Algorithm Development and Analysis for Non-Newtonian Fluids Interacting with Elastic and Poroelastic Structures

非牛顿流体与弹性和多孔弹性结构相互作用的算法开发和分析

基本信息

批准号：
1818842
负责人：
Hyesuk Lee
金额：
$ 23.33万
依托单位：
Clemson University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818842&HistoricalAwards=false
关键词：
Algorithm Development Analysis Non Newtonian

项目摘要

This research concerns the development and rigorous analysis of stable and efficient numerical schemes for non-Newtonian fluid - structure interactions (FSI). The study will be focused on partitioning schemes of an implicit type for the coupled model systems that allow each subproblem to be solved independently using existing local solvers in a fixed/moving domain setting. Stability and accuracy properties of numerical methods will be investigated using non-Newtonian fluid and poroelastic/elastic structure models. The theoretical investigation will provide a solid foundation and guidance to the further development of numerical algorithms. Because of the many important biological and engineering processes involving non-Newtonian fluid flows, there is a great demand for mathematical support in these applications. This research will provide an underlying mathematical foundation for non-Newtonian flows in a multiphysical setting. The technical goal of this project is to develop algorithms and analyze numerical schemes for two coupled systems: (a) quasi-Newtoinan fluid - poroelastic structure and (b) viscoelastic fluid - elastic structure. For system (a) the PI will focus on the development and analysis of a nonlinear operator, where a solution to the operator equation yields subsystem solutions satisfying interface conditions of the whole coupled system. Advantages of this approach over the previously developed optimization approach are the flexibility to choose a nonlinear solver and that no extra coding effort is needed as the adjoint system is no longer involved in a solution process. Since it is expected that the linearized operator is not self-adjoint, the linear operator equation should be solved by an iterative solver for a non-self-adjoint problem. When a partitioned scheme is considered for simulating viscoelastic FSI, extra difficulty is encountered due to the lack of information on the stress along the moving boundary and movement of inlet and outlet boundaries along the interface of two subsystems. The PI will investigate various choices for a stress boundary value and their effect on a solution of FSI. Another issue with the viscoelastic FSI is the size of the fluid problem to be solved in each time step (or in each internal iteration), which may require an operator splitting based on a temporal discretization scheme such as a fractional time step method. To tackle this, the PI will investigate various time stepping schemes.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.

这项研究涉及对非牛顿液 - 结构相互作用（FSI）的稳定和有效数值方案的开发和严格分析。该研究将集中在耦合模型系统的隐式类型的分区方案上，这些方案允许使用固定/移动域设置中的现有本地求解器独立解决每个子问题。数值方法的稳定性和准确性将使用非牛顿流体和毛弹性/弹性结构模型进行研究。理论研究将为数值算法的进一步发展提供坚实的基础和指导。由于涉及非牛顿流体流动的许多重要的生物学和工程过程，因此在这些应用中对数学支持有很大的需求。这项研究将在多物理环境中为非牛顿流提供基础。该项目的技术目标是开发算法并分析两个耦合系统的数值方案：（a）准北植物流体 - 毛弹性结构和（b）粘弹性流体 - 弹性结构。对于系统（a），PI将重点放在非线性操作员的开发和分析上，其中对操作员方程的解决方案得出满足整个耦合系统接口条件的子系统解决方案。这种方法比先前开发的优化方法的优点是选择非线性求解器的灵活性，并且由于不再参与解决方案过程，因此不需要额外的编码工作。由于预计线性化运算符不是自动相互接合的，因此迭代求解器应解决非自动辅助问题问题的线性操作员方程。当考虑了模拟粘弹性FSI的分区方案时，由于缺乏有关沿着两个子系统界面的入口边界以及入口和出口边界运动的压力的信息，因此遇到了额外的困难。 PI将研究应力边界值及其对FSI溶液的影响的各种选择。粘弹性FSI的另一个问题是要在每个时间步（或每个内部迭代中）解决的流体问题的大小，这可能需要基于时间离散化方案（例如分数时间步骤方法）进行操作员分裂。为了解决这个问题，PI将调查各个时间的阶梯计划。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准来评估的。