Collaborative Research: Optimal-Complexity Spectral Methods for Complex Fluids

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，展示了大量有趣的现象，从自发输运和非平衡模式形成到超流体和超导电流的出现。在实验室中，模拟和预测这些流体在真实3D配置下的动力学的计算技术并没有跟上最近在实验设计和数学建模方面的突破。首席研究人员（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，并探索相关的参数制度，以指导当前和下一代的实验。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装置的设计。该项目还为研究生提供研究培训机会。pi将开发基于傅里叶/超球面光谱混合方法的高效数值方法，该方法非常适合精确和稳健地处理复杂流体模型中出现的高阶导数。这个计算框架将能够快速模拟非平衡流体流动，通过由圆柱体、球体和椭球组成的科学相关几何形状。该算法可并行化，可用于下一代硬件加速器的高效仿真。与两位实验合作者合作，pi将研究几何受限非牛顿流体的混沌混合、输运性质和拓扑性质。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.