Analysis and computation of nonlinear hyperbolic problems

非线性双曲问题的分析与计算

• 批准号: 298418-2009
• 负责人: Laforest, Marc
• 金额: $ 1.17万
• 依托单位: École Polytechnique de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=480739
• 关键词: Analysis; computation; nonlinear; hyperbolic; problems

Conservation laws are continuum models for many applications such as nonlinear elasticity, shock waves in general relativity and workflow in factories, but, historically they were primarily studied as models of compressible fluid flow. As continuum models, nonlinear hyperbolic conservation laws occur as scaling limits of molecular, kinetic (statistical) and higher-order models. Invariably, the resulting models are unstable and some of the physics lost in the scaling needs to be re-introduced, typically with an entropy condition, a kinetic relation and possibly additional closures.

守恒定律是许多应用的连续模型，例如非线性弹性、广义相对论中的冲击波和工厂工作流程，但历史上它们主要作为可压缩流体流动模型进行研究。作为连续介质模型，非线性双曲守恒定律作为分子、动力学（统计）和高阶模型的标度极限出现。所得到的模型总是不稳定，并且需要重新引入在缩放中丢失的一些物理原理，通常具有熵条件、动力学关系和可能的附加闭包。