Efficient Numerical Methods for Viscous Incompressible Flows

粘性不可压缩流的高效数值方法

• 批准号: 0107218
• 负责人: Jian-Guo Liu
• 金额: $ 22万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0107218&HistoricalAwards=false
• 关键词: Efficient; Numerical; Methods; Viscous; Incompressible

The investigator proposes to continue the development of efficient and accurate numerical methods for unsteady incompressible flow, with particular emphasis on (i) finding new equivalent formulations of Navier-Stokes equations, often inspired by physical considerations, better suited to numerical computation; (ii) proper handling of boundary conditions, a key difficulty in the subject since important physical interactions frequently occur near the boundary; (iii) rapid computation of three dimensional flows and generalization of schemes for flows in complex geometries; (iv) development of efficient schemes for complex fluids such as magneto-hydrodynamics, liquid crystal polymers, geodynamo, climate modeling, and large eddy turbulence simulations; (v) design of numerical schemes that preserves numerically conserved quantities such as energy and helicity for inviscid flow, and accurately captures their dissipation rates at high Reynolds number. It is widely believed that different dissipation rates for energy and helicity is the key mechanism leading to the formation of large coherent structures of turbulent flows.The numerical simulation of incompressible flows, which plays an important role in numerous scientific and industrial applications of current interest, is a challenging task for both numerical analysts and computational fluid dynamicists. The proposed fast and accurate numerical methods for incompressible flow is expected to become an important tool for simulation and analysis of complex turbulent flow phenomena including vortex breakdown, (massive) flow separation, vortex shedding, transient jets in cross-stream, wake-body interaction, high-swirl flow, etc. It is also an essential tool for the design of advanced flow control mechanisms used, for example, to reduce flow-induced noise and vibration, and to improve lift/drag performance at reduced energy consumption rates. Examples include flow over bluff bodies such as ground or under-water vehicles; in engines; in/around rotating machinery or in data storage units with rotating and moving parts.

研究人员建议继续开发不稳定的不稳定流量的有效，准确的数值方法，特别是（i）找到Navier-Stokes方程的新表述，通常受到物理考虑的启发，更适合数值计算； （ii）正确处理边界条件，这是对象的关键困难，因为重要的物理相互作用经常发生在边界附近； （iii）三维流的快速计算和复杂几何形状流的方案的概括； （iv）开发用于复杂流体的有效方案，例如磁性流体动力学，液晶聚合物，地球瘤，气候建模和大型涡流模拟； （v）设计数值方案的设计，这些方案保留了数值保守的数量，例如能量和无污水流量，并准确地捕获其在较高雷诺数的耗散速率。 人们普遍认为，能量和螺旋性的不同耗散率是导致形成大型湍流相干结构的关键机制。不可压缩流的数值模拟在当前利益的许多科学和工业应用中起着重要的作用，对于数值分析师和计算流体动力学家而言，这是一项具有挑战性的任务。 提出的用于不可压缩流的快速准确的数值方法有望成为模拟和分析复杂湍流现象的重要工具，高旋流流等。它也是设计高级流量控制机制的必不可少的工具，例如减少流动诱导的噪声和振动，并在降低的能耗速率下提高升力/阻力性能。 例子包括在悬崖上的流动，例如地面或水下车辆；在发动机中；在旋转机械或带有旋转和移动部件的数据存储单元中。