On One-dimensional Discrete Velocity Models of The Boltzmann Equation For Mixtures

Abstract

In this work the theorem that exists only two symmetric one‐dimensional discrete velocity models for two‐species mixture without spurious invariants is proved only for certain class of models. Additive invariants are classified for the Boltzmann equation and its discrete models. Approximation of the Boltzmann equation by discrete model in one‐dimensional case is considered and quadrature formula for the collision integral is proposed. Also we consider the size of frame, used for arrangement of values of particles’ momentum belonging to symmetric discrete velocity model of the Boltzmann equation, which has an exchange of energy between the components of mixture.