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

我们的目标是进行基础流体力学研究，旨在弥合差距之间的差距，一方面，详细的，但计算要求的三维流动模拟，从另一方面，简单，但计算速度快的一维流动近似系统开发更好的低维模型内的动脉循环网络的血液流动。这些都是基于系统方法的应用，如主正交分解，POD（也称为Karhunen-Loeve，K-L，分析）与详细的3D和时间相关模拟的结果进行比较（使用光谱方法）仔细选择的测试问题，其中动脉内血流的更多关键特征将被表示，例如：（一）非牛顿血液流动流变学的（粘弹性和粘塑性/触变性）特性及其对内部血液结构的流动诱导各向异性的依赖性; B）假设现实的弹-粘塑性和各向异性壁行为的流体-壁相互作用; c）流体-壁相互作用的惯性特性; d）流体-壁相互作用的惯性特性; e）流体-壁相互作用的惯性特性。（有时也是过渡性的）流动的特征，等等。智力优点：通过系统的K-L方法，（粗粒度）模型适用于控制血流的复杂非线性方程系统，是探索高性能计算工作的新颖方式。它可以是一个变革性的范例，如何复杂的流动系统的分析需要进行，以提高其潜在的使用application.Broader影响：所需的结果是更准确的，但计算管理，新的多尺度模型的血流动脉循环系统。这些新的模型可以真正是变革性的，对医生有直接的帮助（作为工具，例如，帮助解释压力数据），在医学教育中（帮助，例如，分析人体生理学），在药代动力学中（有助于个性化医疗），在更好地理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.