Numerical Methods for Hyperbolic Systems and Related Problems

双曲系统的数值方法及相关问题

• 批准号: 9704957
• 负责人: Shi Jin
• 金额: $ 7.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704957&HistoricalAwards=false
• 关键词: Numerical; Methods; Hyperbolic; Systems; Related

-------------------- Abstract ------------------------ DMS-9704957 PI: Shi Jin Title: Numerical Methods for Hyperbolic Systems and Related Problems I propose to study and design numerical methods for hyperbolic systems of conservation laws and related problems. The underlying physical problems arise from fluid dynamics, rarefied gas dynamics and wave propagation. I plan to work on three main projects: 1. the development of robust shock capturing methods for hyperbolic systems with relaxations, including kinetic equations; 2. the construction and study of relaxation approximations and relaxation schemes for viscous systems of conservations laws and Hamilton-Jacobi equations. 3. asymptotic and numerical study on wave propagation in random media. These projects if successfully carried out will provide attractive numerical methods that are able to simulate a wide variety of challenging physical and industrial problems. They also help to gain more understanding of the underlying physical phenomena. With the development of modern computers, scientific computation has been playing a central role in scientific investigation. The physical and industrial problems we study here arise in complex fluids, optics and materials, which can not be solved by other scientific tools. Nervetheless, numerical computation has been demonstrated to be an effective tool to obtain very good approximations to the solutions of these problems. Our goal, if met, will advance our ability to utilize modern computers to solve these problems of significant importance.

- - DMS-9704957 主要研究者：史进 题目：双曲型方程组的数值方法及相关问题 我建议研究和设计双曲守恒律方程组及相关问题的数值方法。 基本的物理问题来自于流体动力学、稀薄气体动力学和波的传播。 我计划在三个主要项目上工作：1。发展稳健的激波捕捉方法，用于松弛双曲系统，包括动力学方程; 2.建立和研究守恒律和哈密尔顿-雅可比方程的粘性系统的松弛近似和松弛方案。 3.随机介质中波传播的渐近性和数值研究 这些项目如果成功实施，将提供有吸引力的数值方法，能够模拟各种具有挑战性的物理和工业问题。它们还有助于更多地了解潜在的物理现象。 随着现代计算机技术的发展，科学计算在科学研究中的地位越来越重要。我们在这里研究的物理和工业问题出现在复杂的流体，光学和材料中，这些问题无法通过其他科学工具解决。 神经，数值计算已被证明是一个有效的工具，以获得很好的近似这些问题的解决方案。我们的目标如果实现，将提高我们利用现代计算机解决这些重要问题的能力。