High-Order Numerical Algorithms for Steady and Unsteady Simulation of Viscous Compressible Flow

粘性可压缩流稳态和非稳态模拟的高阶数值算法

• 批准号: 0708071
• 负责人: Antony Jameson
• 金额: $ 42.16万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708071&HistoricalAwards=false
• 关键词: Order; Numerical; Algorithms; Steady; Unsteady

The goal of this project if to produce an efficient high-order methodology for 3D, high-speed unsteady viscous fluid flow in complex domains. No existing solver achieves all these goals, despite the fact that significant progress in relevant research areas has been made during the last few years. To achieve this goal, two major objectives may be identified. Firstly, the development of the high-order Spectral Difference (SD) Method for unstructured grids will be addressed. More specifically, the scheme will be extended to three dimensions, and formulated for mixed-element grids. The latter is necessary for efficient resolution of flows at high Reynolds numbers. Furthermore, upon analyzing and validating viable viscous discretization techniques, the scheme will be extended by the principal investigator and his colleagues to the Navier-Stokes equations on mixed grids. The second major objective is to improve the efficiency and robustness of the high-order methodology. Numerical schemes of third or higher spatial order are not yet efficient enough for many problems of practical engineering interest, in particular high-speed viscous flow. To keep the number of degrees of freedom comparable to that of a second order method, the number of grid cells must be reduced as the order is increased. To resolve discontinuities sharply without oscillations h-p adaptively will be introduced. For both steady-state and time- dependent problems a fast solution technique is necessary to solve the arising systems of nonlinear equations. In order to meet this goal, an h-p multigrid strategy will be combined with efficient time stepping and relaxation schemes for both steady and unsteady flows.Computational simulation has revolutionized the engineering design process and is by now the single most important tool in a wide range of high technology industries. That in turn has had a huge impact in many real life applications of great importance to society and science, from aerospace to health to the environment. The proposed research is targeted at advancing the state of the art of numerical algorithms which will be needed for the U.S. to remain at the forefront of computational simulation for both industrial and scientific applications. In the Aerospace Industry simulation methods have been largely responsible for doubling the fuel efficiency of long range commercial aircraft since the advent of jet transport. The need for further improvement is crucial for both the economics and environmental impact of air transport, a jumbo jet releases its take-off weight (around 400 tons) in carbon dioxide emissions during a single flight. The European Union has recognized the importance of advancing simulation techniques with a variety of European wide and national initiatives (such as the German Mega Flow and Mega Design programs.) Simulations and optimized redesign of the 747 wing can save tons" of fuel, travel time and reduce emissions. Computer simulation is equally crucial to advances in numerous other applications. For example, simulations of blood flow through a beating heart and its valves, helps doctors understand and repair the malfunctioning heart; simulation of air traffic control patterns can move that industry faster toward safer skies, reduce the occurrence of mid-air collisions and the time to reroute flights around weather systems; modeling of air flow around computer chips and over the surface of a fast spinning disk drive improve function and reliability. Today's ability to model huge global weather system can change the fate of nations struggling with tsunami's, floods, the devastation of hurricanes; Astrophysics and many studies of importance to National Security all rely on this new aspect of science and mathematics. At the heart of all these is the development of more advanced numerical algorithms which provide the cornerstone of computational simulation. The proposed research intends to extend these to more efficient high-order 3D methods, While the immediate application of the research is to fluid flow problems related to aerospace, an improved fluid flow simulation capability is immediately transferable to other industrial and scientific applications, including those mentioned above as well as many others such as the automotive and marine industries, wind energy, and a wide range of environmental issues. Even the flow patterns in urban areas around buildings can be used to evaluate how germ or chemical particles would be spread by winds circulating through the 'canyons' of clustered tall buildings. Further advances in all aspects of computational simulation and its underlying numerical methology is essential in order to maintain the Unites States' technological leadership and competitiveness in the rapidly evolving global economy. The results of these developments and techniques will play an increasingly pivotal role and have major implications environmentally, scientifically economically and socially as the results filter down into the many applications using them today, as well as future applications that will need to evaluate complex nonlinear partial differential equations for a variety of physics.

如果要在复杂域中为3D，高速不稳定的粘性流体流提供有效的高阶方法，则该项目的目的是。尽管在过去几年中，现有的求解器没有实现所有这些目标，但相关研究领域取得了重大进展。为了实现这一目标，可以确定两个主要目标。首先，将解决非结构化网格的高阶光谱差异（SD）方法的开发。更具体地说，该方案将扩展到三个维度，并为混合元素网格配制。后者对于高雷诺数的有效分辨率有效地解析是必要的。此外，在分析和验证可行的粘性离散技术后，该计划将由首席研究员及其同事扩展到混合网格上的Navier-Stokes方程。第二个主要目标是提高高级方法的效率和鲁棒性。 第三或更高空间顺序的数值方案尚未足够有效，对于许多实用工程感兴趣的问题，尤其是高速粘性流。为了保持与二阶方法相当的自由度的数量，必须随着订单的增加而减少网格单元的数量。为了在没有振荡的情况下急剧解决不连续性，将引入H-P。对于稳态和时间依赖性问题，对于解决非线性方程的系统系统，必须使用快速解决方案技术。为了实现这一目标，H-P Multigrid策略将与有效的时间步进和放松方案相结合，用于稳定和不稳定的流量。Computational仿真彻底改变了工程设计过程，而到目前高科技行业。 反过来，这对从航空到健康再到环境都非常重要的许多现实生活应用产生了巨大影响。 拟议的研究旨在推进数值算法的艺术状态，这些算法将使美国保持在工业和科学应用的计算模拟的最前沿。 在航空航天行业中，模拟方法在很大程度上是自喷气运输出现以来远程商用飞机的燃油效率的一倍。进一步改善的需求对于航空运输的经济和环境影响至关重要，巨型喷气机在一次飞行中释放了其起飞重量（约400吨）的二氧化碳排放。欧盟已经认识到使用各种欧洲范围和国家计划（例如德国大型流量和巨型设计计划）推进模拟技术的重要性。仿真和优化的747机翼的重新设计可以节省大量的燃料，旅行时间减少排放量。更快地朝着更安全的天空，减少空中碰撞的发生，并在天气系统周围重新穿线；全球天气系统可以改变与海啸，洪水，飓风破坏的国家的命运； 天体物理学和许多对国家安全重要性的研究都取决于科学和数学的新方面。 所有这些的核心是开发更先进的数值算法，这些算法提供了计算模拟的基石。拟议的研究旨在将其扩展到更有效的高阶3D方法，而研究的立即应用是在与航空航天相关的流体流问题上，改进的流体流量模拟能力可以立即转移到其他工业和科学应用中，包括上面提到的以及许多其他人，例如汽车和海洋行业，风能以及广泛的环境问题。即使是建筑物周围城市地区的流动模式也可以用来评估通过循环中的风孔或化学颗粒散布的细菌或化学颗粒的方式。在计算模拟的各个方面及其基本的数值甲基甲基化方面的进一步进步对于维持在迅速发展的全球经济中的联合国技术领导力和竞争力至关重要。这些发展和技术的结果将扮演越来越重要的角色，并在经济和社会上在科学和社会上具有重大影响，因为结果将其逐渐渗透到当今的许多应用中，以及未来需要评估复杂非线性偏差的未来应用各种物理的方程式。