Efficient Numerical Methods for Unsteady Viscous Incompressible Flows

非定常粘性不可压缩流的高效数值方法

• 批准号: 9805621
• 负责人: Jian-Guo Liu
• 金额: $ 9.6万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805621&HistoricalAwards=false
• 关键词: Efficient; Numerical; Methods; Unsteady; Viscous

DMS-9805621 EFFICIENT NUMERICAL METHODS FOR VISCOUS INCOMPRESSIBLE FLOWS Jian-Guo Liu Project Summary This project will focus on continuing the development of efficient, accurate, high order finite difference and finite element methods for the unsteady viscous incompressible Navier-Stokes equations (NSE), with emphasis on finding efficient time stepping procedures and new formulations of the equations better suited to numerical computation. Some practical aspects of the methods, including extensions to flows in general 2D and 3D domains, and applications to more challenging physical problems, will be investigated. In the vorticity formulation, a new time-stepping procedure is used for high Reynolds number flows. For such flows the convection and viscous terms are treated explicitly. The stream function, and hence the velocity, is then evaluated from the vorticity via the kinematic equation. The key to the efficiency of the new time-stepping procedure is that the value of the vorticity on the boundary is obtained explicitly from the steam function without any iteration. This eliminates some traditional difficulties associated with the vorticity formulation. More akin to the primitive variable formulation, the investigator is using a new formulation of the NSE in the impulse density variable which differs from the velocity by a gauge transformation. The gauge freedom enables one to assign simple and specific boundary conditions for both the impulse and gauge fields, thus eliminating some traditional difficulties such as the pressure boundary condition. This new class of efficient numerical methods has already been used to study such real world problems as the investigation of the mechanism of drag reduction on airfoils at high velocities, as well as the development of severe storms in tropical latitudes. These methods provide an important tool that allow scientists and engineers to study related fluid problems in manufacturing and industry that were previous unsolvable with currently available numerical techniques. They represent a significant step forward in the efficient computation of solutions to such problems, and are naturally suited for implementation on high performance massively parallel computer architectures.

DMS-9805621 粘性不可压缩流动的有效数值方法 刘建国 项目摘要 该项目将重点继续开发用于非定常粘性不可压缩纳维-斯托克斯方程 (NSE) 的高效、准确、高阶有限差分和有限元方法，重点是寻找有效的时间步进程序和更适合数值计算的新方程公式 计算。 将研究这些方法的一些实际方面，包括一般 2D 和 3D 领域中流的扩展，以及对更具挑战性的物理问题的应用。 在涡度公式中，新的时间步进程序用于高雷诺数流。 对于此类流动，对流和粘性项被明确处理。然后通过运动学方程根据涡度来评估流函数以及速度。 新时间步进程序高效的关键在于，边界上的涡度值是从蒸汽函数中显式获得的，无需任何迭代。 这消除了与涡度公式相关的一些传统困难。 更类似于原始变量公式，研究人员在脉冲密度变量中使用 NSE 的新公式，该公式与规范变换的速度不同。规范自由度使人们能够为脉冲场和规范场分配简单且特定的边界条件，从而消除了一些传统的困难，例如压力边界条件。 这种新型高效数值方法已被用于研究现实世界中的问题，例如研究高速机翼减阻机制以及热带纬度地区严重风暴的发展。 这些方法提供了一个重要的工具，使科学家和工程师能够研究制造和工业中的相关流体问题，这些问题以前无法用当前可用的数值技术解决。 它们代表了在有效计算此类问题的解决方案方面向前迈出的重要一步，并且自然适合在高性能大规模并行计算机体系结构上实现。