Construction and Physicality of Compressible Euler Flows

可压缩欧拉流的构造和物理性

基本信息

批准号：
1813283
负责人：
Helge Jenssen
金额：
$ 32万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-15 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1813283&HistoricalAwards=false
关键词：
Construction Physicality Compressible Euler Flows

项目摘要

This project aims at narrowing the gap between practical applications of fluid dynamics and its theoretical underpinnings through a better understanding of the range of validity of the theoretical models. It is particularly concerned with compressible flows far from equilibrium, a regime of relevance in many applications such as high-speed flight, combustion, implosions, and inertial confinement fusion. Even for standard models little is known rigorously about their range of validity. This effort highlights the critical role of theoretical insights in hydrodynamics. Such understanding goes hand in hand with the computational effort to solve the equations of gas dynamics. One such line of research studies imploding spherical shock waves, now induced and controlled via powerful lasers. Analytic results are important for both aspects: they can provide estimates for non-observable quantities and provide exact solutions that can be used to benchmark numerical codes. This project focuses on methods that provide information beyond abstract mathematical results, thereby helping to evaluate the relevance and limits of models routinely used in practice.This project addresses fundamental, long standing open problems for nonlinear equations describing compressible fluid flow. The overarching goals are to establish existence of possibly singular flows far from equilibrium, and to use such solutions to delimit the range of validity of the standard compressible Euler equations. The focus is on methods with predictive power beyond abstract existence results. The project seeks results that will extend the current near-equilibrium theory in one space dimension, and apply also to radial solutions with collapsing shocks and cavities. The project is primarily motivated by the compressible Euler system, for which many fundamental questions remain open. The methods utilized should give a description of local and global solution behavior, such as local wave interactions and asymptotic behavior, and provide useful insights for the design of reliable computational tools. Emphasis is placed on understanding the role of zero-pressure regions, due either to vanishing temperatures or to vanishing densities (vacuums). The issues considered appear to be essential road blocks that must be overcome to gain a proper understanding of non-linear phenomena in compressible flows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在通过更好地理解理论模型的有效性范围，从而缩小流体动力学的实际应用与其理论基础之间的差异。它特别关注可压缩流远非平衡，这是许多应用中相关性的制度，例如高速飞行，燃烧，内爆和惯性限制融合。即使对于标准模型，也很少知道它们的有效性范围。这项工作突出了理论见解在流体动力学中的关键作用。这种理解与解决气体动力学方程的计算工作汇总。一项这样的研究线研究爆炸了球形冲击波，现在通过强大的激光诱导和控制。分析结果对于这两个方面都很重要：它们可以提供不可观察数量的估计值，并提供可用于基准数值代码的精确解决方案。该项目着重于提供超出抽象数学结果的信息的方法，从而有助于评估通常在实践中使用的模型的相关性和限制。本项目解决了描述可压缩流体流的非线性方程的基本，长期存在的开放问题。总体目标是建立可能远离平衡的奇异流，并使用此类解决方案来界定标准可压缩欧拉方程的有效性范围。重点是超出抽象存在结果的预测能力的方法。该项目寻求结果，将在一个空间维度上扩展当前的近平衡理论，并应用于带有冲击和空腔崩溃的径向溶液。该项目主要是由可压缩的欧拉系统（Euler System）进行的，为此，许多基本问题仍然开放。所使用的方法应对本地和全局解决方案行为进行描述，例如局部波浪相互作用和渐近行为，并为设计可靠的计算工具设计有用的见解。重点放在理解零压区域的作用上，这是由于温度消失或消失的密度（真空）。被认为是必不可少的路障，必须克服这些问题，以便在可压缩流中正确理解非线性现象。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评估评估来获得支持的。