Low-dimensional modeling of non-Newtonian pulsatile flow within (visco)elastic vessels with applications to blood flow

目标是进行基础流体力学研究，旨在通过系统地开发更好的动脉循环网络内血液流动的低维模型，从一方面弥补详细但计算要求高的3D流动模拟和从另一方面简化但计算快速的1D流动近似之间的差距。这些将基于系统方法的应用，例如主正交分解，POD（也称为Karhunen-Loeve， K-L，分析）对精心选择的测试问题的详细3D和时间相关模拟（使用光谱方法）的结果，其中动脉内血液流动的更多关键特征将被表示，例如：a)血流流变学的非牛顿（粘弹性和粘塑性/触变性）特性及其与血流诱导的血液内部结构各向异性的关系；B)假设实际弹粘塑性和各向异性壁面行为的流体-壁面相互作用；C)流动的惯性（有时也有过渡）特性等。智力优势：通过系统的K-L方法，开发适用于复杂非线性血流方程系统的低维（粗粒度）模型，是探索高性能计算工作的一种新方法。它可以是一个变革性的范例，说明如何执行复杂的流系统分析，以增强其在应用程序中的潜在用途。更广泛的影响：期望的结果是更准确，但计算管理，新的多尺度模型的血液流动动脉循环系统。这些新模型可以真正具有变革性，可以直接帮助医生（作为工具，例如，帮助解释压力数据）、医学教育（例如，帮助分析人体生理学）、药物动力学（协助实现个性化医疗）、更好地了解心血管疾病的进展（例如，动脉粥样硬化和血栓形成）等。

The objective is to perform fundamental fluid mechanics research that aims to bridge the gap between, from the one hand, detailed but computationally demanding 3D flow simulations and, from the other hand, simplistic but computationally fast 1D flow approximations by systematically developing better low-dimensional models for blood flow within the arterial circulation network . Those are going to be based on the application of systematic methods, such as Principal Orthogonal Decomposition, POD (also known as Karhunen-Loeve, K-L, analysis) to the results of detailed 3D and time-dependent simulations (using spectral methods) of carefully selected test problems, where a lot more of the key characteristics of the blood flow within arteries are going to be represented such as: a) the Non-Newtonian(viscoelastic and viscoplastic/thixotropic) characteristics of the blood flow rheology and its dependence of the flow-induced anisotropy of the internal blood structure; b) the fluid-wall interactions assuming a realistic elasto-viscoplastic and anisotropic wall behavior; c) the inertial (sometimes also transitional) characteristics of the flow, etc. Intellectual Merit: The development, through a systematic K-L approach, of low dimensional (coarse-grained) models applicable to the complex nonlinear system of equations governing blood flow, is a novel way to explore high performance computational work. It can be a transformative paradigm as to how complex flow system analysis needs to be performed in order to enhance its potential use to applications.Broader Impacts: The desired result are more accurate, yet computationally manageable, new multiscale models for the blood flow arterial circulation systems. These new models can truly be transformative, of direct help to the physician (as a tool, for example, to help interpret pressure data), in medical education (to help, for example, the analysis of human physiology), in pharmacokinetics (assisting towards personalized medicine), in bettering of understanding of the progression of cardiovascular diseases (as for example atherosclerosis and thrombosis) etc.