Alexander Kuzmin

University of Alberta | UAlberta · Department of Chemical and Materials Engineering

After reading this chapter, you will be familiar with how the “lattice units” usually used in simulations and articles can be related to physical units through unit conversion or through dimensionless numbers such as the Reynolds number. Additionally, you will be able to make good choices of simulation parameters and simulation resolution. As these...

After reading this chapter, you will be familiar with the basics of lattice Boltzmann boundary conditions. After also having read Chap. 3, you will be able to implement fluid flow problems with various types of grid-aligned boundaries, representing both no-slip and open surfaces. From the boundary condition theory explained in this chapter together...

After reading this chapter, you will understand the fundamentals of high-performance computing and how to write efficient code for lattice Boltzmann method simulations. You will know how to optimise sequential codes and develop parallel codes for multi-core CPUs, computing clusters, and graphics processing units. The code listings in this chapter a...

After reading this chapter, you will be able to add forces to lattice Boltzmann simulations while retaining their accuracy. You will know how a forcing scheme can be derived by including forces in the derivation of the lattice Boltzmann equation, though you will also know that there are a number of other forcing schemes available. You will understa...

After reading this chapter, you will be familiar with many in-depth aspects of the lattice Boltzmann method. You will have a detailed understanding of how the Chapman-Enskog analysis can be used to determine how the lattice Boltzmann equation and its variations behave on the macroscopic Navier-Stokes level. You will know a number of such variations...

After reading this chapter, you will understand how the lattice Boltzmann equation can be adapted from flow problems to advection-diffusion problems with only small changes. These problems include thermal flows, and you will know how to simulate these as two interlinked lattice Boltzmann simulations, one for the flow and one for the thermal advecti...

After reading this chapter, you will have a working understanding of the equations of fluid mechanics, which describe a fluid’s behaviour through its conservation of mass and momentum. You will understand the basics of the kinetic theory on which the lattice Boltzmann method is founded. Additionally, you will have learned about how different descri...

After reading this chapter, you will understand the fundamentals of sound propagation in a viscous fluid as they apply to lattice Boltzmann simulations, and you will know why sound waves in these simulations do not necessarily propagate according to the “speed of sound” lattice constant. You will have insight into why sound waves can appear spontan...

After reading this chapter, you will have a solid understanding of the general principles of multiple-relaxation-time (MRT) and two-relaxation-time (TRT) collision operators. You will know how to implement these and how to choose the various relaxation times in order to increase the stability, the accuracy, and the possibilities of lattice Boltzman...

After reading this chapter, you will have insight into a number of other fluid simulation methods and their advantages and disadvantages. These methods are divided into two categories. First, conventional numerical methods based on discretising the equations of fluid mechanics, such as finite difference, finite volume, and finite element methods. S...

After reading this chapter, you will be able to expand lattice Boltzmann simulations by including non-ideal fluids, using either the free-energy or the Shan-Chen pseudopotential method. This will allow you to simulate fluids consisting of multiple phases (e.g. liquid water and water vapour) and multiple components (e.g. oil and water). You will als...

After reading this chapter, you will have insight into a large number of more complex lattice Boltzmann boundary conditions, including advanced bounce-back methods, ghost methods, and immersed boundary methods. These boundary conditions will allow you to simulate things like curved boundaries, flows in media with sub-grid porosity, rigid but moveab...

After reading this chapter, you will know the basics of the lattice Boltzmann method, how it can be used to simulate fluids, and how to implement it in code. You will have insight into the derivation of the lattice Boltzmann equation, having seen how the continuous Boltzmann equation is discretised in velocity space through Hermite series expansion...

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamen...

This work presents a procedure for the determination of the volumetric mass transfer coefficient in the context of lattice Boltzmann simulations for the Bretherton/Taylor bubble train flow for capillary numbers 0.1 < Ca < 1.0. We address the case where the hydrodynamic pattern changes from having a vortex in the slug (Ca < 0.7) to not having it (Ca...

The paper analysis the incorporation of the source term in the advection-diffusion equation for the BGK Lattice Boltzmann Method (LBM). The problem is the coupled energy and species conservation equations with the Soret term. The problem is extremely important for people using LBM in simulating multi-physics, because multi-physics effect added as a...

In general, explicit numerical schemes are only conditionally stable. A particularity of lattice Boltzmann multiple-relaxation-time (MRT) schemes is the presence of free (''kinetic'') relaxation parameters. They do not appear in the transport coefficients of the modelled second-order (macroscopic) equations but they have an impact on the effective...

The classical Bretherton problem describes the propagation of gas fingers through liquid media in a narrow channel with thin liquid films between bubbles and channel walls. The bubble shape and flow patterns are complicated functions of the capillary number Ca and Reynolds number Re. Recently, we investigated the applicability and parameter selecti...

This paper presents an analysis of the simultaneous incorporation of force and mass source terms into the multi-relaxation-time (MRT) collision operator. MRT force incorporation was obtained through Chapman-Enskog analysis. The numerical scheme was tested on different benchmark problems, including the decay of a shear wave with different bulk and k...

In general, explicit numerical schemes are only conditionally stable. A particularity of lattice Boltzmann multiple-relaxation-time (MRT) schemes is the presence of free (“kinetic”) relaxation parameters. They do not appear in the transport coefficients of the modelled second-order (macroscopic) equations but they have an impact on the effective ac...

Despite the growing popularity of Lattice Boltzmann schemes for describing multi-dimensional flow and transport governed by non-linear (anisotropic) advection-diffusion equations, there are very few analytical results on their stability, even for the isotropic linear equation. In this paper, the optimal two-relaxation-time (OTRT) model is defined,...

The work presents simulations with the multirange Shan–Chen model developed by Sbragaglia et al. (2007) [18], which improved the Shan–Chen model for the proper surface tension term. Also, by introducing the matrix collision operator and extended equilibrium density distribution function, the density ratio is increased from 100 to 160. The Multi-Rel...

a b s t r a c t Few methods have been introduced and used in simulation fluid flows using lattice Boltzmann method (LBM) with external forces, such as buoyancy, surface tension, magnetic, etc. In some problems, the exter-nal force is constant, for instance gravitational force with constant density flows, while for other prob-lems the force may vary...

This work thoroughly analyzes one of the most popular multiphase models, the Shan-Chen model, for the lattice Boltzmann equation. The advantages and disadvantages are presented. This work extends the applicability of the Shan-Chen model to simulate different phenomena and presents alternatives to some of disadvantages. The model's stability limit i...

A nonisotropic tensorial extension of the single-component Shan-Chen pseudopotential Lattice Boltzmann method for nonideal fluids is presented. Direct comparison with experimental data shows that this extension is able to capture relevant features of ferrofluid behavior, such as the deformation and subsequent rupture of a liquid droplet as a functi...

Multi-relaxation time (MRT) for Lattice Boltzmann method is gaining renewed attention among researchers in the field. The advantage of such formulation over the widely pop-ular single-time relaxation version, is twofold: better numerical stability and wider span of physical applications, extending to non-isotropic flows. In this work, the numerical...