Development of the Single-Relaxation-Time Lattice Boltzmann Method for Application to Thermal Fluid Flows

This work investigates the single-relaxation-time Lattice Boltzmann Method and how to develop it into a full hydrodynamic and thermal modeling scheme. First the single-relaxation time isothermal Lattice Boltzmann Method is outlined, beginning with the fundamentals of the lattice model and then proceeding through the necessary governingequations for the two-dimensional, nine-directional lattice. The governing equations are then presented in a discretized form to be used for simulation, followed by treatment ofboundary conditions. Fluid and dimensional properties are explained in terms of both lattice units and physical units via conversion factors. Next is an introduction to thermalLattice Boltzmann, discussing the changes as well as going through new governing equations pertaining to the internal energy density distribution function. Then the thermalscheme is shown in discretized form along with thermal boundary conditions and updated hydrodynamic boundary conditions. Fluid properties are reviewed alongside thermal properties, as they are essential to know when designing a simulation. Finally, results are shown for some two-dimensional channel flow geometries with hot and cold surfaces: a uniform-width channel, a channel that undergoes sudden expansion, and a channel featuring sudden contraction. The flow within the channel could be dominated by the density stratification or the forced flow introduced at the inlet. These mixed flows of natural and forced convection are characterized by the Reynolds and Rayleigh numbers, the Rayleigh numbers above critical value to allow for formation of natural convection 2 cells when experiencing low-Reynolds flows. The results are presented as contour plots of temperature and stream function

Application of Lattice Boltzmann Method for Surface Runoff in Watershed

Derived from simplifications of the Saint-Venant equations, the kinematic wave model has the ability to describe the behavior of surface runoff in watersheds. This paper aims to obtain the numerical simulation of the flow routing in a natural watershed, by using lattice Boltzmann method. In the computational model, the surface of the basin will be represented by a V-shaped segmented in two lateral planes and one main channel. The simulation considers the effective precipitation flowing on the watershed per unit of width at the exit of each of the planes that represent the surface of the basin. The water flowing from the planes enters the main channel in the form of lateral contribution. Hydrograms of two rain events are obtained, which present the volume drained in the outlet corresponding to the whole basin in each event. Two equilibrium distribution functions were developed by Chapmann-Enskog expansion at time scales and model D1Q3, one suitable for flow on the basin surface and another for the main channel, in order to obtain the variables of interest in each case. The numerical results obtained were compared with the KINEROS2 hydrological model.Peer Reviewe

Modelling wall shear stress in small arteries using LBM and FVM

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In this study a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids is presented. The new scheme is based on the idea of placing the unknown fields at the nodes of the mesh and evolve them based on the fluxes crossing the surfaces of the corresponding control volumes. The method, named unstructured Lattice Boltzmann equation (ULBE) is compared with the classical finite volume method (FVM) and is applied here to the problem of blood flow over the endothelium in small arteries. The study shows a significant variation and a high sensitivity of wall shear stress to the endothelium corrugation degree

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Finite Volume vs.vs. Streaming-based Lattice Boltzmann algorithm for fluid-dynamics simulations: a one-to-one accuracy and performance study

A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB) equation which combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard $streaming$ (ST) Lattice Boltzmann equation algorithm. To our knowledge such a systematic comparison has never been previously reported. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. For this reason the comparative analysis is further extended to the case of realistic flows, in particular thermally driven flows in turbulent conditions. We report the first successful simulation of high-Rayleigh number convective flow performed by a Lattice Boltzmann FV based algorithm with wall grid refinement.Comment: 15 pages, 14 figures (discussion changes, improved figure readability