The Lattice Boltzmann Method (LBM) is introduced in the Computational Fluid Dynamics (CFD) field as a tool for research and development, but its ultimate importance lies in various industrial and academic applications. Owing to its excellent numerical stability and constitutive versatility it plays an essential role as a simulation tool for understanding micro and macro fluid flows. The LBM received a tremendous impetus with their spectacular use in incompressible and compressible fluid flow and heat transfer problems. The applications of LBM to incompressible flows with simple and complex geometries are much less spectacular. From a computational point of view, the present LBM is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The present paper reviews the philosophy and the formal concepts behind the lattice Boltzmann approach and gives progress in the area of incompressible fluid flows, compressible fluid flows and free surface flows.

A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer

Lattice Boltzmann method simulation of 3-D natural convection with double MRT model

Abstract A numerical method to solve the incompressible, 3-D Navier-Stokes and Boussinesq equations in primitive variable form on non-staggered, uniform and non-uniform grids, is discussed. The Neumann-Poisson problem for pressure is solved by using a fast direct method and the velocity and temperature fields are advanced in time with the Douglas-Gunn ADI method. Accurate transient solutions to the 2-D and 3-D convective flow in a shallow box heated from a side have been obtained and compared with available results. Some results for the 3-D lid-driven cavity flow are also presented.

On the numerical solution of incompressible three-dimensional Navier-Stokes equations /

Purpose




The main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid.




Design/methodology/approach




It is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number.




Findings




The results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters.




Research limitations/implications




The present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work.




Originality/value




This work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.

Effects of moving wall on the flow of micropolar fluid inside a right angle triangular cavity

Purpose




The purpose of this paper is to improve the 2D incompressible smoothed particle hydrodynamics (ISPH) method by working on the wall boundary conditions in ISPH method. Here, two different wall boundary conditions in ISPH method including dummy wall particles and analytical kernel renormalization wall boundary conditions have been discussed in details.




Design/methodology/approach




The ISPH algorithm based on the projection method with a divergence velocity condition with improved boundary conditions has been adapted.




Findings




The authors tested the current ISPH method with the improved boundary conditions by a lid-driven cavity for different Reynolds number 100 ≤ Re ≤ 1,000. The results are well validated with the benchmark problems.




Originality/value




In the case of dummy wall boundary particles, the homogeneous Newman boundary condition was applied in solving the linear systems of pressure Poisson equation. In the case of renormalization wall boundary conditions, the authors analytically computed the renormalization factor and its gradient based on a quintic kernel function.

Improved wall boundary conditions in the incompressible smoothed particle hydrodynamics method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

K. Nagendra

Papers

Simulation of laminar flow in a three‐dimensional lid‐driven cavity by lattice Boltzmann method