基于粒子的无方程计算：二维粗糙投影积分和粗糙动力学重整化
Equation-Free Particle-Based Computations: Coarse Projective Integration and Coarse Dynamic Renormalization in 2D
摘要：
无方程方法近年来被提出来用于工程问题中多尺度现象的计算研究，其中粗粒度的系统级行为的发展方程不能明确地获得。在本文中，我们研究了一个扩散粒子系统在层流剪切流的动力学，描述了一个二维布朗运动，特别是，我们进行粗投影积分，并证明了基于粒子的计算粗糙的自相似和渐近自相似的解决方案，这个问题。我们使用边际和条件逆累积分布函数（ICDFs）作为粒子分布演化的宏观观测量。
英文摘要：
Equation-free approaches have been proposed in recent years for the computational study of multiscale phenomena in engineering problems where evolution equations for the coarse-grained, system-level behavior are not explicitly available. In this paper we study the dynamics of a diffusive particle system in a laminar shear flow, described by a two-dimensional Brownian motion; in particular, we perform coarse projective integration and demonstrate the particle-based computation of coarse self-similar and asymptotically self-similar solutions for this problem. We use marginal and conditional Inverse Cumulative Distribution Functions (ICDFs) as the macroscopic observables of the evolving particle distribution.
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