Stability of compressible flow in real media

实际介质中可压缩流的稳定性

基本信息

  • 批准号:
    0300487
  • 负责人:
  • 金额:
    $ 54.31万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2003
  • 资助国家:
    美国
  • 起止时间:
    2003-07-01 至 2009-06-30
  • 项目状态:
    已结题

项目摘要

PI: Kevin Zumbrun, Indiana UniversityDMS-0300487ABSTRACTThe principal investigator proposes to study stability of compressible flows in ``real'' media featuring often-neglected effects such as viscosity, heat conduction, electromagneticdynamics, phase-transition, non-thermoequilibrium, and chemical reaction, in the physically interesting (usually large-amplitude) regime where transition to instability may be expected to occur: for example, multidimensional stability of strong shock and detonation waves, or of classical shear flows. This involves interesting and nonstandard issues in singular perturbation theory, dynamical systems and bifurcation, spectral theory of linear operators, and nonlinear partial differential equations, and should result in the development of new mathematical tools of general application. The ultimate physical goal is an understanding of stability phenomena that is both more complete and more precise than can be obtained within simplified models: on the one hand resolving philosophical puzzles at the level of mathematical foundations and on the other yielding quantitative predictions at the level of practical application. The plan of attack centers around Evans function and related spectral techniques developed recently in the study of stability of viscous shock fronts.The stability of regular flow patterns is an old and central topic in fluid, gas, and plasma dynamics, deciding which (stable) patterns will typically be observed, and which (unstable) are only mathematical and not physically observable solutions. The transition from stability to instability is of particular importance, since it usually signals the arising of alternative, more complicated flow patterns close to the original (now unstable) one- this is a way to understand complicated flows by the study of simpler and better-understood ones. Despite a large and well-known body of theory on this subject, dating back to the late 1800's, there are still many aspects that are poorly understood, particularly for compressive, viscous, or reacting flows. Here, we propose to study several of these issues arising in compressible gas and plasma dynamics, and in combustion, applications in which such usually neglected effects are of considerable practical importance. Our goal is, by including these mathematically problematic terms, to move existing theory from the qualitative to the quantitative regime, obtaining new information of use to practitioners at the same time that we advance the mathematical theory. The planned activities have both analytic and numerical components, and involve collaboration with domestic and foreign colleagues and with current and former graduate students and post doctorates. This may be expected to strengthen and extend existing networks of cooperation across field and institution, and to aid in training of graduate and postdoctoral students. The ultimate aim of these investigations, of quantitative predictions of transition to instability, would, if achieved, be of direct and practical use at the level of engineering, in chemical, manufacturing, and other processes.
Pi:Kevin Zumbrun,印第安纳大学DMS-0300487ABSTRACT首席研究员建议研究具有粘性、热传导、电磁动力学、相变、非热平衡和化学反应等经常被忽略的影响的“真实”介质中可压缩流动的稳定性,在可能发生向不稳定性转变的物理有趣(通常是大幅度)区域:例如,强激波和爆轰波的多维稳定性,或经典剪切流的多维稳定性。这涉及到奇异摄动理论、动力系统和分叉、线性算子的谱理论和非线性偏微分方程中有趣的和非标准的问题,并应导致新的普遍应用的数学工具的发展。最终的物理目标是对稳定性现象的理解,这比在简化模型中可以获得的更完整和更精确:一方面在数学基础层面上解决哲学难题,另一方面在实际应用层面上产生定量预测。在粘性激波前锋稳定性的研究中,攻击计划围绕着Evans函数和相关的谱技术发展起来。规则流型的稳定性是流体、气体和等离子体动力学中一个古老的中心话题,它决定了哪些(稳定的)流型将被典型地观察到,而哪些(不稳定的)流型只是数学上的而不是物理上可观察到的解。从稳定到不稳定的转变是特别重要的,因为它通常标志着接近原始(现在不稳定)的替代的、更复杂的流型的出现--这是通过研究更简单和更好地理解的流型来理解复杂流动的一种方法。尽管早在1800年末的S时期,关于这一问题的大量理论就已经广为人知,但仍然有许多方面是鲜为人知的,特别是关于压缩、粘性或反应流动。在这里,我们建议研究在可压缩气体和等离子体动力学中出现的几个问题,以及在燃烧中的应用,在这些应用中,这种通常被忽略的影响具有相当重要的实际意义。我们的目标是,通过纳入这些数学上有问题的术语,将现有的理论从定性系统转移到定量系统,在我们推进数学理论的同时,获得对实践者有用的新信息。计划的活动既包括分析部分,也包括数字部分,并涉及与国内外同事以及与现任和前任研究生和博士后的合作。预计这将加强和扩大现有的跨领域和跨机构的合作网络,并有助于培养研究生和博士后。这些研究的最终目的,即对过渡到不稳定的定量预测,如果实现,将在工程、化学、制造和其他过程中具有直接和实际的用途。

项目成果

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Kevin Zumbrun其他文献

Pointwise Estimates and Stability for Dispersive–Diffusive Shock Waves
Stability of viscous detonations for Majda’s model
  • DOI:
    10.1016/j.physd.2013.06.001
  • 发表时间:
    2013-09-15
  • 期刊:
  • 影响因子:
  • 作者:
    Jeffrey Humpherys;Gregory Lyng;Kevin Zumbrun
  • 通讯作者:
    Kevin Zumbrun
Erratum to: Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions
Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation
  • DOI:
    10.1007/s00285-010-0379-z
  • 发表时间:
    2010-11-13
  • 期刊:
  • 影响因子:
    2.300
  • 作者:
    Shantia Yarahmadian;Blake Barker;Kevin Zumbrun;Sidney L. Shaw
  • 通讯作者:
    Sidney L. Shaw
Stabilité de profils de choc pour une équation dispersive
  • DOI:
    10.1016/s0764-4442(97)84592-2
  • 发表时间:
    1997-07-01
  • 期刊:
  • 影响因子:
  • 作者:
    Mohamed Khodja;Kevin Zumbrun
  • 通讯作者:
    Kevin Zumbrun

Kevin Zumbrun的其他文献

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{{ truncateString('Kevin Zumbrun', 18)}}的其他基金

Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow
倾斜浅水流的多维和涡度效应
  • 批准号:
    2206105
  • 财政年份:
    2022
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Standard Grant
Frontiers in Modulation, Dynamics, and Pattern Formation for Hyperbolic, Kinetic, and Convection-Reaction-Diffusion Systems
双曲、动力学和对流-反应-扩散系统的调制、动力学和图案形成前沿
  • 批准号:
    2154387
  • 财政年份:
    2022
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Standard Grant
New Tools in the Study of Wave Propagation: Dynamical Systems for Kinetic Equations, Inviscid Limits for Modulated Periodic Waves, and Rigorous Numerical Stability Analysis
波传播研究的新工具:运动方程的动力系统、调制周期波的无粘极限以及严格的数值稳定性分析
  • 批准号:
    1700279
  • 财政年份:
    2017
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Continuing Grant
New problems in continuum mechanics: asymptotic eigenvalue distributions, rigorous numerical stability analysis and weakly nonlinear asymptotics in periodic thin film flow
连续介质力学的新问题:周期性薄膜流中的渐近特征值分布、严格的数值稳定性分析和弱非线性渐近
  • 批准号:
    1400555
  • 财政年份:
    2014
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Continuing Grant
Stability and dynamics of shock, detonation, and boundary layers
冲击、爆炸和边界层的稳定性和动力学
  • 批准号:
    0801745
  • 财政年份:
    2008
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Continuing Grant
Laser-Matter Interactions and Highly Nonlinear Geometrical Optics; Dynamics of Reacting Flows
激光与物质相互作用和高度非线性几何光学;
  • 批准号:
    0505780
  • 财政年份:
    2005
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Standard Grant
Hydrodynamic Stability in viscous, compressible flow
粘性可压缩流中的流体动力学稳定性
  • 批准号:
    0070765
  • 财政年份:
    2000
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Continuing Grant
I. Stability of Waves in Viscous Conservation Laws. II. Phase Transitions and Minimal Surfaces
I. 粘性守恒定律中波的稳定性。
  • 批准号:
    9706842
  • 财政年份:
    1997
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems in Conservation Laws
数学科学:守恒定律问题
  • 批准号:
    9404384
  • 财政年份:
    1994
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
  • 批准号:
    9107990
  • 财政年份:
    1991
  • 资助金额:
    $ 54.31万
  • 项目类别:
    Fellowship Award

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