissipation is only introduced in the region around strong shock
waves. As a consequence, the present SF-GKS can well capture strong shock waves
and thin boundary layers simultaneously. The present SF-GKS is firstly validated by
its application to the inviscid flow problems, including 1-D Euler shock tube, regular
shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous
transonic and hypersonic flow problems. Good agreement between the present
results and those in the literature verifies the accuracy and robustness of SF-GKS. 相似文献
3.
基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法. 相似文献
4.
With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out. 相似文献
5.
Ruairi M. Nestor Mihai Basa Martin Lastiwka Nathan J. Quinlan 《Journal of computational physics》2009,228(5):1733-1749
The finite volume particle method (FVPM) is a mesh-free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods. In this article, the FVPM is extended to viscous flows using a consistency-corrected smoothed particle hydrodynamics (SPH) approximation to evaluate velocity gradients. The accuracy of the viscous FVPM is improved by a higher-order discretisation of the inviscid flux combined with a second-order temporal discretisation. The higher-order inviscid FVPM is validated for a 1-D shock tube problem, in which it demonstrates an enhanced shock capturing ability. For two-dimensional simulations, a small arbitrary Lagrange–Euler correction to fully Lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times. The viscous FVPM is validated for two-dimensional Poiseuille, Taylor–Green and lid-driven cavity flows, and good agreement is achieved with analytic or reference numerical solutions. These results establish the viability of FVPM as a tool for mesh-free simulation of viscous flows in engineering. 相似文献
6.
Simulation of Viscous Flows Around a Moving Airfoil by Field Velocity Method with Viscous Flux Correction
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Ning Gu Zhiliang Lu & Tongqing Guo 《advances in applied mathematics and mechanics.》2012,4(3):294-310
Based on the field velocity method, a novel approach for simulating unsteady
pitching and plunging motion of an airfoil is presented in this paper. Responses
to pitching and plunging motions of the airfoil are simulated under different
conditions. The obtained results are compared with those of moving grid
method and good agreement is achieved. In the conventional field velocity method,
the Euler solver is usually used to simulate the movement of the airfoil. However,
when viscous effect is considered, unsteady Navier-Stokes equations have to be
solved and the viscous flux correction must be taken into account. In this work, the
viscous flux correction is introduced into the conventional field velocity method
when non-uniform grid speed distribution is occurred. Numerical experiments for
the flow around NACA0012 airfoil showed that the proposed approach can well
simulate viscous moving boundary flow problems. 相似文献
7.
In this paper we address the time-reversed simulation of viscous flows by the lattice Boltzmann method (LB). The theoretical derivation of the reversed LB from the Boltzmann equation is detailed, and the method implemented for weakly compressible flows using the D2Q9 scheme. The implementation of boundary conditions is also discussed. The accuracy and stability are illustrated by four test cases, namely the propagation of an acoustic wave in a medium at rest and in an uniform mean flow, the Taylor–Green vortex decay and the vortex pair–wall collision. 相似文献
8.
双分布函数热晶格玻尔兹曼数值方法在微尺度热流动系统中得到广泛的应用. 本文基于晶格玻尔兹曼平衡分布函数低阶Hermite展开式, 创新性地提出了包含黏性热耗散和压缩功的耦合的双分布函数热晶格玻尔兹曼数值方法, 将能量场内温度的变化以动量源的形式引入晶格波尔兹曼动量演化方程, 实现了能量场与动量场之间的耦合. 研究了考虑黏性热耗散和压缩功的和不考虑的两种热自然对流模型, 重点分析了不同瑞利数和普朗特数下流场内的流动情况以及温度、速度和平均努赛尔数的变化趋势. 本文实验结果与文献结果一致, 验证了本文数值方法的可行性和准确性. 研究结果表明: 随着瑞利数和普朗特数的增大, 方腔内对流传热作用逐渐增强, 边界处形成明显的边界层; 考虑黏性热耗散和压缩功的模型对流作用相对增强, 黏性热耗散和压缩功对自然对流的影响在微尺度流动过程中不能忽略. 相似文献
9.
针对流固耦合问题,发展了基于浸入边界-多松弛时间格子玻尔兹曼通量求解法(immersed boundary method multi-relaxation-time lattice Boltzmann flux solver,IB-MRT-LBFS)的弱耦合算法.依据多尺度Chapman-Enskog展开,建立不可压宏观方程状态变量和通量与格子玻尔兹曼方程中粒子密度分布函数之间的关系;采用强制浸入边界法处理流固界面使固壁表面满足无滑移边界条件,根据修正的速度求解动量方程力源项;结构运动方程采用四阶龙格-库塔法求解.格子模型与浸入边界法的引入使流固耦合计算可以在笛卡尔网格下进行,无需生成贴体网格及运用动网格技术,简化了计算过程.数值模拟了单圆柱横向涡激振动、单圆柱及串列双圆柱双自由度涡激振动问题.结果表明,IB-MRT-LBFS能够准确预测圆柱涡激振动的锁定区间、振动响应、受力情况以及捕捉尾流场结构形态,验证了该算法在求解流固耦合问题的有效性和可行性. 相似文献
10.
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12.
The recently proposed boundary condition-enforced immersed boundary-lattice Boltzmann method (IB-LBM) [14] is improved in this work to simulate three-dimensional incompressible viscous flows. In the conventional IB-LBM, the restoring force is pre-calculated, and the non-slip boundary condition is not enforced as compared to body-fitted solvers. As a result, there is a flow penetration to the solid boundary. This drawback was removed by the new version of IB-LBM [14], in which the restoring force is considered as unknown and is determined in such a way that the non-slip boundary condition is enforced. Since Eulerian points are also defined inside the solid boundary, the computational domain is usually regular and the Cartesian mesh is used. On the other hand, to well capture the boundary layer and in the meantime, to save the computational effort, we often use non-uniform mesh in IB-LBM applications. In our previous two-dimensional simulations [14], the Taylor series expansion and least squares-based lattice Boltzmann method (TLLBM) was used on the non-uniform Cartesian mesh to get the flow field. The final expression of TLLBM is an algebraic formulation with some weighting coefficients. These coefficients could be computed in advance and stored for the following computations. However, this way may become impractical for 3D cases as the memory requirement often exceeds the machine capacity. The other way is to calculate the coefficients at every time step. As a result, extra time is consumed significantly. To overcome this drawback, in this study, we propose a more efficient approach to solve lattice Boltzmann equation on the non-uniform Cartesian mesh. As compared to TLLBM, the proposed approach needs much less computational time and virtual storage. Its good accuracy and efficiency are well demonstrated by its application to simulate the 3D lid-driven cubic cavity flow. To valid the combination of proposed approach with the new version of IBM [14] for 3D flows with curved boundaries, the flows over a sphere and torus are simulated. The obtained numerical results compare very well with available data in the literature. 相似文献
13.
It is well known that the lattice Boltzmann equation method (LBE) can model the incompressible Navier-Stokes (NS) equations in the limit where density goes to a constant. In a LBE simulation, however, the density cannot be constant because pressure is equal to density times the square of sound speed, hence a compressibility error seems inevitable for the LBE to model incompressible flows. This work uses a modified equilibrium distribution and a modified velocity to construct an LBE which models time-independent (steady) incompressible flows with significantly reduced compressibility error. Computational results in 2D cavity flow and in a 2D flow with an exact solution are reported. 相似文献
14.
多孔介质中高Péclet数和大黏性比下混溶流体的流动和扩散广泛存在于二氧化碳驱油、化工生产等工业过程中.用数值方法对该问题进行研究时,关键在于如何正确描述高Péclet数和大黏性比下多孔介质内流体的行为.为此,提出了一种基于多松弛模型和格子动理模型的耦合格子Boltzmann模型.通过Chapman-Enskog分析,证明该模型能有效求解不可压Navier-Stokes方程和对流扩散方程.数值结果表明,该模型不仅具有二阶精度和良好的稳健性,而且对于高Péclet数和大黏性比的问题具有良好的数值稳定性,为模拟此类问题提供了有效工具. 相似文献
15.
We introduce a new concept of boundary conditions for realization of the lattice Boltzmann simulations of turbulent flows. The key innovation is the use of a universal distribution function for particles, analogous to the Tamm–Mott-Smith solution for the shock wave in the classical Boltzmann kinetic equation. Turbulent channel flow simulations demonstrate that the new boundary enables accurate results even with severely under-resolved grids. Generalization to complex boundary is illustrated with an example of turbulent flow past a circular cylinder. 相似文献
16.
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
17.
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
18.
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
19.
Kai Li & Chengwen Zhong 《advances in applied mathematics and mechanics.》2016,8(5):795-809
This paper presents a lattice Boltzmann (LB) method based study aimed
at numerical simulation of aeroacoustic phenomenon in flows around a symmetric
obstacle. To simulate the compressible flow accurately, a potential energy double-distribution-function
(DDF) lattice Boltzmann method is used over the entire computational
domain from the near to far fields. The buffer zone and absorbing boundary
condition is employed to eliminate the non-physical reflecting. Through the direct numerical
simulation, the flow around a circular cylinder at $Re$=150, $M$=0.2 and the
flow around a NACA0012 airfoil at $Re$=10000, $M$=0.8, $α$=$0^◦$ are investigated. The
generation and propagation of the sound produced by the vortex shedding are reappeared
clearly. The obtained results increase our understanding of the characteristic
features of the aeroacoustic sound. 相似文献
20.
LI Zhihui ZHANG Hanxin & FU Song ⒈ National Laboratory for CFD Hypervelocity Aerodynamics Institute China Aerodynamics Research Development Center Mianyang China .Department of Engineering Mechanics Tsinghua University Beijing China 《中国科学G辑(英文版)》2005,48(4):496-512
~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66.
2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469.
3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and … 相似文献