Multiscale Modeling and Computation of Multiphase Energetic Materials

多尺度系统在科学和工程中比比皆是。它们的综合处理需要在精细尺度上对过程进行精确的数学建模，以及跨尺度信息流的数学框架。本建议在异构炸药的背景下解决这个问题。它们具有复杂的微观结构，含有含能物质的碎片，颗粒聚集体中存在的空隙和孔隙。当受到足够强的冲击时，就会发生爆炸。虽然结晶均质炸药具有较高的点火阈值，但相对较弱的刺激足以引发非均质聚集体。这是由于出现了分散的地点，或热点，在那里燃烧开始，然后蔓延到消耗整个大块。该系统的多尺度特性对任何尝试从头模拟爆炸现象的方式都是一个令人生畏的障碍，至少在目前是这样。提出了两种主要的数学建模方法。两者都在宏观尺度上生成连续体方程，其中一定程度的均匀化是隐含的，并且精细尺度过程已被纳入子网格模型。第一种方法，以点火-生长模型为代表，将炸药视为两种不同成分的均匀混合物，即未反应的炸药和反应产物，在压力和温度平衡下。对每一种成分都赋予一个状态方程，并假定一个单一的反应速率定律用于炸药到产物的转化。第二种方法明确地认识到爆炸性混合物的两相特性。所得到的模型具有每个相的质量、动量和能量的单独平衡定律，以及允许由相之间的压力差驱动的固相压实的规则。表示质量、动量和能量的界面交换的术语出现，对应于反应、阻力和传热的非平衡过程。这些模型是双曲偏微分方程的系统，可以被认为是气体动力学欧拉方程的推广。这一建议是针对现有的连续介质模型的研究以及精细尺度现象的研究。主要目标将是研究热点的强度和分布如何以定量的方式依赖于炸药的本构性质和点燃刺激的大小，从而提供可用于多尺度描述的重要信息。科学和工程的许多领域，包括天气、燃烧、污染和生物系统等，都涉及到由微观尺度上发生的事件所决定的观察尺度上的行为。对这样的系统进行彻底的处理，一方面需要对微观尺度上的过程有一个基本的理解和精确的数学建模，另一方面，需要发展一个理论和计算框架，以促进信息的跨尺度流动，从而可以可靠和准确地预测观察尺度上的行为。在以科学为基础的爆炸装置管理的背景下，对此类系统的关注尤其及时和恰当，而这一领域的问题构成了本提案的核心。

Multiscale systems abound in science and engineering. Their comprehensive treatment requiresaccurate mathematical modeling of processes at the fine scales and a mathematical framework forflow of information across scales. This proposal addresses this problem in the context of heterogeneousexplosives. These have a complex microstructure with fragments of the energetic material, voids andpores existing within the granular aggregate. When subjected to a sufficiently strong shock, a detonationis initiated. Although the crystalline homogeneous explosive has a high ignition threshold, relativelyweaker stimuli are sufficient to initiate the heterogeneous aggregate. This is caused by the appearanceof discrete sites, or hot spots, where burning commences and then spreads to consume the entire bulk.The multi-scale nature of the system is a daunting obstacle in the way of any attempt at ab-initio modelingof the detonation phenomena, at least at the present time. Two major approaches to mathematicalmodeling have been proposed. Both generate continuum equations at the macro scale, wherein a certaindegree of homogenization is implicit and fine-scale processes have been included as subgrid models.The first approach, typified by the ignition-and-growth model, treats the explosive as a homogeneousmixture of two distinct constituents, the unreacted explosive and the products of reaction, at pressure andtemperature equilibrium. To each constituent is assigned an equation of state, and a single reaction-ratelaw is postulated for the conversion of the explosive to products. The second approach explicitlyrecognizes the two-phase character of the explosive mixture. The resulting model has separatebalance laws of mass, momentum and energy for each phase, plus a rule that allows compaction ofthe solid phase driven by pressure difference between the phases. Terms representing interfacialexchange of mass, momentum and energy appear, corresponding to the nonequilibrium processes ofreaction, drag and heat transfer. These models are systems of hyperbolic partial differential equationsthat can be considered as generalizations of the Euler equations of gasdynamics. This proposal is aimedat studies of existing continuum models as well as the investigation of fine-scale phenomena. The primaryobjective will be to study how the strength and distribution of hot spots depend, in a quantitative way,upon the constitutive properties of the explosive and the size of the igniting stimulus, thus providingimportant information that can be used in attempts at multi-scale descriptions.Many areas in science and engineering, including weather, combustion, pollution, and biological systems,among others, involve behavior at the scale of observation that is determined by the events occurring atmicro scales. A thorough treatment of such systems requires, on the one hand, a fundamentalunderstanding and accurate mathematical modeling of processes at the micro scales, and on the other, development of a theoretical and computational framework that would facilitate flow of informationacross scales, so that behavior at the scale of observation can be predicted reliably and accurately.Attention to such systems is particularly timely and apt in the context of science-based stewardship ofexplosive devices, and it is problems from this arena that form the core of this proposal.