A Discrete Boltzmann Equation Based on a Cub-Octahedron in $\mathbb{R}^3$

Abstract

In this article we introduce a discrete Boltzmann equation in $\mathbb{R}^3$ velocity space based on a cub-octahedron. We present a layer-wise construction of a regular collision model in a bounded grid of the sphere packing problem. The paper contains the analytical results about the basic kinetic features of the regular collision model. We analyze the computational complexity, report the efficiency of the model, and perform numerical experiments based on the discrete model Boltzmann equation for some standard test problem.