Studies on mathematical analysis and numerical computation of the Nevier-Stokes equations

内维-斯托克斯方程的数学分析与数值计算研究

基本信息

  • 批准号:
    07304019
  • 负责人:
  • 金额:
    $ 1.09万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
  • 财政年份:
    1995
  • 资助国家:
    日本
  • 起止时间:
    1995 至 1996
  • 项目状态:
    已结题

项目摘要

The present study carried out mathematical and numerical analysis of the Navier-Stokes equations and the Euler equations, which are the master equations of incompressible fluid. In addition, some abstract analysis of numerical schemes which are necessary for the fluid computations. The study consists of three categories : (1) mathematical analysis of the Navier-Stokes equations, (2) numerical experiments on the bifurcation of water waves, and (3) numerical computation of the Euler equations by the vortex method.(1) mathematical analysis of the Navier-Stokes equations. New exact solutions of the Navier-Stokes equation outside a cylinder are discovered ; they are generalizations of Tamada's solution and Wang's solution. Kolmogorov's problem is studied and we find that some stationary solutions tends to C^1 but not C^2 vector field as the Reynolds number tends to infinity. This solution represents a kind of internal layr, which may well serve as a key to the understanding of the turbulent … More power spectra. Some self-similar solutions of the Navier-Stokes equations, which are represented by the congruent hypergeometric functions, are discovered. Some stationary solutions having inflows and outflows and their stability were considered. Some of them are found to be stable for all the Reynolds number.(2) numerical experiments on the bifurcation of water waves. Two-dimensional irrotational flows with free surface are considered. The free surface are assumed to be periodic in its profile and permanent in time. Varying the Weber number and the Froude number, we compute many now bifurcating solutions. We also compute water waves with negative surface tension. Some of them are, in its limiting form, found to be the same as Euler's elastica.(3) numerical computation of the Euler equations by the vortex method. Two-dimensional vortex sheets in shear flows are computed by the vortex method. Many studies on vortex sheet motion are known, but our research is new in that we study the relation between vortex sheet and background shear flow. Less
本文对不可压缩流体的主方程Navier-Stokes方程和Euler方程进行了数学和数值分析。此外,对流体计算所需的数值格式进行了抽象分析。研究内容包括三个方面:(1)Navier-Stokes方程的数学分析,(2)水波分叉的数值实验,(3)Euler方程的涡方法数值计算。(1)纳维-斯托克斯方程的数学分析。发现了柱外Navier-Stokes方程的新的精确解,它们是Tamada解和Wang解的推广。研究了Kolmogorov问题,发现当雷诺数趋于无穷大时,某些定态解趋于C^1而不是C^2向量场。这个解代表了一种内部层,它可以作为理解湍流的一个关键。 ...更多信息 功率谱发现了Navier-Stokes方程的一些自相似解,这些解用同余超几何函数表示。考虑了一类具有流入流出的定常解及其稳定性。其中一些被发现是稳定的所有雷诺数。(2)水波分叉的数值实验。考虑了二维自由表面无旋流动。假定自由表面在其轮廓上是周期性的,并且在时间上是永久的。通过改变Weber数和Froude数,我们计算出了许多分支解.我们还计算了负表面张力的水波。其中一些在其极限形式下被发现与欧拉的弹性线相同。(3)用涡方法数值计算欧拉方程。本文用涡方法计算了剪切流中的二维涡面。关于涡面运动的研究已有很多,但我们的研究是新的,因为我们研究了涡面与背景切变流之间的关系。少

项目成果

期刊论文数量(11)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
M. taniguchi and Y. Nishiura: "Stability and Characteristic wavelength of Planar interfaces in the large diffusion limit of the inhibitor" to appear in Proc. Roy. Soc. Edingburgh.
M. taniguchi 和 Y. Nishiura:“抑制剂大扩散极限中平面界面的稳定性和特征波长”出现在 Proc 中。
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    0
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今井仁司,石村直之,中村正彰: "磁気ベナ-ル問題のカオス" 日本物理学会学会誌. 50. 697-703 (1995)
Hitoshi Imai、Naoyuki Ishimura、Masaaki Nakamura:“磁贝纳德问题的混沌”日本物理学会杂志 50. 697-703 (1995)。
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    0
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H. Okamoto and M. Shoji: "Two Dimensional, Periodic, Capillary-Gravity Waves With Negative Surfase Tension" Proc. IUTAM Conf. Structure and Dynamics of Nonlinear Waves in Fluids. 363-369 (1995)
H. Okamoto 和 M. Shoji:“具有负表面张力的二维、周期性毛细管重力波”Proc。
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    0
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H. Imai, and et al.: "On Spectral Collocation Methods in Space and Time for Free Boundary Problems" Computational Mechanics '95 (Proc. of ICES '95). 1. 798-803 (1995)
H. Imai 等人:“自由边界问题的空间和时间频谱搭配方法”计算力学 95(Proc. of ICES 95)。
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    0
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  • 通讯作者:
Y. Nishiura, et al.: "Dynamics of inhibitory pulse-coupled oscillators" Applicable Analysis“Dynamical Systems and applications". 4. 549-562 (1995)
Y. Nishiura 等人:“抑制性脉冲耦合振荡器的动力学”适用分析“动态系统和应用”4. 549-562 (1995)。
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OKAMOTO Hisashi其他文献

OKAMOTO Hisashi的其他文献

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{{ truncateString('OKAMOTO Hisashi', 18)}}的其他基金

Applied Analysis on the Navier-Stokes Equations and Related Dynamical Systems
纳维-斯托克斯方程及相关动力系统的应用分析
  • 批准号:
    20244006
  • 财政年份:
    2008
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
A Study of Blow-up Problems and Singular Perturbation Problems arisingin Mathematical Fluid Mechanics
数学流体力学中的爆炸问题和奇异摄动问题的研究
  • 批准号:
    17204008
  • 财政年份:
    2005
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Applications of the dynamical systems theory and the singularity theory to mathematical fluid mechanics
动力系统理论和奇点理论在数学流体力学中的应用
  • 批准号:
    14204007
  • 财政年份:
    2002
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Application of the double exponential transform to integral transformations
双指数变换在积分变换中的应用
  • 批准号:
    11554002
  • 财政年份:
    1999
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Studies on singular perturbation problems in nonlinear mechanics
非线性力学奇异摄动问题的研究
  • 批准号:
    11304005
  • 财政年份:
    1999
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Mathematical Open Problems of the Navier-Stokes Equations
纳维-斯托克斯方程的数学开放问题
  • 批准号:
    09304023
  • 财政年份:
    1997
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
On the research and development of fast solvers arising in scientific computation
科学计算中快速求解器的研究与开发
  • 批准号:
    09554003
  • 财政年份:
    1997
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Mathematical analysis and numerical computation of nonlinear partial differential equations
非线性偏微分方程的数学分析与数值计算
  • 批准号:
    08454028
  • 财政年份:
    1996
  • 资助金额:
    $ 1.09万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

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干细胞数学模型的几何奇异摄动分析
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Phantom:一种分析宏观系统及其奇异摄动的拓扑方法
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    15K13532
  • 财政年份:
    2015
  • 资助金额:
    $ 1.09万
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    Grant-in-Aid for Challenging Exploratory Research
The structure theory of differential equations by the algebraic analysis of singular perturbation theory
奇异摄动理论的代数分析微分方程的结构理论
  • 批准号:
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Singular perturbation/bifurcation analysis of the cardiac sinoatrial node model in consideration of its heterogeneous structure and the study on the generation mechanism of synchronized oscillations
考虑异质结构的心脏窦房结模型奇异摄动/分岔分析及同步振荡产生机制研究
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