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1.
Rotational Slip Flow in Coaxial Cylinders by the Finite-Difference Lattice Boltzmann Methods 下载免费PDF全文
Minoru Watari 《Communications In Computational Physics》2011,9(5):1293-1314
Recent studies on applications of the lattice Boltzmann method (LBM) and
the finite-difference lattice Boltzmann method (FDLBM) to velocity slip simulations
are mostly on one-dimensional (1D) problems such as a shear flow between parallel
plates. Applications to a 2D problem may raise new issues. The author performed
numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D
problem. Two types of 2D models were used. The first were multi-speed FDLBM models
proposed by the author. The second was a standard LBM, the D2Q9 model. The
simulations were performed applying a finite difference scheme to both the models.
The study had two objectives. The first was to investigate the accuracies of LBM and
FDLBM on applications to rotational slip flow. The second was to obtain an experience
on application of the cylindrical coordinate system. The FDLBM model with 8
directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation
time constant or the Knudsen number was large. The FDLBM model with 24
directions showed accurate results even at large Knudsen numbers. 相似文献
2.
Three-Dimensional Simulation of Balloon Dynamics by the Immersed Boundary Method Coupled to the Multiple-Relaxation-Time Lattice Boltzmann Method 下载免费PDF全文
Jiayang Wu Yongguang Cheng Chunze Zhang & Wei Diao 《Communications In Computational Physics》2015,17(5):1271-1300
The immersed boundary method (IBM) has been popular in simulating fluid
structure interaction (FSI) problems involving flexible structures, and the recent introduction
of the lattice Boltzmann method (LBM) into the IBM makes the method more
versatile. In order to test the coupling characteristics of the IBM with the multiple-relaxation-time
LBM (MRT-LBM), the three-dimensional (3D) balloon dynamics, including
inflation, release and breach processes, are simulated. In this paper, some key
issues in the coupling scheme, including the discretization of 3D boundary surfaces,
the calculation of boundary force density, and the introduction of external force into
the LBM, are described. The good volume conservation and pressure retention properties
are verified by two 3D cases. Finally, the three FSI processes of a 3D balloon
dynamics are simulated. The large boundary deformation and oscillation, obvious
elastic wave propagation, sudden stress release at free edge, and recoil phenomena
are all observed. It is evident that the coupling scheme of the IBM and MRT-LBM can
handle complicated 3D FSI problems involving large deformation and large pressure
gradients with very good accuracy and stability. 相似文献
3.
A. Zarghami M. J. Maghrebi J. Ghasemi & S. Ubertini 《Communications In Computational Physics》2012,12(1):42-64
The most severe limitation of the standard Lattice Boltzmann Method is the
use of uniform Cartesian grids especially when there is a need for high resolutions near
the body or the walls. Among the recent advances in lattice Boltzmann research to handle complex geometries, a particularly remarkable option is represented by changing
the solution procedure from the original "stream and collide" to a finite volume technique. However, most of the presented schemes have stability problems. This paper
presents a stable and accurate finite-volume lattice Boltzmann formulation based on a
cell-centred scheme. To enhance stability, upwind second order pressure biasing factors are used as flux correctors on a D2Q9 lattice. The resulting model has been tested
against a uniform flow past a cylinder and typical free shear flow problems at low and
moderate Reynolds numbers: boundary layer, mixing layer and plane jet flows. The
numerical results show a very good accuracy and agreement with the exact solution
of the Navier-Stokes equation and previous numerical results and/or experimental
data. Results in self-similar coordinates are also investigated and show that the time-averaged statistics for velocity and vorticity express self-similarity at low Reynolds
numbers. Furthermore, the scheme is applied to simulate the flow around circular
cylinder and the Reynolds number range is chosen in such a way that the flow is time
dependent. The agreement of the numerical results with previous results is satisfactory. 相似文献
4.
Jianping Meng Yonghao Zhang & Jason M. Reese 《Communications In Computational Physics》2015,17(5):1185-1200
We investigate unidirectional rarefied flows confined between two infinite
parallel plates with specified heat flux boundary conditions. Both Couette and force-driven
Poiseuille flows are considered. The flow behaviors are analyzed numerically
by solving the Shakhov model of the Boltzmann equation. We find that a zero-heat-flux
wall can significantly influence the flow behavior, including the velocity slip and
temperature jump at the wall, especially for high-speed flows. The predicted bimodal-like
temperature profile for force-driven flows cannot even be qualitatively captured
by the Navier-Stokes-Fourier equations. 相似文献
5.
Three-Dimensional Lattice Boltzmann Flux Solver and Its Applications to Incompressible Isothermal and Thermal Flows 下载免费PDF全文
Yan Wang Chang Shu Chiang Juay Teo Jie Wu & Liming Yang 《Communications In Computational Physics》2015,18(3):593-620
A three-dimensional (3D) lattice Boltzmann flux solver (LBFS) is presented
in this paper for the simulation of both isothermal and thermal flows. The present
solver combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice
Boltzmann equation (LBE) solvers. It applies the finite volume method (FVM) to
solve the N-S equations. Different from the conventional N-S solvers, its viscous and
inviscid fluxes at the cell interface are evaluated simultaneously by local reconstruction
of LBE solution. As compared to the conventional LBE solvers, which apply the
lattice Boltzmann method (LBM) globally in the whole computational domain, it only
applies LBM locally at each cell interface, and flow variables at cell centers are given
from the solution of N-S equations. Since LBM is only applied locally in the 3D LBFS,
the drawbacks of the conventional LBM, such as limitation to uniform mesh, tie-up
of mesh spacing and time step, tedious implementation of boundary conditions, are
completely removed. The accuracy, efficiency and stability of the proposed solver are
examined in detail by simulating plane Poiseuille flow, lid-driven cavity flow and natural
convection. Numerical results show that the LBFS has a second order of accuracy
in space. The efficiency of the LBFS is lower than LBM on the same grids. However,
the LBFS needs very less non-uniform grids to get grid-independence results and its
efficiency can be greatly improved and even much higher than LBM. In addition, the
LBFS is more stable and robust. 相似文献
6.
Pierre Lallemand & Franç ois Dubois 《Communications In Computational Physics》2015,17(5):1169-1184
We show that a single particle distribution for the "energy-conserving" D2Q13 lattice Boltzmann scheme can simulate coupled effects involving advection
and diffusion of velocity and temperature. We consider various test cases: non-linear
waves with periodic boundary conditions, a test case with buoyancy, propagation of
transverse waves, Couette and Poiseuille flows. We test various boundary conditions
and propose to mix bounce-back and anti-bounce-back numerical boundary conditions
to take into account velocity and temperature Dirichlet conditions. We present
also first results for the de Vahl Davis heated cavity. Our results are compared with
the coupled D2Q9-D2Q5 lattice Boltzmann approach for the Boussinesq system and
with an elementary finite differences solver for the compressible Navier-Stokes equations.
Our main experimental result is the loss of symmetry in the de Vahl Davis cavity
computed with the single D2Q13 lattice Boltzmann model without the Boussinesq
hypothesis. This result is confirmed by a direct Navier Stokes simulation with finite
differences. 相似文献
7.
V. A. Titarev 《Communications In Computational Physics》2012,12(1):162-192
The paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The
framework consists of a high-order accurate implicit advection scheme on arbitrary
unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application
area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe.
The results show good accuracy of the proposed algorithm across all flow regimes and
its high efficiency and excellent parallel scalability for up to 512 cores. 相似文献
8.
Simulation of Acoustic Behavior of Bubbly Liquids with Hybrid Lattice Boltzmann and Homogeneous Equilibrium Models 下载免费PDF全文
Homogeneous equilibrium model (HEM) has been widely used in cavitating
flow simulations. The major feature of this model is that a single equation of state
(EOS) is proposed to describe the thermal behavior of bubbly liquid, where both kinematic
and thermal equilibrium are assumed between two phases. In this paper, the HEM
was coupled with multi-relaxation-time lattice Boltzmann model (MRT-LBM) and the
acoustic behavior was simulated. Two approaches were applied alternatively: adjusting
speed of sound (Buick, J. Phys. A, 2006, 39:13807-13815) and setting real gas EOS.
Both approaches result in high accuracy in acoustic speed predictions for different void
(gas) volume of fractions. It is demonstrated that LBM could be successfully applied
as a Navier-Stokes equation solver for industrial applications. However, further dissipation
and dispersion analysis shows that Shan-Chen type approaches of LBM are
deficient, especially in large wave-number region. 相似文献
9.
Jaw-Yen Yang Bagus Putra Muljadi Zhi-Hui Li & Han-Xin Zhang 《Communications In Computational Physics》2013,14(1):242-264
An accurate and direct algorithm for solving the semiclassical Boltzmann
equation with relaxation time approximation in phase space is presented for parallel
treatment of rarefied gas flows of particles of three statistics. The discrete ordinate
method is first applied to discretize the velocity space of the distribution function to
render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of
the discretized velocity distribution function in physical space and time. The method
is developed for two space dimensions and implemented on gas particles that obey
the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows are
presented and the results indicating good resolution of the main flow features can be
achieved. Flows of wide range of relaxation times and Knudsen numbers covering
different flow regimes are computed to validate the robustness of the method. The
recovery of quantum statistics to the classical limit is also tested for small fugacity
values. 相似文献
10.
A Hybrid Immersed Boundary-Lattice Boltzmann Method for Simulation of Viscoelastic Fluid Flows Interaction with Complex Boundaries 下载免费PDF全文
M. H. Sedaghat A. A. H. Bagheri M. M. Shahmardan M. Norouzi B. C. Khoo & P. G. Jayathilake 《Communications In Computational Physics》2021,29(5):1411-1445
In this study, a numerical technique based on the Lattice Boltzmann method
is presented to model viscoelastic fluid interaction with complex boundaries which are
commonly seen in biological systems and industrial practices. In order to accomplish
numerical simulation of viscoelastic fluid flows, the Newtonian part of the momentum
equations is solved by the Lattice Boltzmann Method (LBM) and the divergence of the
elastic tensor, which is solved by the finite difference method, is added as a force term
to the governing equations. The fluid-structure interaction forces are implemented
through the Immersed Boundary Method (IBM). The numerical approach is validated
for Newtonian and viscoelastic fluid flows in a straight channel, a four-roll mill geometry as well as flow over a stationary and rotating circular cylinder. Then, a numerical
simulation of Oldroyd-B fluid flow around a confined elliptical cylinder with different
aspect ratios is carried out for the first time. Finally, the present numerical approach
is used to simulate a biological problem which is the mucociliary transport process of
human respiratory system. The present numerical results are compared with appropriate analytical, numerical and experimental results obtained from the literature. 相似文献
11.
Giacomo Falcucci Stefano Ubertini Chiara Biscarini Silvia Di Francesco Daniele Chiappini Silvia Palpacelli Alessandro De Maio & Sauro Succi 《Communications In Computational Physics》2011,9(2):269-296
The simulation of multiphase flows is an outstanding challenge, due to the
inherent complexity of the underlying physical phenomena and to the fact that multiphase
flows are very diverse in nature, and so are the laws governing their dynamics.
In the last two decades, a new class of mesoscopic methods, based on minimal lattice
formulation of Boltzmann kinetic equation, has gained significant interest as an
efficient alternative to continuum methods based on the discretization of the NS equations
for non ideal fluids. In this paper, three different multiphase models based on
the lattice Boltzmann method (LBM) are discussed, in order to assess the capability of
the method to deal with multiphase flows on a wide spectrum of operating conditions
and multiphase phenomena. In particular, the range of application of each method
is highlighted and its effectiveness is qualitatively assessed through comparison with
numerical and experimental literature data. 相似文献
12.
A Compressible Conserved Discrete Unified Gas-Kinetic Scheme with Unstructured Discrete Velocity Space for Multi-Scale Jet Flow Expanding into Vacuum Environment 下载免费PDF全文
Jianfeng Chen Sha Liu Yong Wang & Chengwen Zhong 《Communications In Computational Physics》2020,28(4):1502-1535
The mechanism of jet flow expanding into vacuum environment (or extremely low density environment) is important for the propulsion unit of micro-electro-mechanical systems (MEMS), the thruster of spacecraft, the attitude control system of
satellite, etc.. Since its flow field is often composed of local continuum region and local rarefied region, the jet flow into vacuum has noteworthy multi-scale transportation
behaviors. Therefore, the numerical study of such flows needs the multi-scale schemes
which are valid for both continuum and rarefied flows. In the past few years, a series
of unified methods for whole flow regime (from continuum regime to rarefied regime)
have been developed from the perspective of the direct modeling, and have been verified by sufficient test cases. In this paper, the compressible conserved discrete unified
gas-kinetic scheme is further developed and is utilized for predicting the jet flows into
vacuum environment. In order to cover the working conditions of both aerospace and
MEMS applications, the jet flows with a wide range of inlet Knudsen (Kn) numbers
(from 1E-4 to 100) are considered. The evolution of flow field during the entire startup
and shutdown process with Kn number 100 is predicted by the present method, and
it matches well with the result of analytical collisionless Boltzmann equation. For Kn
numbers from 1E-4 to 10, the flow field properties such as density, momentum, and
pressure are investigated, and the results are provided in details, since the published
results are not sufficient at the present stage. The extent and intensity of the jet flow
influence are especially investigated, because they are strongly related to the plume
contamination and momentum impact on objects facing the jet, such as the solar paddles which face the attitude control thruster during the docking process. 相似文献
13.
This paper presents a gas kinetic study and analytical results on high speed rarefied gas flows from a planar exit. The beginning of this paper reviews the results for planar free jet expanding into a vacuum, followed by an investigation of jet impingement on normally set plates with either a diffuse or a specular surface. Presented results include exact solutions for flowfield and surface properties. Numerical simulations with the direct simulation Monte Carlo method were performed to validate these analytical results, and good agreement with this is obtained for flows at high Knudsen numbers. These highly rarefied jet and jet impingement results can provide references for real jet and jet impingement flows. 相似文献
14.
In this paper the pressure distribution of the gaseous flow in a microchannel is studied via a lattice Boltzmann equation (LBE) method. With effective relaxation times and a generalized second order slip boundary condition, the LBE can be used to simulate rarefied gas flows from slip to transition regimes. The Knudsen minimum phenomena of mass flow rate in the pressure driven flow is also investigated. The effects of Knudsen number (rarefaction effect), pressure ratio and aspect ratio (compression effect) on the pressure distribution are analyzed. It is found the rarefaction effect tends to the curvature of the nonlinear pressure distribution, while the compression effect tends to enhance its nonlinearity. The combined effects lead to a local minimum of the pressure deviation. Furthermore, it is also found that the relationship between the pressure deviation and the aspect ratio follows a pow-law. 相似文献
15.
A Novel Dynamic Quadrature Scheme for Solving Boltzmann Equation with Discrete Ordinate and Lattice Boltzmann Methods 下载免费PDF全文
The Boltzmann equation (BE) for gas flows is a time-dependent nonlinear
differential-integral equation in 6 dimensions. The current simplified practice is to linearize the collision integral in BE by the BGK model using Maxwellian equilibrium
distribution and to approximate the moment integrals by the discrete ordinate method
(DOM) using a finite set of velocity quadrature points. Such simplification reduces
the dimensions from 6 to 3, and leads to a set of linearized discrete BEs. The main
difficulty of the currently used (conventional) numerical procedures occurs when the
mean velocity and the variation of temperature are large that requires an extremely
large number of quadrature points. In this paper, a novel dynamic scheme that requires only a small number of quadrature points is proposed. This is achieved by
a velocity-coordinate transformation consisting of Galilean translation and thermal
normalization so that the transformed velocity space is independent of mean velocity and temperature. This enables the efficient implementation of Gaussian-Hermite
quadrature. The velocity quadrature points in the new velocity space are fixed while
the correspondent quadrature points in the physical space change from time to time
and from position to position. By this dynamic nature in the physical space, this new
quadrature scheme is termed as the dynamic quadrature scheme (DQS). The DQS was
implemented to the DOM and the lattice Boltzmann method (LBM). These new methods with DQS are therefore termed as the dynamic discrete ordinate method (DDOM)
and the dynamic lattice Boltzmann method (DLBM), respectively. The new DDOM
and DLBM have been tested and validated with several testing problems. Of the same
accuracy in numerical results, the proposed schemes are much faster than the conventional schemes. Furthermore, the new DLBM have effectively removed the incompressible and isothermal restrictions encountered by the conventional LBM. 相似文献
16.
Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint? 下载免费PDF全文
The Lattice Boltzmann Method (LBM) has established itself as a popular
numerical method in computational fluid dynamics. Several advancements have been
recently made in LBM, which include multiple-relaxation-time LBM to simulate anisotropic
advection-diffusion processes. Because of the importance of LBM simulations
for transport problems in subsurface and reactive flows, one needs to study the accuracy
and structure preserving properties of numerical solutions under the LBM. The
solutions to advective-diffusive systems are known to satisfy maximum principles,
comparison principles, the non-negative constraint, and the decay property. In this
paper, using several numerical experiments, it will be shown that current single- and
multiple-relaxation-time lattice Boltzmann methods fail to preserve these mathematical
properties for transient diffusion-type equations. We will also show that these
violations may not be removed by simply refining the discretization parameters. More
importantly, it will be shown that meeting stability conditions alone does not guarantee
the preservation of the aforementioned mathematical principles and physical
constraints in the discrete setting. A discussion on the source of these violations and
possible approaches to avoid them is included. A condition to guarantee the non-negativity
of concentration under LBM in the case of isotropic diffusion is also derived.
The impact of this research is twofold. First, the study poses several outstanding research
problems, which should guide researchers to develop LBM-based formulations
for transport problems that respect important mathematical properties and physical
constraints in the discrete setting. This paper can also serve as a good source of benchmark
problems for such future research endeavors. Second, this study cautions the
practitioners of the LBM for transport problems with the associated numerical deficiencies of the LBM, and provides guidelines for performing predictive simulations of
advective-diffusive processes using the LBM. 相似文献
17.
Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane 下载免费PDF全文
Toshiro Murayama Masato Yoshino & Tetsuo Hirata 《Communications In Computational Physics》2011,9(5):1397-1413
The lattice Boltzmann method (LBM) with an elastic model is applied to the
simulation of two-phase flows containing a deformable body with a viscoelastic membrane.
The numerical method is based on the LBM for incompressible two-phase fluid
flows with the same density. The body has an internal fluid covered by a viscoelastic
membrane of a finite thickness. An elastic model is introduced to the LBM in order
to determine the elastic forces acting on the viscoelastic membrane of the body. In the
present method, we take account of changes in surface area of the membrane and in
total volume of the body as well as shear deformation of the membrane. By using this
method, we calculate two problems, the behavior of an initially spherical body under
shear flow and the motion of a body with initially spherical or biconcave discoidal
shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter)
for various shear rates are in good agreement with other numerical results.
Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies
in shear flows, is simulated by the present method. 相似文献
18.
In this study, the Lattice Boltzmann Method (LBM) is implemented through
a finite-volume approach to perform 2-D, incompressible, and turbulent fluid flow
analyses on structured grids. Even though the approach followed in this study necessitates
more computational effort compared to the standard LBM (the so called
stream and collide scheme), using the finite-volume method, the known limitations of
the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy
(CFL) number to be one are removed. Moreover, the curved boundaries in the computational
domain are handled more accurately with less effort. These improvements
pave the way for the possibility of solving fluid flow problems with the LBM using
coarser grids that are refined only where it is necessary and the boundary layers might
be resolved better. 相似文献
19.
Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method 下载免费PDF全文
Qiuxiang Li Ning Hong Baochang Shi & Zhenhua Chai 《Communications In Computational Physics》2014,15(1):265-284
In this paper, the power-law fluid flows in a two-dimensional square cavity
are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the
vortex strength, vortex position and velocity distribution are extensively studied. In
our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to
1.75, covering both cases of shear-thinning and shear-thickening. Compared with the
Newtonian fluid, numerical results show that the flow structure and number of vortex
of power-law fluid are not only dependent on the Reynolds number, but also related
to power-law index. 相似文献
20.
Due to the rapid advances in micro-electro-mechanical systems (MEMS), the
study of microflows becomes increasingly important. Currently, the molecular-based
simulation techniques are the most reliable methods for rarefied flow computation,
even though these methods face statistical scattering problem in the low speed limit.
With discretized particle velocity space, a unified gas-kinetic scheme (UGKS) for entire Knudsen number flow has been constructed recently for flow computation. Contrary to the particle-based direct simulation Monte Carlo (DSMC) method, the unified
scheme is a partial differential equation-based modeling method, where the statistical
noise is totally removed. But the common point between the DSMC and UGKS is that
both methods are constructed through direct modeling in the discretized space. Due
to the multiscale modeling in the unified method, i.e., the update of both macroscopic
flow variables and microscopic gas distribution function, the conventional constraint
of time step being less than the particle collision time in many direct Boltzmann solvers
is released here. The numerical tests show that the unified scheme is more efficient
than the particle-based methods in the low speed rarefied flow computation. The main
purpose of the current study is to validate the accuracy of the unified scheme in the
capturing of non-equilibrium flow phenomena. In the continuum and free molecular
limits, the gas distribution function used in the unified scheme for the flux evaluation
at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions. In the transition regime, the DSMC solution will be used for the validation of
UGKS results. This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows. It not only recovers the DSMC
results whenever available, but also provides high resolution results in cases where
the DSMC can hardly afford the computational cost. In thermal creep flow simulation,
surprising solution, such as the gas flowing from hot to cold regions along the wallsurface, is observed for the first time by the unified scheme, which is confirmed later
through intensive DSMC computation. 相似文献