Numerical Methods for Conservation Laws

守恒定律的数值方法

• 批准号: 9803442
• 负责人: Randall LeVeque
• 金额: $ 24.45万
• 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: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803442&HistoricalAwards=false
• 关键词: Numerical; Methods; Conservation; Laws

Hyperbolic systems of conservation laws arise in many problems where theconservation of physical quantities such a mass, momentum, and energy aremodeled. These equations must typically be solved by approximate numericalmethods. Discontinuities in the data and/or solution (e.g. shock waves)cause difficulties in developing accurate and stable methods. This proposal concerns the development of high-resolution methods and theirimplementation as software that can be widely used in solving problemsthat arise in many different fields. The P.I. has been activelyinvolved in developing the CLAWPACK and AMRCLAW software formulti-dimensional hyperbolic systems. This software is freelyavailable and allows students and researchers studying a wide range ofphenomena to use the technology of high-resolution methods and adaptivemesh refinement. This software will be further developed and used toexplore a number of particular applications in science andengineering. One application concerns computing acoustic or elasticwaves in heterogeneous media. Such problems often arise in geophysicsand materials science, for example. Another application is tonumerical relativity, where there is interest in simulatinggravitational waves that may soon be detectable by astronomers.This can be accomplished by using a hyperbolic formulation of the Einsteinequations.

守恒定律的双曲系统出现在许多物理量守恒的问题中，比如质量、动量和能量。这些方程通常必须用近似数值方法来求解。数据和/或解决方案（如冲击波）的不连续性导致开发准确和稳定的方法的困难。本提案涉及高分辨率方法的发展及其作为软件的实现，可广泛用于解决许多不同领域出现的问题。P.I.一直积极参与开发CLAWPACK和AMRCLAW软件公式维双曲系统。该软件是免费提供的，允许学生和研究人员研究各种现象，使用高分辨率方法和自适应网格细化技术。该软件将进一步开发，并用于探索科学和工程中的一些特定应用。其中一个应用涉及计算异质介质中的声波或弹性波。例如，这类问题经常出现在地球物理学和材料科学中。另一个应用是数值相对论，人们对模拟可能很快被天文学家探测到的引力波很感兴趣。这可以通过使用爱因斯坦方程的双曲公式来实现。