Time-Spectral Method for Unsteady Viscous Flow on Moving and Deformable Grids with the High-order Spectral Difference Method

本项目将三维可压缩粘性流动的高阶谱差分方法推广到具有动边界和可变形网格的系统，并将其与时间谱方法相结合来处理周期非定常流动。与传统的时间精确方法相比，SD-TS方法具有显著降低模拟时间周期流的计算代价的潜力。需要扩展到移动边界，以便能够应用高阶SD方法来精确模拟能源和交通系统中的许多设备，如风力涡轮机、旋翼机和自动扑翼微型飞行器。主要研究人员和他的同事们最近开发的SD方法已经证实了它在处理高雷诺数湍流时的准确性、稳健性和效率。通过改变多项式的阶数，SD方法在选择最优空间离散化方面提供了很大的灵活性。编制了基于四边形/六面体网格单元的基线SD程序。还开发了单元分裂算法，将每个三角形/四面体单元划分为三个或四个四边形/六面体单元。这使得可以使用具有混合元素的常规格线。对于含时高雷诺数问题，隐式上、下对称Gauss-Seidel(LU-SGS)时间步长方法与p-多重网格法相结合，以加快SD求解器的收敛速度。为了实现上述目标，即处理像旋转风力涡轮机一样复杂的设备，拟议的研究必须解决几个主要挑战。研究人员和他的同事们正在进行的研究中承担的主要任务是：1)通过混合映射技术将移动物理区域上的Navier-Stokes方程转换到固定的参考域，将SD方法扩展到移动和可变形网格；2)使用METIS进行区域分解和使用MPI进行消息传递，实现三维求解器的并行化；3)开发带有悬挂节点的非协调六面体单元，以实现几何灵活性和可变顺序；4)实施时间谱方法，以降低模拟周期性时间相关流动的计算成本。该项目正在开发的数值模拟技术对于推动广泛的能源和交通系统的技术进步至关重要，具有显著的减少环境影响的潜力。许多这样的系统需要模拟具有移动边界的流动。这项研究的一个直接目标是提高风力涡轮机设计的最新水平。到目前为止，人们普遍认识到可持续能源对于减少美国对进口石油供应的依赖以及减少化石燃料对环境的破坏的重要性。风力发电是一种潜力巨大的资源。现有的商业流动模拟程序使用的是低阶方法，数值耗散太大，无法准确跟踪对风力机性能至关重要的涡流尾迹。该项目将产生的高阶方法将为未来系统地开发更好的风力涡轮机设计提供基础。可能具有显著经济效益和环境效益的交通系统的潜在应用包括减少道路车辆的阻力，包括客车和卡车，以及提高效率和减少燃气轮机和旋翼机的声学特征，这两种技术都采用了移动叶片。

This project extends the high-order spectral difference (SD) method for three-dimensional compressible viscous flows to systems with moving boundaries and deformable grids, and also to combine it with the time-spectral (TS) method to treat periodic unsteady flows. Compared to conventional time accurate methods, the SD-TS method has the potential to significantly reduce the computational cost of simulating time periodic flows. The extension to moving boundaries is needed to enable application of the high order SD methodology to perform accurate simulations of numerous devices in energy and transportation systems, such as wind turbines, rotorcraft and autonomous flapping wing micro air vehicles. Recent development of the SD method by the principal investigator and his colleagues has confirmed it accuracy, robustness and efficiency in dealing with high Reynolds number turbulent flows. The SD method offers a great flexibility in choosing optimal spatial discretization by varying the polynomial order. A baseline SD code has been developed based on quadrilateral/hexahedral grid elements. An element splitting algorithm has also been developed to partition each triangular/tetrahedral element into three or four quadrilateral/hexahedral elements. This enables the use of general grids with mixed elements. For time-dependent high-Reynolds number problems, implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) time stepping approach has been developed in conjunction with a p-multigrid method to speed up convergence of the SD solver. In order to achieve the above goal of treating devices as complex as a rotating wind turbine, the proposed research must address several major challenges. The main tasks being undertaken in the ongoing research by the investigator and his colleagues are 1) Extension of the SD method to moving and deformable grids by transforming the Navier-Stokes equations on a moving physical domain to a fixed reference domain by a blended mapping technique; 2) Parallelization of the three-dimensional solver using MeTis for domain decomposition and MPI for message passing; 3) Development of non-conforming hexahedral elements with hanging nodes to allow geometric flexibility and variable order; 4) Implementation of the Time Spectral method to reduce the computational cost of simulating periodic time dependent flows. The numerical simulation techniques being developed in this project are crucial to advancing technology in a wide range of energy and transportation systems, with significant potential for reducing environmental impact. Many such systems require simulations of flows with moving boundaries. An immediate target of the research is to improve the state of the art in wind turbine design. The importance of sustainable energy both to reduce U.S. dependence on imported oil supplies and to reduce environmental damage due to fossil fuels is by now widely recognized. Wind power is a resource with tremendous untapped potential. Existing commercial flow simulation codes use low order methods which are too numerically dissipative to allow accurate tracking of the vortex wake which are crucial to wind turbine performance. The high order methods which will result from this project will provide a basis for the systematic future development of superior wind turbine designs. Potential applications to transportation systems which could have significant economic and environmental benefits include drag reduction of road vehicles, both passenger cars and trucks, and improvements in the efficiency and reduction of the acoustic signature of gas turbines and rotorcraft, both of which incorporate moving blades.