Collaborative Research: Adaptive Data Assimilation for Nonlinear, Non-Gaussian, and High-Dimensional Combustion Problems on Supercomputers

清洁燃烧与对流层空气污染、能源安全和气候变化有着直接而密切的联系，因此迫切需要可持续发展。然而，燃烧界仍然缺乏足够精确的理论描述，使湍流燃烧模型在工程应用中变得严格和定量。数据同化是一种强大而通用的方法，可以最大限度地利用来自模型预测和测量的信息，并有助于减少建模系统状态的不确定性。该项目将通过面对将数据同化应用于燃烧的数学挑战，创建一种新的自适应数据同化方法。这项研究最终将为燃烧工程提供准确、易于处理和预测的模型，这将有助于减少昂贵的清洁燃烧技术设计和开发周期的周转时间。该项目产生的软件将适用于燃烧、火灾、等离子体或生物流体的广泛研究社区，并对其有益。燃烧是数据同化的一种新应用。燃烧中的大部分数据同化问题（如果不是全部的话）都是强烈非线性的，很可能是非高斯的，并且是非常高维的。这对当前的数据同化方法提出了挑战。尽管随着计算机能力的提高和数学和统计技术的进步，非线性非高斯数据同化在某些领域（如气象学、海洋学和地球科学）正在成为现实，但不幸的是，这些数据同化方法往往受到一个或多个限制。例如，可以解决非线性和非高斯性的成功数据同化方法包括最大似然集合滤波器（MLEF）和隐式粒子滤波器（IPF）。然而，前者在算法中的某些点仍然隐含地假设高斯概率密度分布，而后者对于高维问题来说可能是灾难性的昂贵。因此，为了确保数据同化在燃烧问题中的成功应用，必须创造新的数据同化方法来有效地解决非线性和非高斯性，有效地解决高维系统，同时在超级计算机上实现高性能。本课题旨在发展一种新的基于MLEF和IPF的非线性、非高斯、高维系统的自适应数据同化方法。该方法将在燃烧科学和工程领域的一个槽式燃烧器的火焰大涡模拟中得到验证。

Clean combustion is in urgent need for sustainability due to its direct and intimate connection with tropospheric air pollution, energy security, and climate change today. However, the combustion community still lacks a theoretical description that is accurate enough to make turbulent combustion models rigorous and quantitative for engineering application. Data assimilation, a powerful and versatile methodology, can maximize the utility of information from model predictions and measurements, and help reduce the uncertainty of the state of the modeling system. The project will create a new adaptive data assimilation methodology by confronting the mathematical challenges of applying data assimilation to combustion. This research will ultimately lead to the development of accurate, tractable, and predictive models for combustion engineering, which will help reduce the turn-around time for the expensive design and development cycle of clean combustion technologies. Software resulting from the project will be applicable, beneficial, and accessible to the broad research communities of combustion, fire, plasma, or biofluids.Combustion is a new application for data assimilation. Most, if not all, data-assimilation problems in combustion are strongly nonlinear, likely non-Gaussian, and very high-dimensional. This presents challenges to current data assimilation methods. Although nonlinear non-Gaussian data assimilation is becoming reality in some fields (e.g., meteorology, oceanography, and geosciences) with increasing computer power and advances in mathematical and statistical techniques, these data assimilation methods, unfortunately, are often subject to one or more constraints. For example, among successful data assimilation methods that can address nonlinearity and non-Gaussianity are the maximum likelihood ensemble filter (MLEF) and implicit particle filters (IPF). However, the former still implicitly assumes Gaussian probability density distribution at some points in the algorithm and the latter can be catastrophically expensive for high-dimensional problems. Therefore, to ensure a successful data assimilation application to combustion problems, new data assimilation methods must be created to effectively address nonlinearity and non-Gaussianity, efficiently solve high-dimensional systems, and simultaneously achieve high performance on supercomputers. This project aims to develop a new adaptive data assimilation method based on MLEF and IPF for nonlinear, non-Gaussian, high-dimensional systems. The new method will be demonstrated on a large-eddy simulation of flame in a slot burner of interest to combustion science and engineering.