From Microscopic to Macroscopic: A Multiscale Numerical Approach

Ta'asan9805582 这位研究者和他的同事们开发了多尺度计算技术来处理各种尺度上的现象。 研究的主要方面是从微观模型（如分子动力学模型）数值构造以偏微分方程形式表示的宏观方程。 数值技术的重点是从分子模型开始的流体建模。 特别强调的是涉及几种类型的原子/分子的混合物的模型，这些模型可能由不同的相互作用所控制，这样的分子模型会引起包括多相流在内的复杂物理现象. 从分子动力学出发，以层次化的方式构造了一系列模型。 该层次中的每一层都代表了前一层的一个更大尺度的动力学（在时间或空间或两者上），并使用统计工具（回归分析）对前一层的模拟数据进行建模，最精细的建模由Hamilton动力学给出，并且是确定性的。 随机粒子动力学模型是由最精细的粒子动力学模型构造而成的，它在弛豫时间量级的时间尺度上描述物理现象。 进一步粗化（平均化）时空的结果在确定性的密度演化模型，这可以被识别为有限差分近似的一些偏微分方程，是宏观极限。 几十年来，数值方法被广泛应用于不同领域的偏微分方程的近似求解，极大地提高了人们的科学认识和工程任务。 这些方程描述了不同区域的物理现象，它们的推导是通过分析技术完成的，而分析技术的使用仅限于相对简单的情况。 处理更复杂的模型，一般来说，不能做分析，它需要另一种方法。 这是这项工作的主题：使用numericaltechniques为'推导'宏观动力学方程从更基本的原则，在微观层面上。 这项任务是通过详细的微观模型和适当的统计数据进行大规模模拟。 在这项工作中处理的问题仅限于多相流体流动，这是至关重要的，在许多领域的应用，包括医疗吸入装置，汽车和航空航天工业（发动机），计算机行业（打印机），和更多。 然而，这里发展的技术是通用的，适用于化学、物理学和经济学的其他领域，从基本问题到真实的世界应用。

Ta'asan9805582 The investigator and his colleagues develop multiscalenumerical techniques for dealing with phenomena on a wide rangeof scales. The main aspect of the research is the numericalconstruction of macroscopic equations in the form of partialdifferential equations from microscopic models such as moleculardynamics models. The numerical techniques focus on fluidsmodeling starting from molecular models. Special emphasize isgiven to models involving mixtures of several types ofatoms/molecules that may be governed by different interactions.Such molecular models give rise to complicated physical phenomenaincluding multiphase flows. A sequence of models is constructednumerically in an hierarchical manner starting from moleculardynamics. Each level in this hierarchy represent a larger scaledynamics (in time or space or both) of the previous level, and isconstructed using statistical tools (regression analysis) appliedto the data resulting from a simulation of the previous level.The finest level of modeling is given by Hamiltonian dynamics andis deterministic. Stochastic particle dynamics models areconstructed from the finest level model, and represent thephysical phenomenon on time scale of the order of the relaxationtime. Further coarsening (averaging) in space-time results indeterministic density evolution models, which can be identifiedas finite difference approximations to some partial differentialequation that is the macroscopic limit. Numerical techniques have been used extensively for severaldecades to obtain approximate solutions of partial differentialequations in different fields, and have improved significantlyscientific insights and engineering tasks. The derivation ofthose equations, which describe physical phenomena in differentareas, was done by analytical techniques whose use is limited torelatively simple cases. The treatment of more complex modelscannot, in general, be done analytically and it calls for anotherapproach. This is the subject of this work: the use of numericaltechniques for 'deriving' macroscopic dynamics equations frommore basic principles given at microscopic levels. This task iscarried out by large scale simulation of the detailed microscopicmodels and appropriate statistics. The problems treated in thiswork are limited to multiphase fluid flows, which are crucial inmany areas of applications, including medical inhalation devices,auto and aerospace industries (engines), computer industries(printers), and more. The techniques developed here, however, arequite general and apply to other areas in chemistry, physics andeconomics, from fundamental questions to real world applications.