Collaborative Research: Efficient Modeling of Incompressible Fluid Dynamics at Moderate Reynolds Numbers by Deconvolution LES Filters - Analysis and Applications to Hemodynamics

计算流体动力学已成为研究心血管系统生理病理和心血管疾病患者特异性手术计划（SP）的有力工具。最近，临床试验——在临床实践中了解疾病和评估治疗和设备影响的标准程序——得到了大量使用数值模拟的支持，以改进从测量数据中提取的知识，从而导致了计算机辅助临床试验（CACT）。对于涉及主动脉（血液循环的主要动脉）的各种疾病，这需要与湍流一起工作。虽然在这种情况下，直接数值模拟可以适用于概念验证，但对于涉及CACT和SP的大量患者，我们需要不同的数值工具来提供临床应用所需的准确性和可靠性与紧迫期限所需的计算效率之间的适当权衡。由于CACT和SP是心血管数学中新兴的概念，因此临床应用的湍流生理流动的适当数值建模现在是一个未满足的需求，我们打算在本提案中解决。在不牺牲精度的情况下限制直接数值模拟的计算成本的一种可能方法是求解流量平均值，并在中尺度和大尺度（已求解）下适当地模拟小尺度（未直接求解）的影响。我们计划仔细研究基于大涡模拟（LES）反卷积滤波技术的扰动流的新前沿方法，最终目标是使数值工具的实际应用能够通过CACT和SP改善知识提取和临床实践。本研究的主要目标是开发和分析一种鲁棒和准确的基于LES的方法，不需要或只需要用户设置，以解决现实的不可压缩流动问题应用于计算血流动力学。我们在以下几点阐述了该项目：(a)对方法中涉及的关键参数进行敏感性分析，以了解它们对解决方案的影响，从而通过物理和数值参数自动设置参数。(b)发展和分析高阶时间方法，特别是计算压力的方法，从而改进质量守恒特性。(c)分析我们的LES方法对非狄利克雷边界条件的影响和可能的回流稳定效果。我们计划在学术和实际的生物工程问题上测试这种方法。最后，我们计划提供一个包含我们研究结果的有限元开源库，可用于CACT和SP。

Computational fluid dynamics has emerged as a powerful tool to study the physiopathology of the cardiovascular system and for patient-specific Surgical Planning (SP) for cardiovascular diseases. Recently, clinical trials - the standard procedure for understanding diseases and assessing the impact of therapies and devices in the clinical practice - have been supported by a massive use of numerical simulations to improve the knowledge extracted from measured data, leading to Computer Aided Clinical Trials (CACT). For a large variety of pathologies involving the aorta - the major artery of the circulation - this requires to work with turbulent flows. While Direct Numerical Simulation in this context can be appropriate for a proof of concept, for the large number of patients involved in CACT and SP we need different numerical tools to provide the appropriate trade-off between accuracy and reliability needed by clinical applications and computational efficiency needed by tight deadlines. As CACT and SP are new emerging concepts in cardiovascular mathematics, an appropriate numerical modeling of turbulent physiological flows for clinical applications is now an unmet need that we intend to solve in this proposal.A possible way to limit the computational costs associated with Direct Numerical Simulations without sacrificing accuracy is to solve the flow average and model properly the effects of the small scales (not directly solved) at the medium and large scales (solved). We intend to investigate carefully new cutting-edge methods for disturbed flows based on Large Eddy Simulation (LES) Deconvolution filtering techniques with the ultimate goal of enabling practical use of numerical tools to improve knowledge extraction and clinical practice through CACT and SP. The main objective of this research is the development and the analysis of a robust and accurate LES based approach requiring no or minimal user's set-up for realistic incompressible flow problems with application to computational hemodynamics. We articulate the project in the following points: (a) Sensitivity analysis of key parameters involved in the method to understand their impact on the solution, leading to an automated parameter set-up through physical and numerical arguments. (b) Development and analysis of high-order in time methods, particularly for the computation of the pressure, with consequent improvement of the mass conservation properties. (c) Analysis of the impact of our LES approach on non-Dirichlet boundary conditions and the possible backflow stabilizing effects. We plan to test the method on both academic and real bioengineering problems. Finally, we plan to deliver a finite element open source library incorporating the findings of our research, available for CACT and SP.