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Abstract <p>The study is aimed at increasing the efficiency of the direct numerical solution of the Boltzmann equation. An approach is proposed to speed up the collision integral computation by means of taking into account only those nodes of the velocity grid that make significant contributions to calculating the distribution function moment of a prescribed order. The algorithm retains the conservatism of the numerical scheme used to calculate the collision integral. The algorithm is tested on the Bobylev–Krook–Wu analytical solution. The tests show that more than a 20-fold speedup of the collision integral computation can be provided with acceptable solution accuracy being retained. A problem of the plane shock wave structure is solved; the numerical solutions obtained with and without the node selection algorithm are found to be in good agreement. The most optimal parameters of the node selection algorithm are determined. The problem of decay of a discontinuity in a microchannel is simulated; the results are found to agree well with the data obtained by the direct simulation Monte Carlo method. The algorithm provides a speedup by a factor of 21.75.</p>

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Pseudo-adaptive Grid for the Boltzmann Solver Based on the Discrete Velocity Method

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • S. O. Poleshkin

摘要

Abstract

The study is aimed at increasing the efficiency of the direct numerical solution of the Boltzmann equation. An approach is proposed to speed up the collision integral computation by means of taking into account only those nodes of the velocity grid that make significant contributions to calculating the distribution function moment of a prescribed order. The algorithm retains the conservatism of the numerical scheme used to calculate the collision integral. The algorithm is tested on the Bobylev–Krook–Wu analytical solution. The tests show that more than a 20-fold speedup of the collision integral computation can be provided with acceptable solution accuracy being retained. A problem of the plane shock wave structure is solved; the numerical solutions obtained with and without the node selection algorithm are found to be in good agreement. The most optimal parameters of the node selection algorithm are determined. The problem of decay of a discontinuity in a microchannel is simulated; the results are found to agree well with the data obtained by the direct simulation Monte Carlo method. The algorithm provides a speedup by a factor of 21.75.