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，有时尚不清楚动态，或变量正在迅速变化。因此，为了准确计算解决方案，可能需要使用小的临时离散参数。例如，在对血流的模拟中，压力在收缩期间迅速增加，然后降低心脏周期的3/8，随后在舒张期间的压力较慢，持续的压力变化较慢，持续了心脏周期的5/8。准确捕获峰值收缩流，必须在该间隔中使用一个小的时间步长。但是，同一时间步骤在舒张期间可能不必要，并且可能导致更长的计算时间。因此，鲁棒的自适应时间稳定对于溶液的准确有效的长期预测至关重要。描述流量问题的部分微分方程的自适应时间稳定方法不足，该项目将在该领域做出重大贡献。该项目中开发的方法将用于建模涉及运输和流体弹性/毛弹性结构相互作用的问题，例如在水文系统中污染物的运输，地表水通过岩石和沙子渗透，毛细血管和组织之间的养分和氧气的运输，或者在疾病越过边界之间传播。该项目将涉及研究生的培训。该项目的重点是针对两类耦合流问题的自适应时间步变方法的开发：流体 - 孔培养基耦合问题和流体结构的相互作用问题。将针对使用Stokes-Darcy系统描述的流体培养基问题开发单层和分区方法。将针对薄和厚结构的流体结构相互作用问题开发分区的数值方法。所提出的方法将根据重构的Cauchy的单足类theta样方法在时间上进行半污点，该方法在可变的时间步中使用时是B稳定的。此外，当Theta为0.5时，该方法也是二阶准确的，并且可以保留所有线性和二次的哈密顿量。但是，将此方法应用于耦合问题，尤其是在设计分区方法时，必须仔细执行以允许使用黑盒和旧版代码。所提出的方法将在数学上和计算上进行分析。将考虑各种自适应策略。每个方法的性能将针对问题中的参数进行研究。在两类的多物理问题中，基础方程将与传输方程相结合。提出的技术也将应用于运输问题，并特别关注质量和能源节能。将研究运输问题的保守特性。该奖项反映了NSF的法定使命，并通过使用基金会的知识分子优点和更广泛的影响评估标准来评估我们被认为是诚实的支持。