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

高阶谱差法求解移动变形网格上非定常粘性流的时谱法

• 批准号: 0915006
• 负责人: Antony Jameson
• 金额: $ 47.44万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915006&HistoricalAwards=false
• 关键词: Time; Spectral; Method; Unsteady; Viscous

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.

该项目将三维可压缩粘性流的高阶光谱差（SD）方法扩展到具有移动边界和可变形网格的系统，并将其与时间元素（TS）方法相结合，以治疗周期性不稳定流量。与常规的时间准确方法相比，SD-TS方法有可能显着降低模拟时间周期性流量的计算成本。需要向移动边界扩展，以实现高级SD方法，以对能源和运输系统中的众多设备进行准确的模拟，例如风力涡轮机，旋翼机和自动拍打机翼微型空中汽车。首席研究员及其同事最近开发了SD方法，证实了它在处理高雷诺数湍流时的准确性，鲁棒性和效率。 SD方法通过改变多项式顺序来选择最佳的空间离散化提供了极大的灵活性。基线SD代码是基于四边形/六面体网格元素开发的。还开发了一种元素分裂算法，以将每个三角形/四面体元件分配为三个或四个四边形/六面体元件。这使使用具有混合元素的一般网格。对于时间依赖性的高雷诺数问题，隐式下Upper对称的高斯 - 塞德尔（LU-SGS）时间步进方法是与P-Multigrid方法一起开发的，以加快SD求解器的收敛性。 为了实现上述目标，即将设备视为旋转风力涡轮机，该研究必须解决一些主要挑战。研究人员及其同事在正在进行的研究中执行的主要任务是1）通过将移动物理域上的Navier-Stokes方程转换为通过混合映射技术将Navier-Stokes方程转换为固定参考域，将SD方法扩展到移动和可变形的网格。 ; 2）使用METIS进行域分解和MPI进行消息传递的三维求解器并行化； 3）开发具有悬挂节点的不合格六面体元素，以允许几何柔韧性和可变顺序； 4）实施时间频谱方法，以减少模拟定期时间依赖流量的计算成本。该项目中开发的数值模拟技术对于在各种能源和运输系统中推进技术至关重要，具有降低环境影响的巨大潜力。许多这样的系统需要模拟具有移动边界的流量。该研究的直接目标是改善风力涡轮机设计的最新技术。可持续能源对减少美国对进口石油供应的依赖以及减少化石燃料造成的环境损害的重要性迄今已被广泛认可。风能是具有巨大潜在潜力的资源。现有的商业流动模拟代码使用低阶方法，这些方法在数值上耗散过多，无法准确跟踪涡流唤醒，这对于风力涡轮机的性能至关重要。该项目将导致的高阶方法将为上级风力涡轮机设计的系统发展提供基础。可能具有重大经济和环境利益的运输系统中的潜在应用包括减少道路车辆，乘用车和卡车，以及提高燃气轮机和转子机的声学效率和降低，这两者都结合了移动的叶片。