Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. A well-known numerical method for the initialization of Boltzmann models is the Constrained Runs algorithm. This algorithm is used in literature for the initializ...

In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the Navi...

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...

In this paper, we prove the H-theorem for generalized chemical kinetics equations. We consider following important physical examples of such a generalization: discrete models quantum kinetic equations (Uehling–Uhlenbeck equations) and Markov process (quantum random walk). that time means coincide with Boltzmann extremals all Liouville equation as well. This gives us an approach to select action...

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...

Hydrodynamics of multiple rising bubbles as a fundamental two-phase phenomenon is studied numerically by lattice Boltzmann method and using Lee two-phase model. Lee model based on Cahn-Hilliard diffuse interface approach uses potential form of intermolecular forces and isotropic finite difference discretization. This approach is able to avoid parasitic currents and leads to a stable procedure t...

In this paper, we present a 3D lattice Boltzmann BGK model for simulation of micro ows with heat transfer. This model is an extension of the two-dimensional model that is based on the kinetic theory and the thermal lattice Boltzmann method. The kinetic relations of the relaxation times in this model were linked with the Knudsen number, and a di use scattering boundary condition for the velocity...

A finite difference lattice Boltzmann method based on the Bhatnagar–Gross–Krook-type modeled Boltzmann equation is proposed. Themethod relies on a different lattice equilibriumparticle distribution function and the use of a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as con...

The goal of this paper is to define a procedure for bounding the error in a conforming finite element method. The new point is that this upper bound is fully explicit and can be computed locally. Numerical tests prove the efficiency of the method. It is presented here for the case of the Poisson equation and a first order finite element approximation.