In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a onedimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on so...

A subgrid turbulence model for the lattice Boltzmann method is proposed for high Reynolds number fluid flow applications. The method, based on the standard Smagorinsky subgrid model and a single-time relaxation lattice Boltzmann method, incorporates the advantages of the lattice Boltzmann method for handling arbitrary boundaries and is easily implemented on parallel machines. The method is appl...

In this paper, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwell-Boltzmann distribution, we obtain a Boltzmann Bhatnagar-Gross-Krook (BGK) equation for thermal flows with viscous heat dissipation in the incompressible limit. The continuous thermal BGK model is then discretized over both time and phase space to form a lattice BGK mod...

The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of l...

In this paper we presented a lattice Boltzmann with square grid for compressible flow problems. Triple level velocity is considered for each cell. Migration step use discrete velocity but continuous parameters are utilized to calculate density, velocity, and energy. So, we called this semi-discrete method. To evaluate the performance of the method the well-known shock tube problem is solved, us...

A three-dimensional lattice Boltzmann model with thirty two discrete velocity distribution functions for viscoelastic fluid is presented in this work. The model is based upon the generalized lattice Boltzmann equation constructed in moment space. The nonlinear equilibria of the model have a number of coupling constants that are free parameters. The dispersion equation of the model is analyzed u...

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...

a two dimensional finite difference lattice boltzmann method (fdlbm) for computing single phase flow problems is developed here. temporal term is discretized with low dissipation-low dispersion. discretization of convective term is implemented with third order upwind method. it will be explained governing equations and numerical method. methodology of imposing boundary conditions in fdlbm is de...

We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding linear equivalent partial differential equations are generated with a new “Berliner version” of the Taylor expansion method. The details of the implementation ar...

Article history: Received 24 July 2015 Received in revised form 22 December 2015 Accepted 19 March 2016 Available online 23 March 2016