This paper investigates the feasibility of improving the aircraft landing performance by design the damping orifice parameters of the landing gear using lattice Boltzmann method coupled with the response surface method. The LBM is utilised to simulate characteristics of the damping orifice after model validation. The numerical model of the landing gear using simulated damping force is validated by single landing gear drop test. Based on the numerical model and the response surface functions, the sensitivity analysis and the optimisation design are performed. The maximum error of mean velocity simulated using LBM with experimental data is 7.07% for sharp-edged orifices. Moreover, the numerical model predicts the landing responses adequately, the maximum error with drop test data is 2.51%. The max overloading of the aircraft decreases by 5.44% after optimisation, which proves that this method is feasible to design the damping orifice for good landing performance.

Lack of flexibility limits the performance enhancement of man-made flapping wing Micro Air Vehicles (MAVs). Active chordwise deformation (bending) is introduced into the flapping wing model at low Reynolds number of Re = 200 in the present study. The lattice Boltzmann method with immersed boundary is adopted in the numerical simulation. The effects of the bending amplitude, bending frequency and phase lag between bending and flapping on the propulsive performance are analysed. The numerical results show that all the chordwise deformation parameters including the bending amplitude, bending frequency and phase lag have a great influence on the flow field, Leading-Edge Vortex (LEV), Trailing-Edge Vortex (TEV) and previous Leading-Edge Vortex (pLEV) of the deformable flapping wing, which leads to the variation of the propulsive performance. With decreasing bending amplitude and increasing bending frequency, both the thrust and energy dissipation coefficients increase. The highest thrust coefficient and highest energy dissipation coefficient occur at a phase lag of 180°. On the other hand, strong dependence of the propulsive efficiency on the vortex tangle is found. The highest propulsive efficiency is obtained for the present model at a dimensionless bending amplitude of 0.2, bending frequency of 0.7Hz, and phase lag of 0°.

Lattice Boltzmann method (LBM) is adopted to compute two and three-dimensional lid driven cavity flows to examine the influence of memory management on the computational performance using Graphics Processing Unit (GPU). Both single and multi-relaxation time LBM are adopted. The computations are conducted on nVIDIA GeForce Titan, Tesla C2050 and GeForce GTX 560Ti. The performance using global memory deteriorates greatly when multi relaxation time (MRT) LBM is used, which is due to the scheme requesting more information from the global memory than its single relaxation time (SRT) LBM counterpart. On the other hand, adopting on chip memory the difference using MRT and SRT is not significant. Also, performance of LBM streaming procedure using offset reading surpasses offset writing ranging from 50% to 100% and this applies to both SRT and MRT LBM. Finally, comparisons using different GPU platforms indicate that Titan as expected outperforms other devices, and attains 227 and 193 speedup over its Intel Core i7-990 CPU counterpart and four times faster than GTX 560Ti and Tesla C2050 for three dimensional cavity flow simulations respectively with single and double precisions.

In this paper, the magnetic field effects on natural convection of power-law nanofluids in rectangular enclosures are investigated numerically with the lattice Boltzmann method. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles and the investigations are carried out for different governing parameters including Hartmann number (0.0≤Ha≤20.0), Rayleigh number (104≤Ra≤106), power-law index (0.5≤n≤1.0), nanopartical volume fraction (0.0≤ϕ≤0.1) and aspect ratio (0.125≤AR≤8.0). The results reveal that the flow oscillations can be suppressed effectively by imposing an external magnetic field and the augmentation of Hartmann number and power-law index generally decreases the heat transfer rate. Additionally, it is observed that the average Nusselt number is increased with the increase of Rayleigh number and nanoparticle volume fraction. Moreover, the present results also indicate that there is a critical value for aspect ratio at which the impact on heat transfer is the most pronounced.

Numerical simulations of two-dimensional (2D) turbulent thermal convection for inhomogeneous boundary condition are investigated using the lattice Boltzmann method (LBM). This study mainly appraises the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. The research results show that the flow is dominated by large-scale structures in the turbulence regime. Mushroom plumes emerge at both ends of each heat source, and smaller plumes increasingly rise. It is found that the gradient of root mean-square (rms) vertical velocities and the gradient of the rms temperature in the bottom boundary layer decreases with time evolution. It is further observed that the temporal evolution of the Kolmogorov scale, the kinetic-energy dissipation rates and thermal dissipation rates agree well with the theoretical predictions. It is also observed that there is a range of linear scaling in the 2nd-order structure functions of the velocity and temperature fluctuations and mixed velocity-temperature structure function.

Almost all schemes existed in the literature to solve the Lattice Boltzmann Equation like stream & collide, finite difference, finite element, finite volume schemes are explicit. However, it is known fact that implicit methods utilizes better stability and faster convergence compared to the explicit methods. In this paper, a method named herein as Implicit Finite Volume Lattice Boltzmann Method (IFVLBM) for incompressible laminar and turbulent flows is proposed and it is applied to some 2D benchmark test cases given in the literature. Alternating Direction Implicit, an approximate factorization method is used to solve the obtained algebraic system. The proposed method presents a very good agreement for all the validation cases with the literature data. The proposed method shows good stability characteristics, the CFL number is eased. IFVLBM has about 2 times faster convergence rate compared with Implicit-Explicit Runge Kutta method even though it possesses a computational burden from the solution of algebraic systems of equations.

A lattice Boltzmann method is utilized for governing equations which control phase separation of binary fluids with reversible chemical reaction in presence of a shear flow in this paper. We first present the morphology modeling of sheared binary fluids with reversible chemical reaction. We then validate the model by taking the unsheared binary fluids as an example. It is found that the results fit well with the references. The paper shows structures of the sheared system and gives the detailed analysis for the morphology of sheared binary fluids with reversible chemical reaction. The phase separation of the domain structures with different chemical reaction rates is discussed. Through simulations of the sheared binary fluids, two interesting phenomena are observed, which do not exist in a binary mixture without reversible chemical reaction. One is that the same results appear in both low and high viscosity, and the other is that the domain growth exponent with both low and high viscosities presents wave due to the competition of the viscosity and phase separation. In addition, we find that the finite size effects resulting in the growth exponent decreasing appear faster than that of the unsheared blend at a large time when the size of domains is comparable with the lattice size.

The lattice Boltzmann method is employed to simulate the steady flow in a two-dimensional lid-driven semi-elliptical cavity. Reynolds number (Re) and vertical-to-horizontal semi-axis ratio (D) are in the range of 500-5000 and 0.1-4, respectively. The effects of Re and D on the vortex structure and pressure field are investigated, and the evolutionary features of the vortex structure with Re and D are analyzed in detail. Simulation results show that the vortex structure and its evolutionary features significantly depend on Re and D. The steady flow is characterized by one vortex in the semi-elliptical cavity when both Re and D are small. As Re increases, the appearance of the vortex structure becomes more complex. When D is less than 1, increasing D makes the large vortexes more round, and the evolution of the vortexes with D becomes more complex with increasing Re. When D is greater than 1, the steady flow consists of a series of large vortexes which superimpose on each other. As Re and D increase, the number of the large vortexes increases. Additionally, a small vortex in the upper-left corner of the semi-elliptical cavity appears at a large Re and its size increases slowly as Re increases. The highest pressures appear in the upper-right corner and the pressure changes drastically in the upper-right region of the cavity. The total pressure differences in the semi-elliptical cavity with a fixed D decrease with increasing Re. In the region of themain vortex, the pressure contours nearly coincide with the streamlines, especially for the cavity flow with a large Re.

In this paper, an alternative lattice Boltzmann (LB)model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretizedwith the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

In this paper, a diffuse-interface immersed boundary method (IBM) is proposed to treat three different thermal boundary conditions (Dirichlet, Neumann, Robin) in thermal flow problems. The novel IBM is implemented combining with the lattice Boltzmann method (LBM). The present algorithm enforces the three types of thermal boundary conditions at the boundary points. Concretely speaking, the IBM for the Dirichlet boundary condition is implemented using an iterative method, and its main feature is to accurately satisfy the given temperature on the boundary. The Neumann and Robin boundary conditions are implemented in IBM by distributing the jump of the heat flux on the boundary to surrounding Eulerian points, and the jump is obtained by applying the jump interface conditions in the normal and tangential directions. A simple analysis of the computational accuracy of IBM is developed. The analysis indicates that the Taylor-Green vortices problem which was used in many previous studies is not an appropriate accuracy test example. The capacity of the present thermal immersed boundary method is validated using four numerical experiments: (1) Natural convection in a cavity with a circular cylinder in the center; (2) Flows over a heated cylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentation of a single isothermal cold particle in a vertical channel. The numerical results show good agreements with the data in the previous literatures.

This paper presents a lattice Boltzmann (LB) method based study aimed at numerical simulation of aeroacoustic phenomenon in flows around a symmetric obstacle. To simulate the compressible flow accurately, a potential energy double-distribution-function (DDF) lattice Boltzmann method is used over the entire computational domain from the near to far fields. The buffer zone and absorbing boundary condition is employed to eliminate the non-physical reflecting. Through the direct numerical simulation, the flow around a circular cylinder at Re=150, M=0.2 and the flow around a NACA0012 airfoil at Re=10000, M=0.8, α=0° are investigated. The generation and propagation of the sound produced by the vortex shedding are reappeared clearly. The obtained results increase our understanding of the characteristic features of the aeroacoustic sound.

In this study long bubble rising in a narrow channel was investigated using multiphase lattice Boltzmann method. The problem is known as a Bretherton or Taylor bubble flow [2] and is used here to verify the performance of the scheme proposed by [13]. The scheme is modified by incorporation of multiple relaxation time (MRT) collision scheme according to the original suggestion of the author. The purpose is to improve the stability of the method. The numerical simulation results show a good agreement with analytic solution provided by [2]. Moreover the convergence study demonstrates that the method achieves more than the first order of convergence. The paper investigates also the influence of simulation parameters on the interface resolution and shape.

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.

In this paper, we propose two initialization techniques for the lattice Boltzmann method. The first one is based on the theory of asymptotic analysis developed in [M. Junk and W.-A. Yong, Asymptotic Anal., 35(2003)]. By selecting consistent macroscopic quantities, this initialization leads to the second-order convergence for both velocity and pressure. Another one is an improvement of the consistent initial conditions proposed in [R. W. Mei, L.-S. Luo, P. Lallemand and D. d’Humières, Comput. Fluids, 35(2006)]. The improvement involves a modification of the collision term and a reconstruction step. Numerical examples confirm the accuracy and efficiency of our techniques.

Our recently developed lattice Boltzmann model is used to simulate droplet dynamical behaviour governed by thermocapillary force in microchannels. One key research challenge for developing droplet-based microfluidic systems is control of droplet motion and its dynamic behaviour. We numerically demonstrate that the thermocapillary force can be exploited for microdroplet manipulations including synchronisation, sorting, and splitting. This work indicates that the lattice Boltzmann method provides a promising design simulation tool for developing complex droplet-based microfluidic devices.

Combining asymptotic analysis and weighted L2 stability estimates, the convergence of lattice Boltzmann methods for the approximation of 1D convection-diffusion-reaction equations is proved. Unlike previous approaches, the proof does not require transformations to equivalent macroscopic equations.

Mixing processes of miscible viscous fluids in anisotropic porous media are studied through a lattice Boltzmann method in this paper. The results show that fluid mixing can be enhanced by the disorder and interfaces induced by viscous fingers. Meanwhile, the permeability anisotropy affects the developments of viscous fingers and the subsequent mixing behaviors significantly. Specifically, as the streamwise (longitudinal) permeability is larger than the spanwise (transverse) one, the mixing process is faster and stronger than that in the contrary case. Furthermore, the anisotropy can lead to different behaviors of the dissipation rates in streamwise and spanwise directions. Generally, the dissipation rate is dominated by the transverse concentration gradients when the longitudinal permeability is higher than the transverse one; on the contrary, as the transverse permeability is higher than the longitudinal one, the contributions to the dissipation rate from longitudinal and transverse concentration gradients are both significant.

Newtonian and non-Newtonian dispersed phase droplet formation in non-Newtonian continuous phase in T-junction and cross junction microchannels are investigated by the immiscible lattice BGK model. The effects of the non-Newtonian fluid power-law exponent, viscosity and interfacial tension on the generation of the droplet are studied. The final droplet size, droplet generation frequency, and detachment point of the droplet change with the power-law exponent. The results reveal that it is necessary to take into account the non-Newtonian rheology instead of simple Newtonian fluid assumption in numerical simulations. The present analysis also demonstrates that the lattice Boltzmann method is of potential to investigate the non-Newtonian droplet generation in multiphase flow.

Conducting lattice Boltzmann method on GPU has been proved to be an effective manner to gain a significant performance benefit, thus the GPU or multi-GPU based lattice Boltzmann method is considered as a promising and competent candidate in the study of large-scale complex fluid flows. In this work, a multi-GPU based lattice Boltzmann algorithm coupled with the sparse lattice representation and message passing interface is presented. Some numerical tests are also carried out, and the results show that a parallel efficiency close to 90% can be achieved on a single-node cluster equipped with four GPU cards. Then the proposed algorithm is adopted to study the hemodynamics of patient-specific cerebral aneurysm with stent implanted. It is found that the stent can apparently reduce the aneurysmal inflow and improve the hemodynamic environment. This work also shows that the lattice Boltzmann method running on the GPU platform is a powerful tool to study the fluid mechanism within the aneurysms and enable us to better understand the pathogenesis and treatment of cerebral aneurysms.