A comparison of the implementation and performance of the Nanbu and Bird direct simulation Monte Carlo methods

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Abstract
Since Bird [Phys. Fluids 6, 1518 (1963)] first proposed the idea of direct simulation Monte Carlo (DSMC) techniques in order to model rarefied gas flows, a concern has been that his method does not provide a solution to the Boltzmann equation. Several simulation schemes have now been developed and, in a review of these methods, Nanbu [J. Phys. Soc. Jpn. 52, 3382 (1983)] showed that only his method [J. Phys. Soc. Jpn. 49, 2042 (1980)] gave a true solution to the Boltzmann equation. However, Nanbu’s simulation method is also the most computationally expensive scheme and in his review paper he recommended the use of the Bird technique for complicated engineering problems. Nanbu’s method also suffers from the apparent disadvantage that momentum and energy are not conserved at each collision. With the advent of the supercomputer the relative expense of the methods will inevitably be of lesser importance so that the testing of the Nanbu method in an engineering context is desirable. A detailed study of the implementation and performance of the Bird and Nanbu simulation schemes has therefore been carried out with reference to the expansion of a gas into vacuum. The results reported herein show, however, that in addition to increased computational overheads, the Nanbu method suffers from further defects that make its implementation more difficult. It is concluded that the Nanbu method is generally less flexible than that of Bird and that greater care must be exercised if meaningful results are to be obtained using the Nanbu approach.