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.

偏微分方程的非线性双曲系统出现在许多科学和工程应用中，其中波传播或传输现象很重要，从而产生冲击波等不连续解。 这些问题通常出现在异质介质中，其中材料参数变化并且在界面上可能不连续。 求解这些方程需要基于弱解数学理论的特殊技术。 研究人员之前开发了一种多维“波传播算法”，为解决此类问题提供了一个非常通用的框架。 这些高分辨率有限体积方法在开源Clawpack软件包中实现，使得研究各种现象的学生和研究人员能够使用高分辨率方法和自适应网格细化技术。 这些算法和软件正在与这些领域的研究人员合作进一步开发，并应用于解决各种问题，特别是在地球物理流和波传播方面。 最近开发了专门用于模拟海啸传播和淹没的 Clawpack 软件 (GeoClaw) 版本，并且正在扩展以处理涉及地形流动的各种相关问题。 对具体应用的研究正在推动新的数学模型和有限体积算法的开发，以更准确、鲁棒地对这些极端流进行建模。这项工作的重点是开发用于模拟与预测相关的地球物理流和波浪传播问题的计算模型和减轻自然灾害。 研究人员和同事多年来一直致力于海啸建模，并开发了一个软件包，该软件包既可用于海啸现象的科学研究，也可用于为太平洋西北部特定社区绘制淹没图。除了继续这项工作之外，该软件还被扩展到对其他相关现象进行建模，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：灾难性溃坝造成的洪水、卡特里娜等飓风引发的风暴潮、海底山体滑坡引发的海啸，以及雷尼尔山等火山喷发造成的洪水和泥石流。冰川。 该研究人员和他的学生正在与美国地质勘探局喀斯喀特火山观测站以及其他几个研究中心的地球科学研究人员合作，开展与该软件开发相关的科学和减灾项目。 用于地震建模的新算法也正在开发中，并将其应用于圣海伦斯火山的地震研究，以帮助确定未来火山喷发的风险。 该研究人员通过接待访问研究生和科学家，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培训。 研究人员还在其他地方教授了几门短期课程，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提高其作为免费教育工具的可用性，供出现类似问题的许多领域的学生和研究人员使用。