Collaborative Research: Time Accurate Fluid-Structure Interactions

合作研究：时间精确的流固耦合

• 批准号: 2208220
• 负责人: Catalin Trenchea
• 金额: $ 22.5万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208220&HistoricalAwards=false
• 关键词: Collaborative; Research; Time; Accurate; Fluid

In realistic problems describing fluid flow, sometimes the dynamics are not known, or the variables are changing rapidly. Hence, to accurately compute the solution, one might need to use small temporal discretization parameters. For example, in simulations of blood flow, the pressure rapidly increases and then decreases during the systole, which lasts 3/8 of the cardiac cycle, followed by slower and smaller changes in the pressure during diastole, lasting 5/8 of the cardiac cycle. To accurately capture the peak systolic flow, a small time step has to be used in that interval. However, that same time step might be unnecessary small during diastole and could lead to longer computational times. Therefore, robust adaptive time-stepping is central to accurate and efficient long-term predictions of the solution. The adaptive time-stepping methods for partial differential equations describing flow problems are under-investigated and this project will make a major contribution in that field. The methods developed in this project will be used to model problems involving transport and fluid-elastic/poroelastic structure interaction, such as the transport of contaminants in hydrological systems where surface water percolates through rocks and sand, transport of nutrients and oxygen between capillaries and tissue, or spread of a disease across a border. This project will involve the training of graduate students. The focus of this project is the development of adaptive time-stepping methods for two classes of coupled flow problems: the fluid-porous medium coupled problems and the fluid-structure interaction problems. A monolithic and a partitioned method will be developed for the fluid-porous medium problem described using the Stokes-Darcy system. Partitioned numerical methods will be developed for the fluid-structure interaction problems with both thin and thick structures. The proposed methods will be semi-discretized in time based on the refactorized Cauchy’s one-legged theta-like method, which is B-stable when used with a variable time step. Furthermore, when theta is 0.5, the method is also second-order accurate and conserves all linear and quadratic Hamiltonians. However, the application of this method to coupled problems, especially when partitioned methods are designed, has to be carefully performed to allow the use of black-box and legacy codes. The proposed methods will be mathematically and computationally analyzed. Various adaptive strategies will be considered. The performance of each method will be investigated with respect to the parameters in the problem. In both classes of multi-physics problems, the underlying equations will be coupled with a transport equation. The proposed techniques will also be applied to the transport problem, with a particular attention to mass and energy conservation. Conservative properties of the transport problem will be investigated.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.

在描述流体流动的现实问题中，有时动力学是未知的，或者变量正在快速变化，因此，为了准确计算解，可能需要使用小的时间离散参数，例如，在血流、压力的模拟中。在收缩期快速增加然后减少，持续 3/8 个心动周期，随后在舒张期压力变化更慢、更小，持续 5/8 个心动周期。然而，在舒张期期间，相同的时间步长可能不必要地小，并且可能导致更长的计算时间，因此，鲁棒的自适应时间步长对于解决方案的准确和有效的长期预测至关重要。描述流动问题的自适应时间步长方法尚未得到充分研究，该项目将在该领域做出重大贡献，该方法将用于模拟涉及传输和流体弹性/多孔弹性的问题。结构相互作用，例如地表水通过岩石和沙子渗透的水文系统中污染物的传输、毛细血管和组织之间的营养物和氧气的传输，或疾病的跨境传播该项目将涉及研究生的培训。是针对两类耦合流动问题开发自适应时间步长方法：流体-多孔介质耦合问题和流体-结构相互作用问题。将针对使用描述的流体-多孔介质问题开发整体方法和分区方法。这Stokes-Darcy 系统将针对薄结构和厚结构的流体-结构相互作用问题开发出基于重构的柯西单腿 theta 方法的时间半离散化方法。此外，当 theta 为 0.5 时，该方法也是二阶精确的，并且保留所有线性和二次哈密顿量。但是，该方法适用于耦合。问题，特别是在设计分区方法时，必须仔细执行，以允许使用黑盒和遗留代码。将对所提出的方法进行数学和计算分析。将考虑每种方法的性能。在这两类多物理问题中，所提出的技术也将与传输方程相结合，特别关注质量和能量。运输问题的保守性质将是。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。