RI: Small: Collaborative Research: An accelerated numerical solver framework for simulation of solid-fluid dynamics

复杂流体的建模和仿真，或涉及固体和流体相相互作用的复杂系统，与工业和工程应用高度相关，也为生物流体研究和循环系统的功能建模等学科提供了有价值的工具。由于控制物理定律的复杂性，对离散近似精度的要求以及适应普通应用所要求的高分辨率的需要，这项任务的挑战更加突出。现代硬件提供了一个独特的机会：随着计算能力的不断提高，原本需要几天时间的模拟现在有可能在几分钟内完成。然而，利用这种潜力需要算法开发和数值和离散化技术的理论创新的协同努力，以促进规律性和暴露并行化的机会。减轻分辨率限制将使模拟具有革命性的新用途。在实时决策和控制中使用仿真是一种很有前景的可能性。一些突破性的研究利用了固体/流体相互作用的控制，但它们仅限于线性方程（低雷诺数流动，格林函数可以有效地使用）。然而，更一般的非线性情况，例如高雷诺数牛顿流和复杂粘弹性流体（所有雷诺数），不能用线性情况下可用的工具来考虑。这项活动将结合计算机工程、数值分析、应用数学和实验物理的专业知识，共同应对这些挑战。该提案通过采用利用常规数据结构的离散化方案，促进了可扩展并行性能的潜力；特别地，它将专注于嵌入切割细胞方法，将固体的拉格朗日表示与流体的欧拉表示相结合。它将开发高阶的方法，这些方法具有很高的计算效率，同时与设计上并行友好的线性代数求解器保持兼容。关键的发展将是隐式方法，专门设计用于适应对称Krylov求解的新型并行多网格预调节器。最后，将根据Co-PI Kavehpour研究组获得的实验数据验证控制方程的建模方法。复杂固流动力学相互作用的研究可以作为开发可扩展的、面向并行的数值求解器的直观证明基础。虽然在固体/流体相互作用的一般领域有几种现有的方法，但在粘弹性流动的情况下仍有很大的改进空间。对提高准确性和效率的方法有明确的需求。很少有方法可以在不产生相关数值线性代数的繁重计算费用的情况下实现高阶精度。然而，大胆的性能提升需要专门为这些新的体系结构规范设计的新颖算法。这项合作活动将参与跨领域干预，以最大限度地提高计算创新的效益，同时努力建立一个准确的模拟框架，以验证实验结果。拓展活动包括在科学计算和大型工程项目中指导代表性不足的高中生。

Modeling and simulation of complex fluids, or intricate systems involving interaction of solid and fluid phases are highly relevant to industrial and engineering applications, and also provides a valuable tool in disciplines such as the study of biofluids and the functional modeling of the circulatory system. The challenges of this task are accentuated by the complexity of the governing physical laws, the demands for accuracy of discrete approximations and the need to accommodate the high resolutions mandated by common applications. Modern hardware offers a unique opportunity: as computational capacity continues to increase, simulations that would have taken days now have the potential of being completed within minutes. However, capitalizing on this potential necessitates a concerted effort of algorithmic development and theoretical innovations in numerics and discretization techniques that promote regularity and expose parallelization opportunities. Alleviating resolution limitations will enable revolutionary new uses of simulation. A promising possibility is the use of simulation in real-time decision making and control. Several ground breaking studies utilize control of solid/fluid interaction but they are limited to linear equations (low Reynolds number flows where Green's functions can be efficiently used). However, the more general nonlinear cases, for example higher Reynolds number Newtonian flows and complex viscoelastic fluids (at all Reynolds numbers) cannot be considered with the tools available in the linear case. This activity will combine expertise from computer engineering, numerical analysis, applied mathematics and experimental physics to jointly address these challenges. The proposal promotes the potential for scalable parallel performance via the adoption of discretization schemes that leverage regular data structures; in particular it will focus on embedded cut cell methods that couple a Lagrangian representation of the solid with an Eulerian representation of the fluid. It will develop higher order methods that are highly computationally efficient while remaining compatible with linear algebra solvers that are parallel-friendly by design. The key developments will be implicit methods  specifically designed to accommodate novel parallel multigrid preconditioners for symmetric Krylov solvers. Finally, the modeling approach for the governing equations will be validated against experimental data obtained in Co-PI Kavehpour's research group. The study of complex solid-fluid dynamic interaction can serve as intuitive proving grounds for the development of scalable, parallelism-oriented numerical solvers. Although there are several existing methods in the general field of solid/fluid interactions, there is still considerable room for improvement especially in the case of viscoelastic flows. There is a clear demand for methods that improve accuracy and efficiency. Very few methods achieve higher order accuracy without incurring burdensome computational expense from associated numerical linear algebra. However, bold performance gains require novel algorithms specifically designed for these new architectural specifications. This collaborative activity will engage in cross-cutting interventions to maximize the benefit of computing innovation while striving for an accurate simulation framework validated against experimental findings.Outreach activities include mentoring underrepresented high school students in scientific computing and large-scale engineering projects.