Accelerating the Solution of the Boltzmann Equation by Controlling Contributions to the Collision Integral

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Abstract

A method of reducing the number of arithmetic operations needed to evaluate the Boltzmann collision integral by the conservative projection method is proposed. This is achieved by eliminating the contributions that are less than a certain threshold. An estimate of the maximum magnitude of this threshold is given. For four such thresholds that differ by an order of magnitude from each other, calculations of the flows of rarefied gas at Mach numbers in the range from 0.5 to 10 are carried out, and the results are compared with those obtained using the basic method. In all cases, there is a slight (within a few percent) difference for the highest threshold and almost complete coincidence for the other thresholds. A multiple acceleration of the solution of the Boltzmann equation was obtained, which is most significant for large Mach numbers.

About the authors

F. G. Tcheremissine

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences

Author for correspondence.
Email: felix.tcher@yandex.ru
119991, Moscow, Russia

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