Collaborative Research: Robust and Scalable Methods for Simulation and Data-Driven Modeling of Particulate Flows

复杂流体是均质流体和可变形或刚性颗粒或纤维的混合物。这些流体在生物系统和工程应用中普遍存在，准确预测它们的行为对于血液动力学建模、细胞内过程模拟和微流体设备建模等一系列问题非常重要。目前，复杂流体的精确模型需要在微观或介观水平上进行非常昂贵的模拟，以解决每个粒子(例如，变形的细胞或纤维)的行为及其相互作用。相比之下，复杂流体的宏观连续介质模型(如果可用)允许更有效的计算。然而，这些模型往往缺乏准确性，并且无法在现实环境中捕捉到流行为的所有重要方面；阻碍了快速预测模型的构建。该项目的目标是能够以数据驱动的方式构建这种模型。研究人员将开发一个基于微观数值模拟的框架。开发这种流体的高效和准确的连续计算模型的挑战是从微观参数到宏观参数的难以分析的过渡。在这项工作中，研究人员专注于(1)用于2D和3D颗粒流的健壮和可扩展的解算器；以及(2)利用我们的框架来探索用于2D复杂流动的数据驱动的宏观模型，并初步探索3D的扩展。该团队将开发用于精确求解大规模3D流动的算法，这些流动具有处理粘性对比度、复杂几何边界和长模拟时间的高体积分数的浸没可变形颗粒。其关键的数学组成部分包括边界积分的表述和计算，三维曲面上奇异和近奇异积分的核无关求积格式，接触处理和密切交互，以及提高时间步长格式的效率。在项目的第二部分，研究人员将应用这一框架来探索复杂流动的宏观特征及其对微观参数和局部几何的依赖；这将为复杂流体的数据驱动连续介质模型奠定基础。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Complex fluids are mixtures of homogeneous fluids and deformable or rigid particles or fibers. These fluids are ubiquitous in biological systems and engineering applications and accurate prediction of their behavior is important for a broad set of problems such as hemodynamics modeling, simulation of intracellular processes, and microfluidics device modeling. Currently, accurate models of complex fluids require highly expensive simulations at microscopic or mesoscopic level, resolving the behavior of each particle (e.g., a deforming cell or fiber) and their interactions. In contrast, macroscopic continuum models for complex fluids (when available) allow for a far more efficient computation. However, these models often lack accuracy, and cannot capture all important aspects of the flow behavior in realistic settings; hindering construction of fast predictive models. The goal of the project is to enable construction of such models in a data-driven way. The investigators will develop a framework based on microscopic numerical simulations. The challenge in developing efficient and accurate continuum computational models of such fluids is the hard-to-analyze transition from microscopic to macroscopic parameters. In this work, the investigators focus on (1) robust and scalable solvers for particulate flow in 2D and 3D; and (2) the utilization of our framework to explore data-driven macroscopic models for the complex flows in 2D, with an initial exploration of extensions to 3D. The team will develop the algorithms for accurate solution of large-scale 3D flows with a high volume fraction of immersed deformable particles handling viscosity contrast, complex geometric boundaries, and long simulation times. Key mathematical components for this include boundary integral formulation and computation, kernel-independent quadrature schemes for singular and near-singular integration on surfaces in 3D, contact handling and close interaction, and improving efficiency of time-stepping schemes. In the second component of the project, the investigators will apply this framework to explore macroscopic characteristics of complex flows and their dependence on microscopic parameters and local geometry; this will create a foundation for data-driven continuum models for complex 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.