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.

多物理问题在现实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，其中涉及由固体力学控制的物体与流体相互作用（例如涡轮机与风相互作用）。拥有针对这些问题的可靠且高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。 FSI 问题通过耦合偏微分方程 (PDE) 进行数学建模。已经开发出复杂的数值方法来近似各个偏微分方程的解。然而，开发最先进的耦合偏微分方程数值方法仍然是一项具有挑战性的任务，并且仍然是一个高度活跃和动态的研究领域。预计将就该项目的主题对至少一名研究生进行培训。作为这项工作的一部分，将寻求开发可证明稳定的 FSI 问题的高阶分裂方法。分裂方法利用针对流体问题和固体问题的微调数值方法。人们分别解决每个问题，并通过边界条件进行通信。挑战在于使这些方法既稳定又高阶准确。事实上，大多数可证明稳定的数值方法在时间上都是低阶准确的。 PI 将建立在与合作者使用 Robin-Robin 方法完成的工作的基础上。先前开发的 Robin-Robin 方法将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智力优点和更广泛的影响审查标准进行评估，被认为值得支持。