Kevrekidis Ioannis G, Samaey Giovanni
Department of Chemical Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
Annu Rev Phys Chem. 2009;60:321-44. doi: 10.1146/annurev.physchem.59.032607.093610.
In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.
在传统的物理化学建模中，人们在感兴趣的（宏观、粗略）尺度上推导演化方程；这些方程被用于使用一系列分析和数值技术执行各种任务（模拟、分岔分析、优化）。然而，对于许多复杂系统，尽管人们在感兴趣的宏观尺度上观察到演化，但准确的模型仅在更详细的（精细尺度、微观）描述水平上给出（例如，格子玻尔兹曼方法、动力学蒙特卡罗方法、分子动力学方法）。在此，我们回顾一种计算机辅助多尺度分析框架，该框架仅通过在短时间和长度尺度上进行适当初始化的微观模拟，就能在扩展的时空尺度上执行宏观计算任务。当这些宏观演化方程在概念上存在但没有封闭形式时，该方法绕过了它们的推导——因此有了“无方程”这一术语。我们有选择地讨论基本算法和基本原理，并通过代表性应用来说明该方法。我们还讨论了潜在的困难，并概述了未来研究的领域。
