We propose fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and \acf{BGK} equations. The methods employ a sequence of small forward-Euler steps, intercalated with large extrapolation steps. The telescopic approach repeats said extrapolations as the basis for an even larger step. This hierarchy renders the computational complexity of the method essentially independent of the stiffness of the problem, which permits the efficient solution of equations in the hyperbolic scaling with very small Knudsen numbers. We validate the schemes on a range of scenarios, demonstrating its prowess in dealing with extreme mass ratios, fluid instabilities, and other complex phenomena.

翻译：我们为多种波尔兹曼和\ac{BGK}方程式提出完全明确的投影集成和远视投影集成计划。 方法采用一系列与大外推步骤相交的小型前向- 外推步骤。 遥测法重复了外推法作为更大步骤的基础。 这种等级制度使得计算方法的复杂程度基本上独立于问题的僵硬性, 这使得双曲缩放中的方程式能够以非常小的Knudsen数字有效解决。 我们验证了一系列假设的方程式, 显示了其在处理极端质量比率、流动性不稳定性和其他复杂现象方面的优势。