Multi-scale description of multi-phase fluid flows using data-driven closures

使用数据驱动闭包对多相流体流动进行多尺度描述

• 批准号: 455865232
• 负责人: Dr. Mohsen Sadr
• 金额: --
• 依托单位: Paul Scherrer Institut (PSI)
• 依托单位国家: 德国
• 项目类别: WBP Fellowship
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/455865232?language=en
• 关键词: Multi; scale; description; multi; phase

An accurate description of multi-phase fluid flows that is accompanied with an efficient numerical method remains one of the challenges in the realm of scientific computing. The target of this research proposal is to devise a continuum model that deploys data-driven mesoscale closures based on underlying molecular interactions. In particular, considering moment equations resulting from the Enskog-Vlasov kinetic equation, the unclosed terms in the conservation laws can be modeled using the moments of conserved quantities and their spatial derivatives. Once an appropriate basis function for solution space is utilized, the closure problem converts to a regression problem of finding the projected coefficients for terms associated with molecular interactions given the moments around the point of interest. Here, an efficient high dimensional regression model from Machine Learning literature such as Artificial Neural Network suitable for the closure problem will be deployed and trained offline. The training data set will be generated by performing Monte Carlo mesoscale simulations in a reference configuration for an applicable range of boundary conditions. Finally, as the target test case, the trained multi-scale solution algorithm will be tested by studying the evolution of Stratospheric aerosols in a relevant simulation setting. As the outcome, this research proposal intends to provide an efficient, accurate, and flexible framework for large scale simulations of fluid flows that allows consistent inclusion of micro-scale physics in the classical conservation laws using efficient high dimensional regression methods.The applicant has chosen Prof. Nicolas G. Hadjiconstantinou at Massachusetts Institute of Technology (MIT) to be the host for this postdoctoral study, because of his extensive research and relevant contributions for variance-reduction Monte Carlo methods in kinetic theory as well as multi-scale modeling. Furthermore, Prof. Youssef Marzouk at MIT, who is an expert in Bayesian inference and uncertainty quantification, will support the applicant with devising a reliable regression model relevant for this research proposal.

多相流体流动的精确描述和有效的数值方法一直是科学计算领域的挑战之一。这项研究的目标是设计一个连续体模型，部署数据驱动的中尺度封闭的基础上潜在的分子相互作用。特别是，考虑到从Enskog-Vlasov动力学方程产生的力矩方程，守恒律中的未闭合项可以使用守恒量及其空间导数的力矩来建模。一旦利用了用于解空间的适当基函数，闭合问题就转换为回归问题，该回归问题找到与分子相互作用相关的项的投影系数，给出了感兴趣点周围的矩。在这里，将部署和离线训练来自机器学习文献的高效高维回归模型，例如适用于闭包问题的人工神经网络。训练数据集将通过在适用范围的边界条件的参考配置中执行蒙特卡罗中尺度模拟来生成。最后，作为目标测试用例，将通过在相关模拟环境中研究平流层气溶胶的演变来测试训练的多尺度解算法。作为结果，本研究提案旨在为大规模流体流动模拟提供一个高效、准确和灵活的框架，该框架允许使用高效的高维回归方法在经典守恒定律中一致地包含微尺度物理。Hadjiconstantinou在马萨诸塞州理工学院（MIT）是这个博士后研究的主持人，因为他广泛的研究和相关贡献的方差减少蒙特卡罗方法在动力学理论以及多尺度建模。此外，麻省理工学院的Youssef Marzouk教授是贝叶斯推理和不确定性量化方面的专家，他将支持申请人设计与本研究提案相关的可靠回归模型。