– The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lat...

In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space....

Mixed convection heat transfer in two-dimensional liddriven rectangular cavity filled with air (Pr =0.71) is studied numerically. A hybrid scheme with multiple relaxation time Lattice Boltzmann Method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the Finite Difference Method (FDM). The main objective of this work is t...

The goal of this thesis is to implement and optimize the lattice–Boltzmann method for the distributed shared memory system Jackal. The lattice Boltzmann method is a new and promising alternative to the traditional Navier–Stokes solvers in the domain of computational fluid dynamics. It is based on cellular automata and operates on a domain, were all cells are normalized in space. Because of the ...

abstract: since the field of micro electromechanical systems (mems) continues to grow, the flow in micro devices have become an area that receives a significant attention. the microscopic flows are usually characterized by the knudsen number (kn). when the characteristic size of the particle decreases down to a value comparable to the mean free path of the molecules, the continuum assumption fa...

By realizing the insufficient degree of Galilean invariance of the traditional multiple-relaxation-time collision operators, Geier [Phys. Rev. E 73, 066705 (2006)] proposed to relax differently the moments shifted by the macroscopic velocity, leading to the so-called cascaded lattice Boltzmann method (LBM). This paper points out that (a) the cascaded LBM essentially consists in adopting a gener...

The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving hydrodynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Because the method often uses uniform regular Cartesian lattices in space, curved boundaries are often...

Lattice Boltzmann method is relatively new method in the field of computational fluid dynamics. It has been derived from lattice gas automata and is still under development. Basic steps of the LBM (collision, streaming, boundary conditions, macroscopic quantities) will be presented. Comparison with the finite difference method that uses Navier-Stokes equation on a lid driven cavity benchmark te...

Lack of energy conservation in lattice Boltzmann models leads to unrealistically high values of the bulk viscosity. For this reason, the lattice Boltzmann method remains a computational tool rather than a model of a fluid. A novel lattice Boltzmann model with energy conservation is derived from Boltzmann's kinetic theory. Simulations demonstrate that the new lattice Boltzmann model is the valid...