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

计算流体动力学已经成为研究心血管系统的生理病理学和针对心血管疾病的患者特定手术计划（SP）的有力工具。最近，临床试验-了解疾病和评估临床实践中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，以改善从测量数据中提取的知识，从而导致计算机辅助临床试验（CACT）。对于涉及主动脉（循环的主要动脉）的多种病理，这需要与湍流一起工作。虽然直接数值模拟在这种情况下可以是适当的概念验证，对于大量的患者参与CACT和SP，我们需要不同的数值工具，以提供适当的权衡准确性和可靠性所需的临床应用和计算效率所需的紧迫的最后期限。由于CACT和SP是心血管数学中的新兴概念，在不牺牲精确度的前提下，限制直接数值模拟的计算成本的一种可能的方法是求解流动平均值，并适当地模拟小尺度的影响（未直接解决）在中、大规模（已解决）。我们打算仔细研究基于大涡模拟（LES）反卷积滤波技术的扰动流的新的尖端方法，最终目标是使实际使用的数值工具，以提高知识提取和临床实践，通过CACT和SP。本研究的主要目标是开发和分析一个强大的和准确的LES为基础的方法，不需要或最小的用户集-应用于计算血液动力学的实际不可压缩流动问题。我们在以下几点中阐述了该项目：（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，从而改进质量守恒性质。(c)分析我们的LES方法对非Dirichlet边界条件的影响以及可能的回流稳定效应。 我们计划在学术和真实的生物工程问题上测试该方法。最后，我们计划提供一个有限元开源库，结合我们的研究结果，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.