Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

Modified lattice Boltzmann scheme for nonlinear convection diffusion equations

In order to analyze the fluid-structure interaction between a flow and a flexible structure, an algorithm was presented to couple the lattice Boltzmann method (LBM) and the finite element method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e., one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also introduced for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.

The last decade the Lattice Boltzmann method has evolved into a powerfull solver for flow through porous media, where the solid phase is represented fully resolved on the computational grid (Hill, 2001). Packed and stored fresh agricultural produce are frequently modeled as porous media and therefore we envision Lattice Boltzmann to be an important tool for simulating heat and mass transport in these systems via forced or natural convection. However, practical package and storage systems have too large lengthscales for fully resolved simulations. Consequently, simulations on the full system scale have to be performed at the volume-averaged scale. For the volume-averaged scale closure relations are needed such as the drag force, effective diffusivity or conductivity. Also here Lattice Boltzmann can play a vital role. Lattice Boltzmann is also capable of simulations at the volume-averaged scale, though it has not frequently used for this scale. With this capability, we can build a multiscale simulation approach, similar to what is developed for fluidized beds (van der Hoef, 2004). In this contribution we will present the general framework, and applications of Lattice Boltzmann to forced flow through package with spherical produce (fully resolved), natural convection in bulk containers of seed potatoes (volume-averaged) (van der Sman,1997 & 1999), and some benchmark problems like natural convection in cavity (van der Sman, 2006) and flow in a channel with a porous layer (Beavers and Joseph benchmark). References o Hill R.J., Koch D.L., and Ladd A.J.C. Moderate-Reynolds-number flows in ordered and random arrays of spheres JOURNAL OF FLUID MECHANICS 448: 243-278 (2001). o van der Hoef M.A., Annaland M.V., Kuipers J.A.M. Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy. CHEMICAL ENGINEERING SCIENCE 59 (22-23): 5157-5165 (2004). o van der Sman R.G.M. Solving the vent hole design problem for seed potato packagings, with the Lattice Boltzmann scheme. INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 11 (3-4): 237-248 (1999). o VanderSman R.G.M. Lattice-Boltzmann scheme for natural convection in porous media INTERNATIONAL JOURNAL OF MODERN PHYSICS C 8 (4): 879-888 (1997) o van der Sman R.G.M. Lattice Boltzmann scheme for natural convection on square and rectangular grids. in revision Phys. Rev. E (2006). IUFoST 2006 DOI: 10.1051/IUFoST:20060990

In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013)PLEEE81539-375510.1103/PhysRevE.87.023306] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, x dipoles, and xx quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at r=7.5; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the RLB scheme with the AMS method is capable of accurately simulating 2D and 3D acoustic generation, propagation, and scattering at zero viscosity.

Fishways are designed to provide a canal for fishes to migrate upstream and downstream when there is a presence of natural or man-made obstructions. In designing the fishway, correct prediction and simulation of the flows play a crucial role. A well designed and constructed fishway will provide a path that allow fish to continue migrating past the obstructions. This paper presents numerical modelling of flows in fishway using Lattice Boltzmann Method for Shallow Water Equations (LABSWE™) in order to demonstrate its simple applicability and accuracy in solving complex flow problems. Lattice Boltzmann Method (LBM) is an alternative numerical method in solving complex fluid flows problems. LBM was found to be efficient and accurate after series complex shallow water problems have been solved. The flow is simulated by using Bhatnagar-Gross-Kook (BGK) collision term. Lattice Boltzmann equation was derived based on shallow water equations. A D2Q9 model was implemented for a more accurate result. The BGK-LBM equations was coded up in MATLAB and the numerical results yield from LBM were then compared with the numerical results solved using Finite Volume Method (FVM). The result comparison was done on velocity vectors, velocity contour and depth contour. From the result comparison, there is good agreement between LBM and FVM which shows that LBM can mimic the flow perfectly. In fact, LBM yield a more detailed and accurate results.

Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current

A novel coupled lattice Boltzmann model for low Mach number combustion simulation

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow Pxy in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

A three-dimensional model of wave interactions with permeable structures using the lattice Boltzmann method

Generation process of laser induced weakly ionized helium plasma is simulated using the lattice Boltzmann method (LBM). Maxwell equations, which are used to model the propagation of laser, are calculated by the finite difference time domain (FDTD) method. Employing coefficients of distribution functions, processes of multi-photon ionization, electron impact ionization and three-body recombination are included in Boltzmann equations. Using D2Q9 model in LBM, number densities of particles in plasma can be obtained after solving Boltzmann equations. For the energy transformation in plasma, the finite volume method (FVM) is applied to calculate the macroscopic energy equations directly coming from the continuous Boltzmann equations. Interaction between laser and plasma as well as laser induced weakly ionized plasma are demonstrate to validate the hybrid model.

In the lattice Boltzmann method (LBM), macroscopic flow behavior is described by simulating a very simple, fully discrete, microscopic gas model instead of discretizing the flow equations directly. Based on the frequently used D2Q9 model (nine discrete velocities in two space dimensions), we show how surface tension effects can be combined with LBM. The applicability of the two-phase lattice Boltzmann method is demonstrated with simulations of filtration processes.

Lattice Boltzmann modeling of phonon transport