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
基本信息
- 批准号:9805621
- 负责人:
- 金额:$ 9.6万
- 依托单位:
- 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:
- 关键词:
项目摘要
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。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Jian-Guo Liu其他文献
On the mean field limit for Brownian particles with Coulomb interaction in 3D
三维库仑相互作用布朗粒子的平均场极限
- DOI:
10.1063/1.5114854 - 发表时间:
2018-11 - 期刊:
- 影响因子:1.3
- 作者:
Lei Li;Jian-Guo Liu;Pu Yu - 通讯作者:
Pu Yu
Soliton structures for the (3 + 1)-dimensional Painlevé integrable equation in fluid mediums.
- DOI:
10.1038/s41598-024-62314-6 - 发表时间:
2024-05 - 期刊:
- 影响因子:4.6
- 作者:
Jian-Guo Liu - 通讯作者:
Jian-Guo Liu
<span> </span> <br class="MsoNormal" /> <span><span style="color: rgb(51, 51, 51); font-family: ;" Roman?,?serif?;?="" New="" Times="">Existence and uniqueness of global weak
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:1
- 作者:
Xiuqing Chen;Xiaolong Li;Jian-Guo Liu; - 通讯作者:
Nonsymmetric traveling wave solution to a Hele-Shaw type tumor growth model
一个 Hele-Shaw 型肿瘤生长模型的非对称行波解
- DOI:
10.1016/j.jde.2025.113433 - 发表时间:
2025-09-25 - 期刊:
- 影响因子:2.300
- 作者:
Yu Feng;Qingyou He;Jian-Guo Liu;Zhennan Zhou - 通讯作者:
Zhennan Zhou
Multiple-soliton solutions, soliton-type solutions and rational solutions for the $$\varvec{(3+1)}$$ -dimensional generalized shallow water equation in oceans, estuaries and impoundments
- DOI:
10.1007/s11071-016-2914-y - 发表时间:
2016-07-01 - 期刊:
- 影响因子:6.000
- 作者:
Zhi-Fang Zeng;Jian-Guo Liu;Bin Nie - 通讯作者:
Bin Nie
Jian-Guo Liu的其他文献
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{{ truncateString('Jian-Guo Liu', 18)}}的其他基金
Collaborative Research: Dynamics, singularities, and variational structure in models of fluids and clustering
合作研究:流体和聚类模型中的动力学、奇点和变分结构
- 批准号:
2106988 - 财政年份:2021
- 资助金额:
$ 9.6万 - 项目类别:
Standard Grant
Collaborative Research: Nonlocal Models of Aggregation and Dispersion
合作研究:聚集和分散的非局部模型
- 批准号:
1812573 - 财政年份:2018
- 资助金额:
$ 9.6万 - 项目类别:
Standard Grant
Collaborative Research: Kinetic Models of Aggregation and Dispersion
合作研究:聚集和分散的动力学模型
- 批准号:
1514826 - 财政年份:2015
- 资助金额:
$ 9.6万 - 项目类别:
Standard Grant
Efficient Numerical Methods for Viscous Incompressible Flows
粘性不可压缩流的高效数值方法
- 批准号:
1011738 - 财政年份:2009
- 资助金额:
$ 9.6万 - 项目类别:
Continuing Grant
Efficient Numerical Methods for Viscous Incompressible Flows
粘性不可压缩流的高效数值方法
- 批准号:
0811177 - 财政年份:2008
- 资助金额:
$ 9.6万 - 项目类别:
Continuing Grant
Efficient Numerical Methods for Viscous Incompressible Flows
粘性不可压缩流的高效数值方法
- 批准号:
0512176 - 财政年份:2005
- 资助金额:
$ 9.6万 - 项目类别:
Standard Grant
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 - 财政年份:2001
- 资助金额:
$ 9.6万 - 项目类别:
Continuing Grant
Mathematical Sciences: Efficient Numerical Methods for Large Reynolds Number Unsteady Viscous Incompressible Flows
数学科学:大雷诺数不稳定粘性不可压缩流的有效数值方法
- 批准号:
9505275 - 财政年份:1995
- 资助金额:
$ 9.6万 - 项目类别:
Standard Grant
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