Mathematical Sciences: Development and Application of Advanced Numerical Methods to Outstanding Problems in Experimental Shock Waves Geophysics

数学科学：先进数值方法在实验冲击波地球物理突出问题中的发展和应用

• 批准号: 9316529
• 负责人: Elbridge Puckett
• 金额: $ 3.13万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9316529&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Development; Application; Advanced

9316529 Puckett The central focus of this research is the design and development of a numerical method for modeling complex nonlinear wave interactions in condensed matter at high pressures and temperatures. This numerical method is based on a collection of numerical algorithms that have been used with great success to model shock wave refraction in gases. The extension of these algorithms to problems involving condensed matter involves modifications to accommodate a realistic condensed phase equation of state, the inclusion of realistic constitutive relations for modeling the strength effects in solids, and the development of robust algorithms for describing vacuum states. It is also expected that a better understanding of wave phenomena in condensed matter gained from the numerical computations will contribute to the understanding of the wave structure that characterize solutions of more general systems of hyperbolic conservation laws than those that govern the flow of gases, and thus aid in the mathematical analysis of these equations. This work includes extensive experimental validation of numerical results. This project is concerned with developing advanced computational methods, based on methods originally developed to address aerospace and defense problems, and applying the new methods to important problems in the geosciences. These new computational methods are used to design an improved experimental technique for determining sound speeds in geophysical materials. Accurate knowledge of sound speeds is important for the correct interpretation of seismic data. The new computational methods are also used to model the effect the impact of a large comet or asteroid would have on the Earth. Such impacts have been proposed to explain the mass extinction of species (e.g., dinosaurs) and may have been responsible for the periodic loss of the Earth's early atmosphere. The specific nature of such large shocks, and the consequences they might hav e for the atmosphere and the Earth's magnetic field, are addressed. The use of the computational methods to model explosive volcanic eruptions is also investigated. The computational methods developed in this research will have a wide range of applications in other areas of science and technology.

9316529 Puckett这项研究的主要重点是设计和开发一种数值方法，用于在高压和温度下对凝结物质中复杂的非线性波相互作用进行建模。 这种数值方法基于数​​值算法的集合，这些算法已成功地用于模拟气体中的冲击波折射。 将这些算法扩展到涉及冷凝物质的问题涉及修改以适应现实的凝结相位方程，其中包含用于建模固体强度效应的现实本质关系以及用于描述真空状态的鲁棒算法的发展。 还可以预期，从数值计算中获得的凝结物质中的波浪现象的更好理解将有助于对波浪结构的理解，而波浪结构比控制气体流动的人的多光纤保守法更通用的解决方案，从而有助于对这些方程的数学分析。 这项工作包括对数值结果的广泛实验验证。 该项目涉及开发基于最初用于解决航空航天和防御问题的方法，并将新方法应用于地球科学中的重要问题。 这些新的计算方法用于设计改进的实验技术，用于确定地球物理材料中的声速。 准确的声速知识对于正确解释地震数据很重要。 新的计算方法还用于模拟大型彗星或小行星对地球的影响。 已经提出了这样的影响来解释物种的大规模灭绝（例如恐龙），并可能导致了地球早期大气的周期性丧失。 解决了如此大的冲击的特定性质，以及它们可能对大气和地球磁场的后果。 还研究了计算方法对爆炸性火山喷发进行建模的使用。 这项研究中开发的计算方法将在其他科学技术领域中具有广泛的应用。