We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the asymptotic-preserving (AP) strategies to compute multiscale physical problems efficiently. Specifically, we will first study the asymptotic transition from quantum to classical mechanics, from classical mechanics to kinetic theory, and then from kinetic theory to hydrodynamics. We then review some representative AP schemes that mimic these asymptotic transitions at the discrete level, and hence can be used crossing scales and, in particular, capture the macroscopic behaviour without resolving the microscopic physical scale numerically.

中文翻译：

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多尺度物理问题的渐近保持方案

我们介绍了从微观物理到宏观物理的渐近过渡、它们的计算挑战以及有效计算多尺度物理问题的渐近保持 (AP) 策略。具体来说，我们将首先研究从量子到经典力学，从经典力学到动力学理论，然后从动力学理论到流体动力学的渐近过渡。然后，我们回顾了一些在离散水平上模拟这些渐近转换的代表性 AP 方案，因此可以跨尺度使用，特别是在不解析微观物理尺度的情况下捕捉宏观行为。