TABLE OF CONTENTS The general form of the Boltzmann equation for a simple dilute gas, Eq. (2.6.10) described in Chap. 2, defines the relationship between the velocity distribution function and its dependent variables. It is the governing equation for gases in the entire transition regime of interest in this study. The Boltzmann equation is derived from the fundamental principles of classical kinetic theory and is restricted to dilute gas flows in molecular chaos.
The DSMC method, on the other hand, is derived from the same first principles as the Boltzmann equation, but not from the equation itself. Due to its ties to classical kinetic theory, the DSMC method is subject to the same restrictions of dilute gas and molecular chaos. Unlike the Boltzmann equation, however, the DSMC method does not require the existence of inverse collisions that are dictated by symmetry considerations of binary dynamics. This allows the application of the method to some complex phenomena, such as ternary chemical reactions, that are inaccessible to the Boltzmann equation.
A derivation of the Boltzmann equation from DSMC procedures could be obtained for hard sphere molecules based on the NTC collision technique. The left-hand side of Eq. (2.6.10) states that the quantity nf remains constant in the phase space in the absence of collisions if one moves along with a group of molecules in a Lagrangian manner. Similarly, the DSMC procedures trace the paths of the simulated molecules in the phase space,...
