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.

双曲守恒定律系统出现在许多对质量、动量和能量等物理量守恒进行建模的问题中。这些方程通常必须通过近似数值方法来求解。 数据和/或解决方案（例如冲击波）的不连续性导致开发准确和稳定的方法的困难。该提案涉及高分辨率方法的开发及其作为可广泛用于解决许多不同领域中出现的问题的软件的实现。 P.I.一直积极参与开发多维双曲系统的 CLAWPACK 和 AMRCLAW 软件。 该软件免费提供，允许研究各种现象的学生和研究人员使用高分辨率方法和自适应网格细化技术。 该软件将被进一步开发并用于探索科学和工程中的许多特定应用。 一种应用涉及计算异质介质中的声波或弹性波。 例如，此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，其中有兴趣模拟天文学家可能很快就能检测到的引力波。这可以通过使用爱因斯坦方程的双曲公式来完成。