Collaborative Research: Optimal-Complexity Spectral Methods for Complex Fluids

合作研究：复杂流体的最优复杂谱方法

• 批准号: 1952706
• 负责人: Joern Dunkel
• 金额: $ 12万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1952706&HistoricalAwards=false
• 关键词: Collaborative; Research; Optimal; Complexity; Spectral

Complex fluids, such as microbial suspensions in biology or quantum fluids in physics, exhibit a wealth of intriguing phenomena, ranging from spontaneous transport and non-equilibrium pattern formation to the emergence of superfluid and superconductive currents. Computational techniques for simulating and predicting the dynamics of these fluids in realistic 3D configurations found in laboratories are not keeping pace with the recent breakthroughs in experimental design and mathematical modeling. The Principal Investigators (PIs) will develop a collection of computational advancements that are urgently needed to validate current mathematical models and explore relevant parameter regimes to guide current and next-generation experiments. These efforts will pave the way for a better understanding of biological and physical transport phenomena, promising improved designs of micro-fluidic and quantum-fluidic devices. The project also provides research training opportunities for graduate students. The PIs will be developing highly efficient numerical methods based on a hybrid of Fourier/ultraspherical spectral methods that are ideally suited for accurately and robustly treating the high-order derivatives that appear in the complex fluid models. This computational framework will enable the fast simulation of non-equilibrium fluid flows through scientifically relevant geometries composed of cylinders, spheres, and ellipsoids. The algorithms will be parallelizable for efficient simulation on next-generation hardware accelerators. Working with two experimental collaborators, the PIs will investigate chaotic mixing, transport properties, and topological nature of geometrically confined non-Newtonian fluids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

复杂流体，如生物学中的微生物悬浮液或物理学中的量子流体，表现出大量有趣的现象，从自发输运和非平衡模式形成到超流体和湍流的出现。在实验室中发现的用于模拟和预测这些流体在现实3D配置中的动力学的计算技术没有跟上实验设计和数学建模的最新突破。主要研究人员（PI）将开发一系列迫切需要的计算进步，以验证当前的数学模型，并探索相关的参数机制，以指导当前和下一代实验。这些努力将为更好地理解生物和物理传输现象铺平道路，有望改进微流体和量子流体设备的设计。该项目还为研究生提供研究培训机会。PI将开发基于傅立叶/超球面谱方法混合的高效数值方法，这些方法非常适合准确和鲁棒地处理复杂流体模型中出现的高阶导数。这种计算框架将使非平衡流体流动的快速模拟，通过科学相关的几何形状组成的圆柱体，球体和椭球体。 这些算法将是并行的，以便在下一代硬件加速器上进行高效仿真。与两名实验合作者合作，PI将调查混沌混合，传输特性和几何约束的非牛顿流体的拓扑性质。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。