- Lattice Boltzmann Method, Turbulence modeling, GPU Computing, Lattice Boltzmann method for fluid dynamics, Phase Change, Applied Mathematics, and 9 moreFluid Dynamics, Heat Transfer, Finite Volume Methods, Porous Media, Lattice Boltzmann Equation, Incompressible Flow, Mechanical Engineering, Mathematics, and Chemical Engineeringedit
Multiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas... more
Multiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas kinetic scheme (DUGKS) is a recently developed numerical approach for simulating multiscale flows based on kinetic models. The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux. Particularly, the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time, such that the particle transport and collision effects are coupled, accumulated, and evaluated in a numerical time step scale. Consequently, the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time. As a result, the DUGKS can capture the flow behaviors in all regimes without resolving the...
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The problem of mixed convection in a driven cavity packed with porous medium is studied with lattice Boltzmann method. A lattice Boltzmann model for incompressible flow in porous media and another thermal lattice Boltzmann model for... more
The problem of mixed convection in a driven cavity packed with porous medium is studied with lattice Boltzmann method. A lattice Boltzmann model for incompressible flow in porous media and another thermal lattice Boltzmann model for solving the energy equation are proposed based on the generalized volume-averaged flow model. The present models have been validated by simulating mixed convection in a driven cavity (without porous medium) and it is found that the numerical results predicted by present models are in good agreement with available data reported in previous studies. Extensive parametric studies on mixed convection in a driven cavity filled with porous medium are carried out for various values of Reynolds number, Richardson number and Darcy number. It is found that the flow and temperature patterns change greatly with variations of these parameters.
Research Interests: Mechanical Engineering, Heat Transfer, Nanoparticle, Mathematical Sciences, Porous Media, and 18 moreMixed Convection, Physical sciences, Eccentricity, Computers and Mathematics with Applications 59 (2010) 35783582, Lattice Boltzmann, Anisotropic Diffusion, Lattice Boltzmann Method, Nonlinear system, Interdisciplinary Engineering, Nusselt Number, Porous Medium, Incompressible Flow, Convection Diffusion Equation, Reynolds Number, Annulus, Inclination, Discrete Nonlinear Schrödinger Equation, and Parametric Study
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Our recent efforts focusing on improving the lattice Boltzmann method (LBM) are introduced, including an incompressible LB model without compressible effect, a flexible thermal LBM with simple structure for Bousinesq fluids, and a robust... more
Our recent efforts focusing on improving the lattice Boltzmann method (LBM) are introduced, including an incompressible LB model without compressible effect, a flexible thermal LBM with simple structure for Bousinesq fluids, and a robust boundary scheme. We use them to simulate the lid-driven cavity flow at Reynolds numbers 5000–50000, the natural convection due to internal heat generation in a square cavity at Rayleigh number up to 1012, respectively. The numerical results agree well with those of previous studies.
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Research Interests: Engineering, Mixture Models (Mathematics), Modeling and Simulation, Fluid Dynamics, Mathematical Sciences, and 8 morePhysical sciences, Lattice Boltzmann method for fluid dynamics, Rarefied Gas Dynamics, Lattice Boltzmann Equation, Boundary Condition, Gas Flow, Kinetic Theory of Non equiibrium Systems, and Computational Method
The standard Lattice BGK (LBGK) scheme often encounters numerical instability in simulation of fluid flow with small kinematic viscosity or as the nondimensional relaxation time τ is close to 0.5. In this paper, based on a time-splitting... more
The standard Lattice BGK (LBGK) scheme often encounters numerical instability in simulation of fluid flow with small kinematic viscosity or as the nondimensional relaxation time τ is close to 0.5. In this paper, based on a time-splitting scheme for the Boltzmann equation with discrete velocities, a new LBGK scheme with general propagation step is proposed to address this problem. In this model, two free parameters are introduced into the propagation step, which can be adjusted to obtain a small kinematic viscosity and improved numerical stability as well. Numerical simulations of the two-dimensional Taylor vortex and the unsteady Womersley flow are carried out to test the kinematic viscosity, numerical diffusion, and numerical stability of the proposed scheme.
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We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is... more
We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Several other existing force treatments are also examined.
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Research Interests: Engineering, Fluid Dynamics, Chaos Theory Evolution Equation, Mathematical Sciences, Natural Convection, and 8 morePhysical sciences, Lattice Boltzmann Equation, Velocity Distribution in Open Channel, Boltzmann equation, Lumping Kinetic Model, Low Mach Number, Computational Method, and Viscous Dissipation
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Research Interests: Mechanical Engineering, Applied Mathematics, Fluid Mechanics, Heat Transfer, Numerical Method, and 17 moreNatural Convection, Theoretical and Applied Mechanics, Thermal Sciences, Lattice Boltzmann, Temperature Distribution, Thermal Conductivity, Lattice Boltzmann Method, Second Order, Finite Temperature Field Theory, Interdisciplinary Engineering, Finite Volume Method, Nusselt Number, Experimental Data, Aspect Ratio, Physical Properties, Effective thermal conductivity, and Volume Fraction
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Research Interests: Engineering, Computational Physics, Finite Volume Methods, Kinetics, Comparative Study, and 18 moreIncompressible Flows, Models, Mathematical Sciences, Physical sciences, Laminar Flow, Lattice Boltzmann Equation, Interpolation, Finite Volume, Unsteady flow, Finite Difference Method, Boltzmann equation, Finite Volume Method, Calculation, Compressible Flow, Low Mach Number, Incompressible Flow, Reynolds Number, and Mach Number
Abstract: Due to the mesoscopic and kinetic nature, the lattice Boltzmann equation (LBE) method has become an efficient and powerful tool for modeling and simulating interfacial dynamics of multi-phase flows. In this work we discuss... more
Abstract: Due to the mesoscopic and kinetic nature, the lattice Boltzmann equation (LBE) method has become an efficient and powerful tool for modeling and simulating interfacial dynamics of multi-phase flows. In this work we discuss several fundamental properties of two-phase LBE models. Particularly, the effects of force discretization, spurious currents in the vicinity of interfaces, and checkerboard effects with the underlying lattices, are investigated. Keywords: Two-phase flows, lattice Boltzmann equation.
Gas flows in microchannels have been receiving increased attention over the last decade 1, 2 with the rapid development of microfabrication technologies. It is found that a gas flowing through a small-sized device exhibits some unusual... more
Gas flows in microchannels have been receiving increased attention over the last decade 1, 2 with the rapid development of microfabrication technologies. It is found that a gas flowing through a small-sized device exhibits some unusual dynamic behaviors, and the conventional Navier-Stokes equations with the nonslip boundary condition fail to give an accurate description 1, 2.
In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate nonequilibrium flows. In this paper, instead of using three temperatures in... more
In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate nonequilibrium flows. In this paper, instead of using three temperatures in the x−, y−, and z-directions, we further define the translational temperature as a second-order symmetric tensor.
Abstract In an early approach, a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate non-equilibrium flows was proposed. In this paper, instead of using three... more
Abstract In an early approach, a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate non-equilibrium flows was proposed. In this paper, instead of using three temperatures in the x, y and z-directions, we define the translational temperature as a second-order symmetric tensor. Under the new framework, the differences between the temperature tensor and the pressure tensor will be explicitly pointed out.
In this paper, a finite difference-based lattice BGK model for thermal flows is proposed based on the double-distribution function approach. We applied this model to simulate natural convection heat transfer in a horizontal concentric... more
In this paper, a finite difference-based lattice BGK model for thermal flows is proposed based on the double-distribution function approach. We applied this model to simulate natural convection heat transfer in a horizontal concentric annulus bounded by two stationary cylinders with different temperatures. Velocity and temperature distributions as well as Nusselt numbers were obtained for the Rayleigh numbers ranging from 2.38× 103 to 1.02× 105 with the Prandtl number around 0.718.
The lattice Boltzmann equation LBE method has been considered as a powerful numerical tool for simulating complex athermal or isothermal fluid flows and associated transport phenomena 1, 2. LBE was first proposed as a numerical scheme by... more
The lattice Boltzmann equation LBE method has been considered as a powerful numerical tool for simulating complex athermal or isothermal fluid flows and associated transport phenomena 1, 2. LBE was first proposed as a numerical scheme by McNamara and Zanetti 3, which obtained a smoother macroscopic behavior than the lattice gas. Unlike conventional numerical schemes based on discretization of the macroscopic continuum equation, the LBE is based on the microscopic or mesoscopic kinetic equation.
Abstract: At the macroscale, the hydrodynamics of a fluid can be well described by conventional hydrodynamic models such as the Navier-Stokes equations. However, as the flow passage is shrunk down to the nanometer size, the... more
Abstract: At the macroscale, the hydrodynamics of a fluid can be well described by conventional hydrodynamic models such as the Navier-Stokes equations. However, as the flow passage is shrunk down to the nanometer size, the micro-interaction between the fluid and the confined solid walls becomes significant, and the conventional hydrodynamic model will become insufficient for describing such a flow system.
In this paper, a discrete velocity model and a lattice Boltzmann model are proposed for binary mixtures of nonideal fluids based on the Enskog theory. The velocity space of the Enskog equation for each component is first discretized by... more
In this paper, a discrete velocity model and a lattice Boltzmann model are proposed for binary mixtures of nonideal fluids based on the Enskog theory. The velocity space of the Enskog equation for each component is first discretized by applying a Gaussian quadrature, resulting in a discrete velocity model that can be solved by suitable numerical schemes. A lattice Boltzmann model is then derived from the discrete velocity model with a slightly modified equilibrium.
Laminar convection of a fluid with a temperature-dependent viscosity in an enclosure filled with a porous medium is studied numerically based on a Lattice Boltzmann method. It is shown that the variation in viscosity has significant... more
Laminar convection of a fluid with a temperature-dependent viscosity in an enclosure filled with a porous medium is studied numerically based on a Lattice Boltzmann method. It is shown that the variation in viscosity has significant influences on both flow and heat transfer behaviours. In comparison with the results for constant viscosity, the fluid with variable viscosity exhibits a higher heat transfer rate. The non-Darcy effects on fluid flow and heat transfer are also studied for both constant and variable viscosity.
ABSTRACT A lattice Boltzmann model for convection heat transfer in porous media is proposed. In this model, a new distribution function is introduced to simulate the temperature field in addition to the density distribution function for... more
ABSTRACT A lattice Boltzmann model for convection heat transfer in porous media is proposed. In this model, a new distribution function is introduced to simulate the temperature field in addition to the density distribution function for the velocity field. The macroscopic equations for convection heat transfer in porous media are recovered from the model through the Chapman-Enskog procedure.
To drive a fluid in a porous media, a large pressure drop is usually required. Under such cases, the standard lattice Boltzmann equation, which uses the equation of state of ideal gases, may fail to work due to compressibility effect. In... more
To drive a fluid in a porous media, a large pressure drop is usually required. Under such cases, the standard lattice Boltzmann equation, which uses the equation of state of ideal gases, may fail to work due to compressibility effect. In this paper, we propose an incompressible lattice Boltzmann model for porous flows, which can overcome this difficulty. Numerical results demonstrate that the model can use a large pressure without the compressibility effect.
Abstract At the microscale level, it is impossible to obtain a completely smooth wall surface, and the effect of surface roughness may be a main factor responsible for some different characteristics between fluid flow in the microchannels... more
Abstract At the microscale level, it is impossible to obtain a completely smooth wall surface, and the effect of surface roughness may be a main factor responsible for some different characteristics between fluid flow in the microchannels and that in conventional size channels. In the present work, the lattice Boltzmann method is applied to investigate the gaseous flow in a microchannel with surface roughness which is modeled by an array of rectangular modules.
Abstract This paper presents an analysis of the simultaneous incorporation of force and mass source terms into the multi-relaxation-time (MRT) collision operator. MRT force incorporation was obtained through Chapman–Enskog analysis. The... more
Abstract This paper presents an analysis of the simultaneous incorporation of force and mass source terms into the multi-relaxation-time (MRT) collision operator. MRT force incorporation was obtained through Chapman–Enskog analysis. The numerical scheme was tested on different benchmark problems, including the decay of a shear wave with different bulk and kinematic viscosities and axisymmetric flow.
We perform a numerical simulation for steady stably-stratified ёow over a two-dimensional backward-facing step with the Froude number of 16/9, the Reynolds number of 800 and the Prandtl number of 1.0 by using a newly developed thermal... more
We perform a numerical simulation for steady stably-stratified ёow over a two-dimensional backward-facing step with the Froude number of 16/9, the Reynolds number of 800 and the Prandtl number of 1.0 by using a newly developed thermal lattice Bhatnagar-Gross-Krook model. A detailed analysis is presented. Excellent agreement between the present results and other numerical data shows that the lattice Boltzmann method is an efficient simulation method for complex ёows.
Modeling and simulating mixtures of dense fluids is a challenging task in both science and engineering because such a system usually involves large range scales in both time and space, which may cause a significant obstacle for many... more
Modeling and simulating mixtures of dense fluids is a challenging task in both science and engineering because such a system usually involves large range scales in both time and space, which may cause a significant obstacle for many conventional numerical methods based on the Navier-Stokes equations. On the other hand, it is well understood that macroscopic phenomena occurring on large time and space scales are nothing but results of microscopic interactions between molecules.
In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium... more
In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the nonequilibrium part of the distribution at the neighbouring fiuid node. Schemes for velocity and pressure boundary conditions are constructed based on this method.
We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is... more
We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Several other existing force treatments are also examined.
The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to... more
The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to neglect the details in the thin EDL and replace its effects on the bulk flow and heat transfer with effective velocity-slip and temperature-jump boundary conditions outside the EDL.
Abstract In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate non-equilibrium flows. In this paper, instead of using three... more
Abstract In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate non-equilibrium flows. In this paper, instead of using three temperatures in the x−, y−, and z-directions, we further define the translational temperature as a second-order symmetric tensor.
Small-scale gaseous flows under atmospheric pressure have received particular attention in recent years with the rapid development in microscience and nanoscience and technology 1–3. The mean free path of the gas, say, is usually not very... more
Small-scale gaseous flows under atmospheric pressure have received particular attention in recent years with the rapid development in microscience and nanoscience and technology 1–3. The mean free path of the gas, say, is usually not very small in comparison with the characteristic length of the flow regions, L. As such, the Knudsen number of the flow, Kn=/L, may be relatively large, and the continuum assumption may break down.
The lattice Boltzmann Bhatnagar-Gross-Krook LBGK method has been rapidly developed as a promising numerical algorithm for computation fluid dynamics over the last decade 1–5. Among its various applications, it has been successfully... more
The lattice Boltzmann Bhatnagar-Gross-Krook LBGK method has been rapidly developed as a promising numerical algorithm for computation fluid dynamics over the last decade 1–5. Among its various applications, it has been successfully applied to simulation of incompressible flows. However, the LBGK method virtually solves the compressible Navier-Stokes equations in the incompressible limit.
In this paper, a finite-difference-based lattice Boltzmann (LB) algorithm is proposed to simulate electro-osmotic flows (EOF) with the effect of Joule heating. This new algorithm enables a nonuniform mesh to be adapted, which is desirable... more
In this paper, a finite-difference-based lattice Boltzmann (LB) algorithm is proposed to simulate electro-osmotic flows (EOF) with the effect of Joule heating. This new algorithm enables a nonuniform mesh to be adapted, which is desirable for handling the extremely thin electrical double layer in EOF. The LB algorithm has been validated by simulating a problem with an available analytical solution and it is found that the numerical results predicted by the algorithm are in good agreement with the analytical solution.
In this paper we present a product system and give a representation for cosine functions with the system. Based on the formula, two new algorithms are designed for computing the discrete cosine transform. Both algorithms have a regular... more
In this paper we present a product system and give a representation for cosine functions with the system. Based on the formula, two new algorithms are designed for computing the discrete cosine transform. Both algorithms have a regular recursive structure and good numerical stability and are easy to be implemented on parallel computers. Furthermore, this paper also provides a frame to design fast algorithms for discrete transforms.
Based on a multiple stage BGK-type collision model and the Chapman–Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The new gas dynamic equations have the same structure as... more
Based on a multiple stage BGK-type collision model and the Chapman–Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The new gas dynamic equations have the same structure as the Navier–Stokes equations, but the stress strain relationship in the Navier–Stokes equations is replaced by an algebraic equation with temperature differences. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier–Stokes equations.
Fluid flows in the nanometer scale can be studied by molecular dynamics or Monte Carlo methods, but the time and length scales are usually limited to rather short ranges due to the computational expense. Kinetic theory is an alternative... more
Fluid flows in the nanometer scale can be studied by molecular dynamics or Monte Carlo methods, but the time and length scales are usually limited to rather short ranges due to the computational expense. Kinetic theory is an alternative tool for studying nanoscale flows, but the existing models are rather complicated and difficult to implement. In this paper, we propose a simple Enskog-like kinetic model for nanoscale flows.
This paper deals with the numerical simulation of gas-solid two-phase fiows in an Eulerian-Lagrangian scheme. The particle tracks are calculated using a recently developed exponential Lagrangian scheme, and the approach presently used for... more
This paper deals with the numerical simulation of gas-solid two-phase fiows in an Eulerian-Lagrangian scheme. The particle tracks are calculated using a recently developed exponential Lagrangian scheme, and the approach presently used for the computation of fiuid phase is based on a modified Lattice-BGK model. Different from earlier publications, the present study employs a two-way coupling mechanism to handle the interactions between carrier phase and dispersed phase in the model.
Axisymmetric flows of incompressible fluids are frequently encountered in fundamental researches in fluid dynamics. Such flows can be treated as a two-dimensional 2D problem in the meridian plane so that computational costs can be... more
Axisymmetric flows of incompressible fluids are frequently encountered in fundamental researches in fluid dynamics. Such flows can be treated as a two-dimensional 2D problem in the meridian plane so that computational costs can be significantly reduced compared with fully threedimensional 3D computations. The lattice Boltzmann equation LBE, which appeared as an effective mesoscopical method for modeling and simulating fluid flows about two decades ago 1–5, has also been applied to axisymmetric flows recently.
Abstract The problems of fluid flow in porous media have an important researchful value and many applications to engineering thermophysics. In this paper, the multi-relaxation-time lattice Boltzmann method is used to predict permeability... more
Abstract The problems of fluid flow in porous media have an important researchful value and many applications to engineering thermophysics. In this paper, the multi-relaxation-time lattice Boltzmann method is used to predict permeability of two kinds of two-dimensional porous media.