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.

本计画将三维可压缩黏性流动的高阶谱差分法推广至动边界及可变形网格系统，并将其与时间谱法结合以处理周期性非定常流动。与传统的时间精确方法相比，SD-TS方法有可能显着降低模拟时间周期流的计算成本。移动边界的扩展是必要的，使高阶SD方法的应用，以执行精确的模拟能源和运输系统中的许多设备，如风力涡轮机，旋翼机和自主扑翼微型飞行器。主要研究者和他的同事们最近发展的SD方法已经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阶数在选择最佳空间离散化方面提供了很大的灵活性。基于四边形/六面体网格单元开发了一个基本的SD代码。一个单元分裂算法也已经开发出分区每个三角形/四面体单元成三个或四个四边形/六面体单元。这使得可以使用具有混合元素的通用网格。对于与时间相关的高雷诺数问题，隐式下-上对称高斯-赛德尔（LU-SGS）时间步进方法已开发结合p-多重网格方法，以加快SD求解器的收敛。 为了实现上述处理像旋转风力涡轮机一样复杂的设备的目标，所提出的研究必须解决几个主要挑战。研究者和他的同事们正在进行的研究的主要任务是：1）通过混合映射技术将运动物理区域上的Navier-Stokes方程变换到固定参考区域上，将SD方法扩展到运动和可变形网格; 2）使用MeTis进行区域分解和MPI进行消息传递，将三维求解器离散化; 3）开发具有悬挂节点的非协调六面体单元，以允许几何灵活性和可变阶数; 4）实施时间谱方法，以减少模拟周期性时间相关流的计算成本。该项目正在开发的数值模拟技术对于推进各种能源和运输系统的技术至关重要，具有减少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动。研究的直接目标是提高风力涡轮机设计的最新水平。可持续能源对于减少美国对进口石油供应的依赖和减少化石燃料对环境的破坏的重要性现在已得到广泛认可。风力发电是一种具有巨大潜力的资源。现有的商业流动模拟代码使用低阶方法，其数值耗散太大，无法精确跟踪对风力涡轮机性能至关重要的涡流尾流。该项目产生的高阶方法将为未来系统开发上级风力涡轮机设计提供基础。对运输系统的潜在应用可能具有显著的经济和环境效益，包括公路车辆（客车汽车和卡车）的减阻，以及燃气涡轮机和旋翼飞机（两者都包括动叶片）的效率的提高和声学特征的减少。