Interrelations between Various Direct Simulation Methods for Solving the Boltzmann Equation

Interrelations between the five direct simulation methods of Nanbu, Belotserkovskiy and Yanitskiy, Koura, Deshpande, and Bird are examined by means of probability consideration. These methods are divided into two groups; one based on the Boltzmann equation and the other based on the Kac master equation. Nanbu's method belongs to the first group while all other methods belong to the second group. The methods of Koura, Deshpande, and Bird are modifications of that of Belotserkovskiy and Yanitskiy. Although the probability law for simulating molecular collisions is different from method to method, the mean rate of collision is essentially the same for all methods. This implies that there is no significant difference at least among macroscopic properties resulting from all methods.