Accurate Prediction of Fluid Motion

流体运动的准确预测

基本信息

批准号：
1817542
负责人：
William Layton
金额：
$ 31.95万
依托单位：
University of Pittsburgh
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1817542&HistoricalAwards=false
关键词：
Accurate Prediction Fluid Motion

项目摘要

Accurate prediction of fluid motion and materials thereby transported is essential for many critical engineering and scientific applications. As two examples, flow predictions are key to limiting damage of hurricanes to human life and to the economy (the latter estimated to be hundreds of billions of dollars in 2017) and to energy efficiency optimization (85% of US energy is generated by combustion for which accurate simulation of turbulent mixing is critical). Unfortunately, fundamental barriers to accurate, efficient and reliable prediction of fluid flow exist in these and other applications addressed in the proposed research. Accurate prediction with uncertain data requires reliable and efficient ensemble simulations. The cost of current methods limits prediction accuracy by limiting ensemble sizes. Further improvement requires new computational tools with a fundamental decrease in simulation cost and memory requirements. Algorithms which address these needs will be developed in this project. Artificial compression methods are by far the most efficient per time step but little used due to low time accuracy, restrictive time step conditions, stability problems, ill-conditioning and nonphysical acoustic waves. Their resolution will resurrect artificial compression methods into accurate, reliable and efficient methods for the prediction of fluid motion, expanding ensemble simulations and coupled flow prediction markedly beyond their current limitations. Artificial compression methods exhibit parasitic pressure waves that become resonant at higher Reynolds numbers. This research will develop a method dependent Lighthill theory of flow generated sound and apply it to design time filters to suppress parasitic acoustics. Time accuracy will be achieved by development of a new family of variable step, variable order methods. Variable step, variable order method have proven to be the most efficient, accurate and reliable methods to solve smaller systems of ordinary differential equations. However, previous variable step, variable order methods have limited penetration into computational fluid dynamics practice due partially to their implementation complexity and increased cost per step. The new methods have (to leading order) the same cognitive and computational complexity as the fully implicit method. Uncoupling of velocity and pressure in artificial compression methods introduces an extra grad-div term in the velocity solve, decreasing sparsity and increasing ill conditioning. Thus, the efficiency of artificial compression methods is lost with increased storage and solver cost per step. The research will develop a new realization, modular Grad-Div, reducing storage and turnaround time by a factor of 30 in preliminary tests. While each development has independent interest, they will be integrated into an ensemble, artificial compression method and tested on problems of compelling interest. The proposed research develops expertise of PhD students in analysis, numerical analysis and application areas while working on compelling mathematics problems of broad impact advancing the accurate prediction of fluid motion. It is carefully integrated with the development of the PI's PhD students and undergraduate researchers. Within the project, each PhD student can develop their own research agenda and collaborate at the points of contact among the research problems.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.

对于许多关键的工程和科学应用来说，准确预测流体运动和材料是必不可少的。作为两个例子，流动预测是将飓风损害损害到人类生命和经济的关键（后者估计在2017年为数千亿美元）和能源效率优化（85％的美国能源是由燃烧产生的，这些能源的准确模拟对湍流混合至关重要）。不幸的是，在拟议的研究中涉及的这些和其他应用中，存在准确，高效和可靠预测流体流动的基本障碍。不确定数据的准确预测需要可靠，有效的集合模拟。当前方法的成本通过限制整体尺寸限制了预测准确性。进一步的改进需要新的计算工具，并减少模拟成本和内存需求。满足这些需求的算法将在此项目中开发。人工压缩方法是迄今为止每次步骤最有效的，但由于时间准确性，限制性时间步骤条件，稳定性问题，不良条件和非物理声波而几乎没有使用。他们的分辨率将使人工压缩方法复活到准确，可靠和有效的方法中，以预测流体运动，扩展集合模拟和耦合流量预测，明显超出了当前局限性。人工压缩方法表现出寄生压力波在较高的雷诺数下变为共鸣。这项研究将开发一种依赖于方法的流动声音理论，并将其应用于设计时间过滤器以抑制寄生声。时间准确性将通过开发新的可变步骤，可变顺序方法来实现。可变步骤，可变顺序方法已被证明是解决较小的普通微分方程系统的最有效，最准确和可靠的方法。但是，以前的变量步骤，可变顺序方法有限地渗透到计算流体动力学实践中，部分原因是它们的实现复杂性和每步增加的成本增加。新方法（领导顺序）与完全隐式方法具有相同的认知和计算复杂性。人工压缩方法中速度和压力的解耦合在速度求解中引入了一个额外的毕业阶段，从而降低了稀疏性并增加了不良条件。因此，人工压缩方法的效率随着每步的存储和求解器成本的增加而丢失。这项研究将在初步测试中开发新的实现，模块化的GRAD-DIV，将存储时间和周转时间减少30倍。尽管每个开发都具有独立的兴趣，但它们将被整合到一种合奏，人工压缩的方法中，并根据引人注目的兴趣问题进行了测试。拟议的研究开发了博士生在分析，数值分析和应用领域方面的专业知识，同时致力于引人入胜的数学问题，这些问题广泛影响，推进了流体运动的准确预测。它与PI博士学位学生和本科研究人员的成长进行了仔细的整合。在该项目中，每个博士生都可以在研究问题之间建立自己的研究议程并在联系点上进行合作。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。