Sound Propagation Properties of the Discrete-Velocity Boltzmann Equation

A New Consistent Discrete-velocity Model for the Boltzmann Equation

This paper discusses the convergence of a new discrete-velocity model to the Boltz-mann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modiied model to DiPerna-Lions solutions of the Boltz-mann equation. As a test numerical example, the solutions to the discrete problems are compared to the exact solut...

Theory of the lattice Boltzmann equation: symmetry properties of discrete velocity sets.

The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality ...

Investigation of a Discrete Velocity Monte Carlo Boltzmann Equation Solver

A Study of the Wave Propagation Velocity in Granular Soils Using Discrete Element Method (DEM)

In the present paper, discrete element method (DEM) is used to study wave propagation phenomenon in granular soils. The effect of factors such as coefficient of friction, frequency, normal stiffness and soil gradation on the wave velocity is studied. Using the wall motion based on the sinusoidal function is the method of loading used in this simulation, through which the pressure wave is transf...

The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problem of sound-wave propagation in a rarefied gas. The analysis and the numerical work are based on a rigorous form of the linearized Boltzmann equation (for rigid-sphere interactions), and in contrast to many other works formulated (for an infinite m...