Truncation Procedure for the Spatially Homogeneous Boltzmann Equation

Abstract

The usual truncation procedure for coefficient equations is shown to be inconsistent for a certain class of initial-value problems in that it retains terms of one magnitude while neglecting terms of the same or greater magnitude. Moreover, it predicts moments which are strongly dependent on the zero-order function used in the expansion of the distribution function. A truncation procedure is developed for spatially homogeneous (time relaxation) problems which gives rise to moments which are independent of the particular zero-order function used in the expansion; and which, for certain general initial distribution functions, are correct in value and first-derivative both initially and in equilibrium. As an example, this procedure is used to solve the two-temperature single-gas mixture problem.