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粘性不可压缩流的有效数值方法Jian-guo Liu项目摘要该项目将重点侧重于继续开发高效，准确，高阶的有限差和有限元元素方法，用于不稳定的不稳定粘性不可压缩的Navier-Stokes等方程（NSE），，，，，，，差异重点是寻找有效的时间步进程序和更适合数值计算的方程式的新公式。 这些方法的某些实际方面将被研究，包括对一般2D和3D域中流量的扩展，以及在更具挑战性的物理问题上的应用。 在涡度配方中，用于高雷诺数流的新时间步骤。 对于这种流动，对流和粘性术语被明确处理。然后，通过运动学方程从涡度评估流函数及其速度。 新的时间稳定过程效率的关键是，边界上涡度的值是从蒸汽函数明确获得的，而无需任何迭代。 这消除了与涡度配方相关的一些传统困难。 研究者更类似于原始变量公式，在脉冲密度变量中使用了NSE的新公式，该公式与量规变换不同于速度。规格自由使一个人能够为冲动和量规场分配简单而特定的边界条件，从而消除了一些传统的困难，例如压力边界条件。 这种新的有效数值方法已经被用来研究现实世界中的问题，例如研究高速降速器上的拖曳机理，以及热带纬度中严重风暴的发展。 这些方法提供了一个重要的工具，使科学家和工程师可以研究制造和行业中相关的流体问题，这些问题以前无法解决目前可用的数值技术。 它们在有效计算此类问题的解决方案方面是向前迈出的重要一步，并且自然适合在高性能的大规模平行计算机架构上实现。