Finite Volume Methods and Software for Hyperbolic Problems

双曲问题的有限体积方法和软件

• 批准号: 0914942
• 负责人: Randall LeVeque
• 金额: $ 49.02万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0914942&HistoricalAwards=false
• 关键词: Finite; Volume; Methods; Software; Hyperbolic

Nonlinear hyperbolic systems of partial differential equations arise in many scientific and engineering applications where wave propagation or transport phenomena are important, giving rise to discontinuous solutions such as shock waves. Often the problems are posed in heterogeneous media in which the material parameters vary and may be discontinuous across interfaces. Solving these equations requires special techniques based on the mathematical theory of weak solutions. The investigator has previously developed a multidimensional "wave-propagation algorithm" that yields a very general framework for solving such problems. These high-resolution finite volume methods are implemented in the open source Clawpack software package, which allows students and researchers studying a wide range of phenomena to use the technology of high-resolution methods and adaptive mesh refinement. These algorithms and the software are being further developed and brought to bear on a variety of problems, particularly in geophysical flow and wave propagation, in collaboration with researchers in these fields. A version of the Clawpack software (GeoClaw) specifically tuned to model tsunami propagation and innundation has recently been developed and is being extended to handle various related problems involving flow over topography. The study of specific applications is motivating the development of new mathematical models and finite volume algorithms to more accurately and robustly model these extreme flows.This work focuses on the development of computational models for simulating geophysical flow and wave propagation problems that are related to the prediction and mitigation of natural disasters. The investigator and coworkers been working on tsunami modeling for several years and have developed a software package that has been used both for scientific research on tsunami phenomena and for the preparation of innundation maps for specific communities in the Pacific Northwest. In addition to continuing this work, the software is being extended to model other related phenomena, which often requires the development of new mathematical models and computational algorithms. Applications being studied include: flooding due to catastrophic dam breaks, storm surges generated by hurricanes such as Katrina, tsunamis generated by submarine landslides, and the flooding and debris flows that would result from the eruption of volcanoes such as Mt. Rainier that are covered with glaciers. The investigator and his students are working with researchers in earth sciences, at the USGS Cascades Volcano Observatory, and at several other research centers on scientific and hazard mitigation projects related to this software development. New algorithms for modeling earthquakes are also being developed and applied to the study of tremors at Mount St. Helens in order to help determine the risk of future eruptions. The investigator is actively involved in training students and postdoctoral fellows at the University of Washington as well as at other institutions by hosting visiting graduate students and scientists. The investigator has also taught several short courses elsewhere and has developed lecture notes, textbooks, software, and other educational material based on this research. The software enhancements under way will further improve its usability as a freely-available educational tool for students and researchers in many fields where similar problems arise.

在许多科学和工程应用中出现了部分微分方程的非线性双曲系统，在这些科学和工程应用中，波传播或运输现象很重要，从而引起了不连续的解决方案，例如冲击波。 这些问题通常在异质介质中构成，其中材料参数变化，并且在界面之间可能是不连续的。 解决这些方程式需要基于弱解决方案的数学理论的特殊技术。 研究人员以前已经开发了一种多维“波传播算法”，该算法产生了解决此类问题的非常通用的框架。 这些高分辨率有限的体积方法是在开源ClawPack软件包中实现的，该软件包允许研究广泛现象的学生和研究人员使用高分辨率方法和自适应网格改进的技术。 这些算法和软件正在进一步开发，并带来各种问题，尤其是在地球物理流和波传播方面，与这些领域的研究人员合作。 最近已经开发了针对海啸传播和Innundation模型的Clawpack软件（GeoClaw）版本，并正在扩展以处理涉及地形上流动流量的各种相关问题。 对特定应用的研究是激发新的数学模型和有限体积算法的开发，以更准确，更稳定地对这些极端流进行建模。这项工作重点是开发用于模拟与自然灾害预测和缓解自然灾害有关的地球物理流量和波浪传播问题的计算模型。 研究人员和同事从事海啸建模工作了几年，并开发了一个软件包，该软件包既用于海啸现象的科学研究，又用于为西北太平洋地区的特定社区制定Innundation图。除了继续这项工作外，该软件还扩展到建模其他相关现象，这通常需要开发新的数学模型和计算算法。 正在研究的应用包括：由于灾难性的大坝断裂，诸如卡特里娜飓风，海底山体滑坡产生的海啸以及洪水和碎屑流造成的飓风所产生的洪水潮流，这些洪水和碎屑流由火山爆发，例如覆盖着冰川的雷尼尔山。 研究人员和他的学生正在与地球科学研究人员，USGS Cascades火山天文台以及其他一些与该软件开发有关的科学和危害缓解项目中心合作。 还开发了用于建模地震的新算法，并将其应用于圣海伦斯山的震颤研究，以帮助确定未来喷发的风险。 调查人员通过主持访客的研究生和科学家，积极参与华盛顿大学以及其他机构的学生和博士后研究员的参与。 研究人员还在其他地方教授了几门简短的课程，并根据这项研究开发了讲义，教科书，软件和其他教育材料。 正在进行的软件增强功能将进一步改善其作为一种自由提供的教育工具，适用于出现类似问题的许多领域的学生和研究人员。