L. M. Yang

Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

This paper at first shows the details of finite volume-based lattice Boltz- mann 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 conser- vation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parame- ter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three mod- els for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test prob- lems. 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. AMS subject classifications: 76T10

A fractional-step lattice Boltzmann flux solver for axisymmetric thermal flows

ABSTRACT A fractional-step lattice Boltzmann flux solver is proposed in this work for effective simulation of axisymmetric thermal flows with rotating walls. The predictor and corrector steps are introduced in the solver. In the predictor step, excluding axisymmetric effects, the intermediate flow variables are predicted by the lattice Boltzmann flux solver (LBFS), which applies the finite-volume method to discretize the conservative equations recovered by the standard lattice Boltzmann method (LBM). The fluxes of the LBFS at the cell interfaces are reconstructed by local application of the lattice Boltzmann (LB) model with three distribution functions. These three distribution functions are used respectively for calculating axial and radial velocities, azimuthal velocity, and internal energy. In the corrector step, the intermediate flow variables are corrected by considering the axisymmetric effects. The present method not only retains the simplicity of the LBM but also eliminates the complicated derivation process in the axisymmetric LB model. The reliability of the proposed solver is examined by its application to simulate natural convection in an annulus, the Rayleigh-Benard convection, mixed convection in a vertical tall annulus, and Wheeler’s benchmark problem in crystal growth. The numerical results obtained agree well with the published data.

A Boundary Condition-Implemented Immersed Boundary-Lattice Boltzmann Method and Its Application for Simulation of Flows Around a Circular Cylinder

A boundary condition-implemented immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this work. The present approach is an improvement to the conventional IB-LBM. In the conventional IB-LBM, the no-slip boundary condi- tion is only approximately satisfied. As a result, there is flow penetration to the solid boundary. Another drawback of conventional IB-LBM is the use of Dirac delta func- tion interpolation, which only has the first order of accuracy. In this work, the no-slip boundary condition is directly implemented, and used to correct the velocity at two adjacent mesh points from both sides of the boundary point. The velocity correction is made through the second-order polynomial interpolation rather than the first-order delta function interpolation. Obviously, the two drawbacks of conventional IB-LBM are removed in the present study. Another important contribution of this paper is to present a simple way to compute the hydrodynamic forces on the boundary from Newtons second law. To validate the proposed method, the two-dimensional vor- tex decaying problem and incompressible flow over a circular cylinder are simulated. As shown in the present results, the flow penetration problem is eliminated, and the obtained results compare very well with available data in the literature. AMS subject classifications: 76M28, 76M25

A simple gas kinetic scheme for simulation of 3D incompressible thermal flows

ABSTRACT In this work, a simple gas kinetic scheme is presented for solving the 3D incompressible thermal flow problems. In the scheme, the macroscopic-governing equations are discretized by finite volume method, and the numerical fluxes at cell interface are reconstructed by the local solution of the Boltzmann equation. To compute the numerical fluxes, two equilibrium distribution functions are introduced. One is the sphere function for calculating the fluxes of mass and momentum equations, and the other is the D3Q6 discrete velocity model for evaluating the flux of energy equation. Using the difference of equilibrium distribution functions at the cell interface and its surrounding points to approximate the nonequilibrium distribution function, and at the same time considering the incompressible limit, the numerical fluxes of macroscopic governing equations at the cell interface can be given explicitly and concisely. Numerical results showed that the present scheme can predict accurately the thermal flow properties at a wide range of the Rayleigh numbers.

Numerical Simulation of Microflows by a DOM With Streaming and Collision Processes

Inspired from the idea of developing lattice Boltzmann method (LBM), a discrete ordinate method (DOM) with streaming and collision processes is presented for simulation of microflows in this work. The current method is quite different from the conventional discrete ordinate method (DOM), unified gas kinetic scheme (UGKS) and discrete unified gas kinetic scheme (DUGKS), in which the finite volume method (FVM) or the finite difference method (FDM) is usually utilized to discretize the discrete velocity Boltzmann equation (DVBE). Due to the application of FVM or FDM, the evaluation of the flux of distribution function at the cell interface becomes an essential step for these approaches. Besides that, for the UGKS and DUGKS, not only the flux of distribution functions but also the conservative variables at the cell interface are needed to be computed. These processes require a lot of computational efforts. In contrast, for the developed method, it only needs interpolations within the cell to perform the streaming process. Thus, the computational efficiency can be improved accordingly. To compare the accuracy and efficiency of present scheme with those of DSMC and/or UGKS, several numerical examples including the Couette flow, pressure driven Poiseuille flow and thermal transpiration flow are simulated. Numerical results showed that the solution accuracy of current scheme is comparable to that of DSMC and UGKS. However, as far as the computational efficiency is concerned, the present scheme is more efficient than UGKS.Copyright