X. D. Niu

Application of lattice Boltzmann method to simulate microchannel flows

Microflow has become a popular field of interest due to the advent of microelectromechanical systems. In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional isothermal pressure driven microchannel flow. Two boundary treatment schemes are incorporated to investigate their impacts to the entire flow field. We pay particular attention to the pressure and the slip velocity distributions along the channel in our simulation. We also look at the mass flow rate which is constant throughout the channel and the overall average velocity for the pressure-driven flow. In addition, we include a simulation of shear-driven flow in our results for verification. Our numerical results compare well with those obtained analytically and experimentally. From this study, we may conclude that the lattice Boltzmann method is an efficient approach for simulation of microflows.

Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows

The immersed boundary-lattice Boltzmann method was presented recently to simulate the rigid particle motion. It combines the desirable features of the lattice Boltzmann and immersed boundary methods. It uses a regular Eulerian grid for the flow domain and a Lagrangian grid for the boundary. For the lattice Boltzmann method, as compared with the single-relaxation-time collision scheme, the multi-relaxation-time collision scheme has better computational stability due to separation of the relaxations of various kinetic models, especially near the geometric singularity. So the multi-relaxation-time collision scheme is used to replace the single-relaxation-time collision scheme in the original immersed boundary-lattice Boltzmann method. In order to obtain an accurate result, very fine lattice grid is needed near the solid boundary. To reduce the computational effort, local grid refinement is adopted to offer high resolution near a solid body and to place the outer boundary far away from the body. So the multi-block scheme with the multi-relaxation-time collision model is used in the immersed boundary-lattice Boltzmann method. In each block, uniform lattice spacing can still be used. In order to validate the multi-block approach for the immersed boundary-lattice Boltzmann method with multi-relaxation-time collision scheme, the numerical simulations of steady and unsteady flows past a circular cylinder and airfoil are carried out and good results are obtained.

Simulation of flows around an impulsively started circular cylinder by Taylor series expansion-and least squares-based lattice Boltzmann method

The two-dimensional incompressible viscous flow past an impulsively started circular cylinder for a wide range of Reynolds numbers (Re = 20-9500) is studied computationally by using an explicit Taylor series expansion-and least squares-based lattice Boltzmann method. The final equation for distribution function in our method is in an explicit form and essentially has no limitation on choice of mesh structure and lattice model. It can be easily applied to simulation of flows with curved boundaries such as the problem considered in this work. For the flow past an impulsively started circular cylinder, numerical results obtained by present method agree very well with experimental data and computational results of Navier-Stokes equations available in the literature.

A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids

A new differential lattice Boltzmann equation (LBE) is presented in this work, which is derived from the standard LBE by using Taylor series expansion only in spatial direction with truncation to the second-order derivatives. The obtained differential equation is not a wave-like equation. When a uniform grid is used, the new differential LBE can be exactly reduced to the standard LBE. The new differential LBE can be applied to solve irregular problems with the help of coordinate transformation. The present scheme inherits the merits of the standard LBE. The 2-D driven cavity flow is chosen as a test case to validate the present method. Favorable results are obtained and indicate that the present scheme has good prospects in practical applications.

A fractional step lattice Boltzmann method for simulating high Reynolds number flows

A fractional step lattice Boltzmann scheme is presented to greatly improve the stability of the lattice Boltzmann method (LBM) in modelling incompressible flows at high Reynolds number. This method combines the good features of the conventional LBM and the fractional step technique. Through the fractional step, the flow at an extreme case of infinite Reynolds number (inviscid flow) can be effectively simulated. In addition, the non-slip boundary condition can be directly implemented.

Taylor series expansion- and least square-based Lattice Boltzmann method: an efficient approach for simulation of incompressible viscous flows

The Taylor series expansion- and least-square-based Lattice Boltzmann method (TLLBM) is a flexible Lattice Boltzmann approach capable of simulating incompressible viscous flows with arbitrary geometry. The method is based on the standard Lattice Boltzmann equation (LBE), Taylor series expansion and the least square optimisation. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Successful applications of isothermal and thermal incompressible viscous flows have shown that the TLLBM is an efficient and promising version of LBM. In this paper, we will give the details of TLLBM and present some examples of its application.