Zhaoli Guo

An extrapolation method for boundary conditions in lattice Boltzmann method

A boundary treatment for curved walls in lattice Boltzmann method is proposed. The distribution function at a wall node who has a link across the physical boundary is decomposed into its equilibrium and nonequilibrium parts. The equilibrium part is then approximated with a fictitious one where the boundary condition is enforced, and the nonequilibrium part is approximated using a first-order extrapolation based on the nonequilibrium part of the distribution on the neighboring fluid node. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.

A LATTICE BOLTZMANN MODEL FOR CONVECTION HEAT TRANSFER IN POROUS MEDIA

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. The model is validated by several benchmark problems, and it is found that the numerical results are in good agreement with the well-documented results in the literature.

Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows

In this paper, we study systematically the physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation (LBE) for microgas flows in both the slip and transition regimes. We show that the physical symmetry and the spatial accuracy of the existing LBE models are inadequate for simulating microgas flows in the transition regime. Our analysis further indicates that for a microgas flow, the channel wall confinement exerts a nonlinear effect on the relaxation time, which should be considered in the LBE for modeling microgas flows.

Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer

In this work, we apply the lattice Boltzmann equation (LBE) with multiple relaxation times (MRTs) to simulate the Poiseuille flow in the slip flow regime. We analyse in detail the discrete diffusive and combined bounce-back-specular-reflection boundary conditions for the LBE, the discrete effects at the boundary, and determinations of the relaxation times for the Poiseuille flow in the slip flow regime. In particular, we implement second-order slip boundary conditions with the MRT–LBE model and validate our numerical results for the slip Poiseuille flow with the Knudsen number Kn ≤ 0.2 by using the analytic solution. Our analysis shows that the lattice Bhatnagar–Gross–Krook (BGK) model cannot yield correct results for the Poiseuille flow in the slip-flow regime. We also discuss the possibilities of extending the LBE for the Knudsen layer in micro flows.

A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows

We compare the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS) applied to 2D incompressible laminar flows. Although both methods are derived from the Boltzmann equation thus share a common kinetic origin, numerically they are rather different. The LBE is a finite difference method, while the GKS is a finite-volume one. In addition, the LBE is valid for near incompressible flows with low-Mach number restriction Ma<0.3, while the GKS is valid for fully compressible flows. In this study, we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxation-time (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We use both the LBE and GKS methods to simulate the flow past a square block symmetrically placed in a 2D channel with the Reynolds number Re between 10 and 300. The LBE and GKS results are validated against the well-resolved results obtained using finite-volume method. Our results show that both the LBE and GKS yield quantitatively similar results for laminar flow simulations, and agree well with existing ones, provided that sufficient grid resolution is given. For 2D problems, the LBE is about 10 and 3 times faster than the GKS for steady and unsteady flow calculations, respectively, while the GKS uses less memory. We also observe that the GKS method is much more robust and stable for under-resolved cases due to its upwinding nature and interpolations used in calculating fluxes.

A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices

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. The LB algorithm is also applied to modeling a mixed electro-osmotic/pressure driven flow in a channel. The numerical results show that Joule heating plays an important role in EOF.

Lattice Boltzmann simulation of natural convection with temperature-dependent viscosity in a porous cavity

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.

Discrete unified gas kinetic scheme for all Knudsen number flows. II. Thermal compressible case.

This paper is a continuation of our work on the development of multiscale numerical scheme from low-speed isothermal flow to compressible flows at high Mach numbers. In our earlier work [Z. L. Guo et al., Phys. Rev. E 88, 033305 (2013)], a discrete unified gas kinetic scheme (DUGKS) was developed for low-speed flows in which the Mach number is small so that the flow is nearly incompressible. In the current work, we extend the scheme to compressible flows with the inclusion of thermal effect and shock discontinuity based on the gas kinetic Shakhov model. This method is an explicit finite-volume scheme with the coupling of particle transport and collision in the flux evaluation at a cell interface. As a result, the time step of the method is not limited by the particle collision time. With the variation of the ratio between the time step and particle collision time, the scheme is an asymptotic preserving (AP) method, where both the Chapman-Enskog expansion for the Navier-Stokes solution in the continuum regime and the free transport mechanism in the rarefied limit can be precisely recovered with a second-order accuracy in both space and time. The DUGKS is an idealized multiscale method for all Knudsen number flow simulations. A number of numerical tests, including the shock structure problem, the Sod tube problem in a whole range of degree of rarefaction, and the two-dimensional Riemann problem in both continuum and rarefied regimes, are performed to validate the scheme. Comparisons with the results of direct simulation Monte Carlo (DSMC) and other benchmark data demonstrate that the DUGKS is a reliable and efficient method for multiscale flow problems.

Lattice Boltzmann Simulations of Fluid Flows

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.

A Multiple-Relaxation-Time Lattice Boltzmann Model for General Nonlinear Anisotropic Convection---Diffusion Equations

In this paper, based on the previous work (Shi and Guo in Phys Rev E 79:016701, 2009), we develop a multiple-relaxation-time (MRT) lattice Boltzmann model for general nonlinear anisotropic convection–diffusion equation (NACDE), and show that the NACDE can be recovered correctly from the present model through the Chapman–Enskog analysis. We then test the MRT model through some classic CDEs, and find that the numerical results are in good agreement with analytical solutions or some available results. Besides, the numerical results also show that similar to the single-relaxation-time lattice Boltzmann model or so-called BGK model, the present MRT model also has a second-order convergence rate in space. Finally, we also perform a comparative study on the accuracy and stability of the MRT model and BGK model by using two examples. In terms of the accuracy, both the analysis and numerical results show that a numerical slip on the boundary would be caused in the BGK model, and cannot be eliminated unless the relaxation parameter is fixed to be a special value, while the numerical slip in the MRT model can be overcome once the relaxation parameters satisfy some constrains. The results in terms of stability also demonstrate that the MRT model could be more stable than the BGK model through tuning the free relaxation parameters.