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.
