EAPSI: Establishing New Mathematical Methods for Analyzing Simulated Models of Fuel Combustion

一种被称为充量压缩点火（HCCI）的内燃形式导致相对低的排放和高效率。燃料和氧化剂混合，然后压缩到自动点火点，尽管目前还不知道如何控制点火的确切时间，这方面需要精确的理解才能在商业上实现。名古屋大学的Takashi Ishihara博士假设，在燃料流场中引入搅拌或运动将控制点火开始的时间，对模拟数据的初步研究支持这一想法。在这个项目中，EAPSI研究员将研究3D燃烧模拟，以了解如何在燃料室中引入流动控制点火开始的时间。这项研究将需要开发新的数学工具，这反过来又将对流体分析问题产生进一步的影响，例如天气模拟和洋流研究。将使用拓扑数据分析中称为持久同源性的数学工具研究跟踪温度、速度和化学物质的时变3D流体模型的数值模拟。使用这种方法，模拟中的每个时间点将生成一个称为持久性图的数学对象集合，该持久性图对模拟数据的临界点（例如，局部最小值，最大值和鞍点）的关系进行编码。然后将使用已建立的统计技术挖掘这些数据，以揭示物理学家感兴趣的现有测量的相关性，并深入了解流体动力学控制点火开始时间的机制。东亚和太平洋夏季研究所计划下的这个奖项支持美国研究生的夏季研究，由NSF和日本科学促进会共同资助。

A form of internal combustion called homogeneous-charge compression ignition (HCCI) results in relatively low emissions and high efficiency. The fuel and oxidizer are mixed and then compressed to the point of auto-ignition, though it is currently unknown how to control the exact timing of the ignition, an aspect that requires a precise understanding in order to be implemented commercially. Dr. Takashi Ishihara of Nagoya University has hypothesized that introducing stirring, or movement, in the fuel flow field will control the timing of the onset of ignition, and initial studies on simulated data support this idea. In this project, the EAPSI fellow will study 3D combustion simulations to understand how introducing a flow in the fuel chamber controls the timing of the onset of ignition. This investigation will require the development of new mathematical tools, which in turn will have further implications in problems of fluid analysis, e.g. weather simulations and the study of ocean currents.Numerical simulations of time-varying 3D fluid models tracking temperature, velocity, and chemical species, will be studied using a mathematical tool in topological data analysis called persistent homology. With this method, each time point in the simulation will generate a collection of mathematical objects called persistence diagrams, which encode the relationships of the critical points of the simulated data (e.g. local minima, maxima, and saddle points). This data will then be mined using established statistical techniques to uncover correlations with existing measurements of interest to physicists and gain insight into the mechanisms by which the dynamics of the fluid control the timing of the onset of ignition. This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Japan Society for the Promotion of Science.