Optimization-Based Moment Models for Multiscale Kinetic Equations

基于优化的多尺度动力学方程力矩模型

• 批准号: 1217170
• 负责人: Cory Hauck
• 金额: $ 63.57万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1217170&HistoricalAwards=false
• 关键词: Optimization; Based; Moment; Models; Multiscale

The focus of this proposal is the design, analysis, and implementation of optimization-based moment models for solving collisional kinetic equations with diffusive limits. In the field of computational kinetic theory, moment methods are an effective, yet highly complex tool for discretizing kinetic equations and capturing multiscale phenomena. They reduce the kinetic description of a many-particle system to a set of partial differential equations for velocity averages of the kinetic distribution. Optimization-based moment models are derived via the solution of a physically motivated, convex optimization problem that enforces important properties of the underlying kinetic equation. The driving application for this effort will be neutrino transport in core-collapse supernovae simulations, where the computational requirements for a fully resolved kinetic simulation are well beyond the capabilities of the largest supercomputers.The design of tractable reduced models for complex systems is both timely and important. Indeed, for a broad range of physical, biological, and social science problems, methodologies are needed to extract relevant macroscopic features from intractable amounts of microscopic data. In this context, the design and implementation of moment models is an important part of understanding the behavior of many-particle systems, for which direct numerical simulation is not possible. Important examples include rarefied gases, radiation, and charged-particle transport---all of which play critical roles in advanced energy and technology applications of national interest. Thus, among other things, the project will provide a rewarding and relevant research experience to students and postdocs.

本建议的重点是设计，分析和实施的优化为基础的时刻模型求解碰撞动力学方程的扩散限制。在计算动力学理论领域，矩量法是一种有效的，但高度复杂的工具，用于离散动力学方程和捕捉多尺度现象。他们减少了动力学描述的多粒子系统的一组偏微分方程的平均速度的动力学分布。基于优化的力矩模型是通过解决一个物理激励的凸优化问题来推导的，该问题强制执行基本动力学方程的重要属性。这一努力的驱动应用将是核心坍缩超新星模拟中的中微子输运，其中完全解析动力学模拟的计算要求远远超出了最大的超级计算机的能力，为复杂系统设计易于处理的简化模型既及时又重要。事实上，对于广泛的物理，生物和社会科学问题，需要从大量难以处理的微观数据中提取相关的宏观特征的方法。 在这种情况下，矩模型的设计和实现是理解多粒子系统行为的重要组成部分，直接数值模拟是不可能的。 重要的例子包括稀薄气体，辐射和带电粒子传输-所有这些都在国家利益的先进能源和技术应用中发挥着关键作用。 因此，除其他外，该项目将为学生和博士后提供有益的和相关的研究经验。