High Order Methods for Direct Numerical Simulation of Incompressible Flows and Applications to Transition to Turbulence

该发现基金的目标是：A）推进自适应高阶谱间断Galerkin方法的最新技术，用于不可压缩流向湍流过渡的直接数值模拟; B）使用高阶方法发现复杂几何形状过渡过程中的新机制，并在可能的情况下，发现实际应用，如庞巴迪航空航天公司的层流变形机翼; C）推进血液粘度建模和结合红细胞聚集效应的现实微循环几何形状中的血流建模的最新技术水平;以及D）开发用于研究和教育目的的3D打印复杂层流和过渡流结构的方法。** 这项工作建立在上一次发现基金的一系列成果之上：即，发展了求解不可压Navier-Stokes方程的高阶h-p自适应间断Galerkin方法及其在混合Open MP / MPI方法中的并行实现;使用谱元Nek 5000开放源代码开发复杂流的详细高雷诺数（Re）模拟，例如Re=600，000的变形机翼;壁射流和飞机机翼前缘模型的稳定性和控制机制的发现;以及红细胞聚集的定量和表征及其对微循环中血液粘度的影响。** 这项工作的影响将在全世界范围内感受到，主要是在有助于工程行业的研究领域，包括航空航天和汽车，通过更少的燃料消耗和排放来实现更清洁的环境，以及医学。虽然有超过250名用户使用开源光谱元素Nek 5000代码，但其中许多人正在尝试如此复杂的流动，他们需要自适应网格来实现适当的分辨率。h-p自适应方法的发展将使这一群体受益匪浅。流体动力学稳定性和模拟工作的影响将有利于对此类流动的基本理解，并有助于阐明众所周知难以破解的转捩和湍流机制。血液粘度建模和血流模拟不仅会影响对生物流体力学特性的理解，而且在未来可能会影响对血液微循环的病理性疾病（如糖尿病）的治疗。在培训和教育领域，将影响到一些研究生和博士后研究人员以及许多本科生，首先是通过他们直接参与研究和研究技能培训，但也通过课程，这将加强研究。3D打印方法还将使学生通过以前未探索过的有形和可操纵的流体方法更好地理解流体力学。

The objectives of this Discovery Grant are: A) to advance the state of the art of adaptive high order spectral Discontinuous Galerkin methods for the Direct Numerical Simulation of incompressible flows in the transition to turbulence regime; B) to use high order methods to discover new mechanisms in the transition process for complex geometries and, where possible, practical applications such as a laminar morphing wing of Bombardier Aerospace; C) to advance the state of the art in blood viscosity modeling and modeling of blood flow in realistic microcirculation geometries incorporating the effect of Red Blood Cell aggregation; and D) to develop a methodology to 3D print complex laminar and transitional flow structures for research and educational purposes. ******The work builds on a series of achievements under the last Discovery Grant: namely, the development of a high order h-p adaptive Discontinuous Galerkin method for the incompressible Navier-Stokes equations and its parallel implementation in a hybrid Open MP / MPI approach; development of detailed high Reynolds number (Re) simulations of complex flows with the spectral element Nek5000 open source code, for example at Re=600,000 for the morphing wing; discovery of stability and control mechanisms for the wall jet and models of aircraft wing leading edges; and quantification and characterization of Red Blood Cell aggregation and its effect on blood viscosity in microcirculation. ******The impact of this work will be felt worldwide, mostly in research arenas that contribute to engineering industry, including aerospace and automotive, to a cleaner environment through leaner fuel consumption and emissions, and to medicine. While over 250 users work with the open source spectral element Nek5000 code, many of these are attempting such complex flows that they need adaptive grids to achieve the proper resolution. The development of h-p adaptive methods will greatly benefit this community. The impact of the fluid dynamics stability and simulation work will benefit the fundamental understanding of such flows and help to elucidate transition and turbulence mechanisms, notoriously difficult to crack. The blood viscosity modeling and blood flow simulations will impact not only biofluid mechanical property understanding but also, potentially in the future, treatment of pathological diseases that affect blood microcirculation, such as diabetes. In the training and education realm, the impact will be on several graduate students and postdoctoral researchers as well as many undergraduate students, first through their direct participation in the research and research skills training, but also through coursework which will be enhanced by the research. The 3D printed methodology will also allow students to better understand fluid mechanics through a previously unexplored tangible and manipulatable approach to fluids.