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

这项发现拨款的目标是：a)推进用于向湍流区域过渡的不可压缩流动的直接数值模拟的自适应高阶谱不连续Galerkin方法的最先进水平；b)使用高阶方法来发现复杂几何形状的过渡过程中的新机制，并在可能的情况下发现实际应用，如庞巴迪航空航天的层流变形翼；c)推进血液粘度建模和现实微循环几何中的血液流动建模的最先进水平；以及d)开发一种用于研究和教学目的的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拨款下取得的一系列成就的基础上，即：针对不可压缩的Navier-Stokes方程开发高阶h-p自适应间断Galerkin方法并在Open MP/MPI混合方法中并行实施；开发使用谱元素Nek5000开放源代码详细的高雷诺数(Re)模拟复杂流动，例如在Re=600,000处的变形机翼；发现壁面射流的稳定性和控制机制；飞机机翼前缘的模型；红细胞聚集的量化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世界范围内感受到，主要是在研究领域，这些领域有助于工程行业，包括航空航天和汽车，通过减少燃料消耗和排放来创造更清洁的环境，以及对医学做出贡献。虽然有超过250名用户使用开源光谱元素Nek5000代码，但其中许多用户正在尝试如此复杂的流动，以至于他们需要自适应网格来实现适当的分辨率。惠普自适应方法的发展将极大地造福于这个社区。流体动力学稳定性和模拟工作的影响将有助于从根本上理解这种流动，并有助于阐明以难以破解而闻名的过渡和湍流机制。血液粘度建模和血流模拟不仅将影响对生物流体力学性质的理解，而且可能在未来影响影响血液微循环的病理性疾病的治疗，如糖尿病。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，但也是通过课程工作，研究将得到加强。3D打印方法还将允许学生通过一种以前从未探索过的有形和可操作的流体方法来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.