The motion and structure of shock and expansion waves in a simple particle system, a lattice gas and cellular automaton, are determined in an exact computation. Shock wave solutions, also exact, of a continuum description, a model Boltzmann equation, are compared with the lattice results. The comparison demonstrates that, as proved by Caprino et al. “A derivation of the Broadwell equation,” Com...

We compare the lattice Boltzmann method (LBM) and Pseudo-Spectral (PS) method for direct numerical simulation of decaying homogeneous isotropic turbulence. In this study we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxationtime (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We first compare the instantaneous flow ...

This paper presents a new finite-volume discretization of a generalised Lattice Boltzmann equation (LBE) on unstructured grids. This equation is the continuum LBE, with the addition of a second order time derivative term (memory), and is derived from a second-order differential form of the semi-discrete Boltzmann equation in its implicit form. The new scheme, named unstructured lattice Boltzman...

1. Abstract This paper presents a topology optimization method using the lattice Boltzmann method for the design of a flow channel considering two-phase fluid flows. This approach enables the design of fluidic devices such as two-phase microchannels that achieve a desired flow with maximal performances such as mixing and reaction, and extraction efficiencies. The optimization problems are formu...

Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions, mesoscopic variables, of the lattice Boltzmann model. Several methods proposed as lifting operators have been tested and discussed in the literature. The most famous methods are an analytically found l...

The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it may be interpreted as a Lagrangian finite-difference method for the numerical simulation of the discrete-velocity Boltzmann equation that makes use of a BGK ...

The Lattice Boltzmann method, a molecule kinetic-based approach, is presented to solve fluid dynamics. Based on the theory of turbulence and molecule kinetics, an extended Lattice Boltzmann equation is put forward to solve turbulent flow with high Reynolds number, in which sub-grid turbulence model is used to simulate vortex viscosity as well as turbulence relaxation time is introduced to modif...

If we consider a finite difference method simply as a set of equations containing a small parameter (the grid spacing), it is evident that the tools of asymptotic analysis can give us useful information about the method. The applicability of this approach for studying consistency, long time behavior and stability is demonstrated. As example, we use a simple lattice Boltzmann scheme for the 1D a...