Higher order methods for fluid structure interaction problems

流体结构相互作用问题的高阶方法

• 批准号: 2309606
• 负责人: Johnny Guzman
• 金额: $ 34.36万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309606&HistoricalAwards=false
• 关键词: Higher; order; methods; fluid; structure

Multi-physics problems are ubiquitous in the real world and in engineering design. An important class of multi-physics problems are those of fluid-structure interactions (FSI) which involve an object governed by solid mechanics interacting with a fluid (e.g. a turbine interacting with the wind). Having reliable and efficient computer models for these problems are vital to understanding different natural physical systems and essential engineering problems. FSI problems are modeled mathematically by coupled partial differential equations (PDEs). Sophisticated numerical methods have been developed to approximate solutions of individual PDEs. However, the development of the state-of-the-art numerical methods for coupled PDEs remains a challenging task and continues to be a highly active and dynamic area of research. Training of at least one graduate student on the topics of the project is expected.As part of this effort, the development of provably stable higher-order splitting methods for FSI problems will be pursued. Splitting methods take advantage of fine-tuned numerical methods for fluid problems and solid problems. One solves each problem separately and they communicate via boundary conditions. The challenge is to make the methods both stable and higher-order accurate. Indeed, most of the numerical methods that are provably stable are low order accurate in time. The PI will build on the work done with collaborators using Robin-Robin methods. The Robin-Robin methods previously developed will be used as a base method for a more sophisticated correction method.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.

多物理场问题在真实的世界和工程设计中普遍存在。一类重要的多物理问题是流体-结构相互作用（FSI）问题，其涉及由固体力学控制的对象与流体相互作用（例如，涡轮机与风相互作用）。为这些问题建立可靠和有效的计算机模型对于理解不同的自然物理系统和基本工程问题至关重要。流固耦合问题的数学模型耦合偏微分方程（PDE）。复杂的数值方法已经发展到近似的解决方案的个人偏微分方程。然而，国家的最先进的耦合偏微分方程的数值方法的发展仍然是一个具有挑战性的任务，仍然是一个高度活跃和动态的研究领域。预计至少有一名研究生将接受关于该项目主题的培训，作为这项工作的一部分，将继续开发用于流固耦合问题的可证明稳定的高阶分裂方法。分裂方法利用了流体问题和固体问题的微调数值方法。一个人单独解决每个问题，他们通过边界条件进行沟通。挑战在于使这些方法既稳定又具有更高的精度。事实上，大多数可证明稳定的数值方法在时间上是低阶精度的。PI将建立在与合作者使用罗宾-罗宾方法所做的工作基础上。先前开发的Robin-Robin方法将被用作更复杂的校正方法的基础方法。该奖项反映了NSF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。