Three-dimensional electrohydrodynamic flows by a central-moments-based lattice Boltzmann method

Parallel Computation of Three-dimensional Two-phase Flows by the Lattice Boltzmann Method

An alternative lattice Boltzmann model for three-dimensional incompressible flow

The asymptotic theory proposed by Sone [in Rarefied Gas Dynamics, edited by D. Dini (Editrice Tecnico Scientifica, Pisa, 1971), p. 737] is applied to the investigation of the accuracy of the lattice Boltzmann method (LBM) for small Knudsen number with finite Reynolds number. The S-expansion procedure of the asymptotic theory is applied to LBM with the nine-velocity model and fluid-dynamic type equations are obtained. From the fluid-dynamic type equations it is found that by using the LBM we can obtain the macroscopic flow velocities and the pressure gradient for incompressible fluid with relative errors of O(ε′2) where ε′ is a modified Knudsen number which is of the same order as the lattice spacing and is related to a dimensionless relaxation time. In two problems, the Couette flow with flow injection and suction through porous walls and a three-dimensional flow through a square duct, the accuracy of LBM is examined for relaxation times between 0.8 and 1.7 and the validity of the asymptotic theory for LBM is shown.

Two and three-dimensional flows around solid boundaries are interesting and important subjects to both scientists and engineers. Lattice Boltzmann Method (LBM) is a relatively new computational method to simulate fluid flows by tracking the collision, advection and propagation of mesoscopic fluid particles. LBM is originated from the Cellular automata combined with kinetic theory and the Boltzmann equation. The method solves the explicit finite difference scheme lattice Boltzmann equations which are second order in space and first order in time. LBM does not attempt to solve the Navier-Stokes equations directly, however, it obeys them. The two-dimensional flows around square and circular cylinders are simulated with uniform and nonuniform grid structures using LBM. The boundary-layer growth and wake region physics are captured with small scale details, and the results are discussed in comparison with the available references for Reynolds numbers between 50 and 350. The compatibility of the method to simulate a flow around ship-shaped geometries and a combination of objects is also provided.

Lattice Boltzmann method of two-and three-dimensional thermosolutal convection is investigated in this paper. Lattice Boltzmann method with multiple components was applied to simulate two-dimensional thermosolutal convection flow on a square cavity. The numerical results agree well with those of high order finite difference method. It shows that the numerical scheme is efficient. Therefore the lattice Boltzmann method is extended to investigate three-dimensional thermosolutal convection flow in cubic cavity. The comparison between the proposed lattice Boltzmann method and a finite difference method shows a satisfactory agreement. The limitation of the lattice Boltzmann model in the double-diffusive convection is discussed.

Consistent and conservative lattice Boltzmann method for axisymmetric multiphase electrohydrodynamic flows

ABSTRACTFree-surface flow problems occur in numerous disaster simulations, such as tsunami inland penetration in urban areas. Simulation models for these problems must be non-hydrostatic, three-dimensional and highly resolved because of the strong non-linearity and higher-order physical phenomena. However, three-dimensional large-scale tsunami simulations based on conventional computational fluid dynamics (CFD) solving the Navier-Stokes equations are challenging due to the pressure Poisson equation in incompressible Navier-Stokes fluid modeling. The lattice Boltzmann method (LBM) is an alternative simulation tool that is attracting attention as a fully explicit and efficient approach. The LBM does not have to iteratively solve the pressure Poisson equation and is therefore considered to have an advantage over other methods when executing high-performance three-dimensional tsunami simulations. In the current study, we developed a fully explicit free-surface model using the LBM in which the more advanced multiple-relaxation-time (MRT) collision model is used, along with the piecewise linear interface calculation (PLIC) approach. Through classic dam-break problems, we validated the appropriate parameter settings, including the weak compressibility, for tsunami simulations. The benchmark tests showed that our model accurately simulates the three-dimensional dam-break flows and controls the compressibility drop in the second-order value of the Mach number.

In this paper, two sub-grid scale (SGS) models are introduced into the Lattice Boltzmann Method (LBM), i.e., the dynamics SGS model and the dynamical system SGS model, and applied to numerically solving three-dimensional high Re turbulent cavity flows. Results are compared with those obtained from the Smagorinsky model and direct numerical simulation for the same cases. It is shown that the method with LBM dynamics SGS model has advantages of fast computation speed, suitable to simulate high Re turbulent flows. In addition, it can capture detailed fine structures of turbulent flow fields. The method with LBM dynamical system SGS model dose not contain any adjustable parameters, and can be used in simulations of various complicated turbulent flows to obtain correct information of sub-grid flow field, such as the backscatter of energy transportation between large and small scales. A new average method of eliminating the inherent unphysical oscillation of LBM is also given in the paper.

The calculation of wind load of high-rise buildings depends on the wind pressure distribution data and wind pressure coefficient on the outer surface of the building, but the actual wind pressure measurement of high-rise buildings is difficult to carry out. In order to obtain the effective wind pressure coefficient of the building and the application of the extended lattice Boltzmann method (LBM) in the wind resistance of high-rise buildings, in this paper, the wall-adapting local eddy (WALE) model, dynamic Smagorinsky model (DSM), and Smagorinsky model (SM) are embedded into LBM with multiple-relaxation-time (MRT) format. Three LBM large eddy simulation models, MRT-LBM-WALE, MRT-LBM-DSM, and MRT-LBM-SM, which can simulate the flow around a bluff body with high Rayleigh number, are constructed by using the subgrid eddy viscosity to modify the kinematic viscosity of LBM. Finally, the three turbulence models are used to simulate and analyze the three-dimensional steady wind flow field of a single high-rise building of the standard CAARC high-rise building model in the atmospheric boundary layer, and the numerical results are analyzed and compared with the wind tunnel test results. The results show that the numerical simulation better reflects the flow characteristics and surface wind pressure of the wind environment around the high-rise building. On the windward side, it fits well with the test results. On the crosswind side and leeward side, the numerical simulation results are between the NPL and TJ-2 test results. The windward side is subject to positive pressure, which is the highest at 2/3 of the height of the windward side and low on both sides and below. The leeward and crosswind surfaces of the building are all under negative pressure. The simulation results of the three turbulence models have little difference, which provides a basis for the study of the flow around the bluff body of high-rise buildings. It is proved that the numerical solutions of the three models are in good agreement with the experimental solutions, and the real subgrid eddy viscosity near the wall can be obtained, which can accurately predict the development of turbulent flow.

The lattice Boltzmann method (LBM) is applied to simulate the complete three-dimensional transient flow and noise generated on the Advanced Noise Control Fan (ANCF) geometry. The ANCF is a model developed by NASA Glenn composed by a rotor–stator system enclosed by a duct. The experimental noise spectra provided by NASA at 30 microphones around the fan are used to validate the results obtained with the LBM. Overall, the predicted sound spectra pattern and the main tonal frequencies agree well with the noise measurements; in terms of tonal noise levels, the agreement varies depending on the frequency and microphone position. The noise at the 30 microphone positions is also computed by employing the porous Ffowcs Williams and Hawkings (FW–H) formulation with noise sources located on two integral surfaces placed at the ANCF openings. The good agreement obtained between the sound levels calculated with the FW–H formulation and those computed by the LBM show that the FW–H analogy may be applied in place of the LBM numerical simulation. In addition, the FW–H formulation is applied to compute the sound generation with sources located on different physical surfaces of the ANCF model such as the rotor, stator, hub, and nacelle, procedure known as noise source breakdown. A comparison of the FW–H results applied on different surfaces of the ANCF model with the noise computed by the LBM shows that most of the tonal noise levels observed at the far-field microphones (predicted by the LBM simulation) correspond to the noise sources generated on the stator vane surfaces. Such a study of the noise sources breakdown also evidences the interaction effect between the rotor and the stator, whose mechanism is the main contributor to the tonal noise generation content.

Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number

Multilayer shallow water flow using lattice Boltzmann method with high performance computing

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum-exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second-order accuracy based on our recent works [Mei et al., J. Comput. Phys. 155, 307 (1999); ibid. 161, 680 (2000)]. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

This paper further develops the parallel algorithm, lattice Boltzmann (LB) model for simulation of transport phenomena. The lattice Boltzmann model is based on concepts that lay between the molecular and continuum extremes and is capable of drawing information and producing phenomena from both scales. Transport processes are simulated on a lattice array of nodes or points of local interaction, making natural parallel computations. Three-dimensional laminar and turbulent flow in a cavity driven by a moving wall are simulated. The model and computer simulation correctly predicts the unsteady Taylor-Görtler-Like (TGL) vortices and corner vortices observed in experiments for mediate Reynolds numbers. Quantitative comparisons are made to those from a 2-D simulation and a 3-D experiment. The excellent agreement between the LB method and experimental work shows that the LB method has great potential for solving complex, unsteady 3-D flow. The subgrid turbulent model is introduced on the lattice Boltzmann framework and applied to 3-D cavity flow. Detailed information-rich results are obtained over a range of the Reynolds number.

Numerical simulation using the lattice Boltzmann Method is presented for three-dimensional decaying homogeneous isotropic turbulence. Fifteen-velocity cubic lattice model is used for the simulation. The LBGK method is able to reproduce the dynamic of decaying turbulence and could be an alternative for solving the Navier-Stokes equations. The lattice Boltzmann method is parallelized by using domain decomposition and implemented on a distributed memory computer, Hitachi SR2201. It is found that the larger the number of subdomains, the worse the parallel efficiency because of the data communication. Further investigation is needed on the accuracy and efficiency of cubic LBGK method.