A General Discrete Velocity Model Including Internal Degrees of Freedom

This paper deals with the problem of describing spatially inhomogeneous gases by applying model Boltzmann equations. A plane discrete velocity model is presented, capable of describing a gas of particles with internal degrees of freedom. The number of particle speeds is variable. All possible collisions, both elastic and inelastic, are calculated. The corresponding equation system for 2L+1 speeds is given explicitly, where L is a nonnegative integer. For the case L = 1 solutions in the form of shock waves are found numerically.