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

RI：小型：协作研究：用于模拟固液动力学的加速数值求解器框架

• 批准号: 1422795
• 负责人: Joseph Teran
• 金额: $ 25.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1422795&HistoricalAwards=false
• 关键词: RI; Small; Collaborative; Research; accelerated

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. We promote the potential for scalable parallel performance via the adoption of discretization schemes that leverage regular data structures; in particular we will focus on embedded cut cell methods that couple a Lagrangian representation of the solid with an Eulerian representation of the fluid. We 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, our 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.

复杂流体或涉及固液相相互作用的复杂系统的建模和仿真与工业和工程应用密切相关，也为生物流体研究和循环系统功能建模等学科提供了宝贵的工具。这项任务的挑战因支配物理定律的复杂性、对离散近似精度的要求以及需要适应共同应用所要求的高分辨率而更加突出。现代硬件提供了一个独特的机会：随着计算能力的不断增加，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，利用这一潜力需要算法开发和理论创新的协同努力，在数值和离散化技术方面促进正则性并揭示并行化机会。缓解分辨率限制将使模拟的革命性新用途成为可能。一种很有希望的可能性是在实时决策和控制中使用模拟。一些开创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，可以有效地使用格林函数)。然而，更一般的非线性情况，例如高雷诺数牛顿流动和复杂粘弹性流体(在所有的雷诺数下)都不能用线性情况下的工具来考虑。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。我们通过采用利用常规数据结构的离散化方案来促进可扩展并行性能的潜力；特别是我们将重点介绍将固体的拉格朗日表示与流体的欧拉表示相耦合的嵌入式切割单元方法。我们将开发计算效率高的高阶方法，同时保持与设计上并行友好的线性代数求解器的兼容性。关键的发展将是专门设计的隐式方法，以适应对称Krylov解算器的新型并行多重网格预条件。最后，我们对控制方程的建模方法将根据Co-Pi Kavehour研究小组获得的实验数据进行验证。复杂固液动力相互作用的研究可以为开发可伸缩的、面向并行的数值求解器提供直观的验证依据。虽然在固体/流体相互作用的一般领域中有几种现有的方法，但仍有相当大的改进空间，特别是在粘弹性流动的情况下。对提高精度和效率的方法有着明确的需求。很少有方法在不引起相关数值线性代数的繁重计算费用的情况下达到更高的阶数精度。然而，大幅提高性能需要专门为这些新的体系结构规范设计的新颖算法。这一协作活动将采取交叉干预措施，以最大限度地发挥计算创新的好处，同时努力建立一个经过实验结果验证的准确模拟框架。推广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。