Accurate, Robust Simulations of Aerodynamics Flows, Especially Wakes and Shocks

我的研究领域是为计算流体动力学（CFD）和网格生成开发更准确，高效和鲁棒的算法。 我的团队的中期研究目标是将我们在流场求解算法、网格生成和自适应、误差分析和数值稳定性方面的工作结合起来，以便更一致地产生可靠的模拟结果，用于外部空气动力学的分析和设计。 这里的技术挑战不仅是获得特定流动问题的数值解，而且要尽可能减少在此过程中人类用户干预和干扰的需要，同时为工程感兴趣的输出量（包括例如力和热通量）的误差提供严格的定量界限。 这些进步将改进工程师用来设计更安静、更省油的飞机和陆地运输车辆的CFD分析工具。 在拟议的发现补助金期限内，我们的战略目标是： 1.相互配合。 虽然自适应网格即将取代计算流体动力学，但在计算空气动力学中仍然需要更好的非自适应网格，特别是对于像增升系统这样的复杂构型。我们将继续我们目前的工作，一个完全各向异性的三维网格生成器，最大限度地提高整个网格的内部结构。 2.高精度流量求解器。 雷诺平均Navier-Stokes方程有时是一种被恶意中伤的湍流模型，但仍然是大规模空气动力学模拟的唯一可行的替代方案。即使该模型不是流动物理的精确表示，模拟也不应使该问题与数值误差复合。我们将完成我们的四阶精确非结构网格有限体积RANS流解算器的工作，并证明其实用性，准确性和效率的飞机在巡航和高升力配置。 3.激波的数值处理。 计算流体力学中的现代数值方法依赖于光滑解的假设，这在有激波的跨音速和超音速流动中是行不通的。激波拟合是一种将这种流动明确地视为不连续的范例。 我们正在开发三维流激波拟合的网格工具，包括复杂的激波-激波和激波-边界相互作用。我们也将开始内部工作，发展一个高阶激波拟合方案。 4.稳态收敛。 大多数商业CFD软件需要数百或数千次迭代才能完全收敛到稳态。我们将利用我们所学到的关于非结构网格流求解器的特征系统和收敛性的知识，在我们的稳定性工作中将收敛速度提高一个数量级。 总之，这些功能将对CFD模拟的可靠性和鲁棒性产生重大影响，这反过来又将使其用于更广泛的工业分析和设计应用。

My research area is the development of more accurate, efficient, and robust algorithms for computational fluid dynamics (CFD) and mesh generation. My medium term research goal for my group is to bring together our work in algorithms for flow solution, mesh generation and adaptation, error analysis, and numerical stability to more consistently produce reliable simulation results for analysis and design in external aerodynamics. The technical challenge here is not just to obtain a numerical solution for a particular flow problem, but to reduce as much as possible the need for a human user to intervene and iterate during this process, while at the same time providing tight quantitative bounds on the error in output quantities of engineering interest, including for example forces and heat fluxes. These advances will improve the CFD analysis tools engineers use to design quieter, more fuel efficient aircraft and land transportation vehicles. Our strategic objectives during the term of the proposed Discovery Grant are: 1. Meshing. While adaptive meshing is poised to take over CFD, there is still a need in computational aerodynamics for better non-adaptive meshing, especially for complex configurations like high-lift systems. We will continue our current work on a fully anisotropic 3D mesh generator which maximizes internal structure throughout the mesh. 2. Highly-Accurate Flow Solvers. The Reynolds-averaged Navier-Stokes equations are a sometimes maligned model for turbulent flow, but remain the only feasible alternative for large-scale aerodynamic simulations. Even though the model is not an exact representation of the flow physics, simulations should not compound that problem with numerical error. We will complete work on our fourth-order accurate unstructured mesh finite-volume RANS flow solver, and demonstrate its usefulness, accuracy, and efficiency for aircraft in cruise and high-lift configurations. 3. Numerical Treatment of Shock Waves. Modern numerical methods in CFD rely for accuracy on the assumption of smooth solutions, which breaks down for transonic and supersonic flows with shock waves. Shock fitting is a paradigm that treats such flows explicitly as discontinuous. We are developing meshing tools for shock fitting for 3D flows, including complex shock-shock and shock-boundary interaction. We will also begin work in-house on developing a high-order shock-fitting scheme. 4. Steady-State Convergence. Most commercial CFD software requires hundreds or thousands of iterations to reach full convergence to steady state. We will leverage what we have learned about eigensystems and convergence for unstructured mesh flow solvers in our stability work to improve convergence rates by an order of magnitude. Taken together, these capabilities will have a significant impact on the reliability and robustness of CFD simulations, which in turn will open their use to a wider range of industrial analysis and design applications.