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.

中文翻译：

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非线性动力学混合物的射影和伸缩射影积分

我们为多物种 Boltzmann 和 \acf{BGK} 方程提出了完全显式的射影积分和伸缩射影积分方案。该方法采用一系列小的前向欧拉步骤，插入大的外推步骤。伸缩方法重复所述外推，作为更大步骤的基础。这种层次结构使得该方法的计算复杂度基本上与问题的刚度无关，这允许在具有非常小的 Knudsen 数的双曲线标度中有效地求解方程。我们在一系列场景中验证了这些方案，展示了其在处理极端质量比、流体不稳定性和其他复杂现象方面的能力。