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Filtering Strategies for Radiation Transport Equations

辐射传输方程的过滤策略

基本信息

批准号：
1913277
负责人：
Cory Hauck
金额：
$ 10万
依托单位：
University of Tennessee Knoxville
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913277&HistoricalAwards=false
关键词：
Filtering Strategies Radiation Transport Equations

项目摘要

Radiation is the fundamental mechanism of energy exchange in many physical processes and in the operations of devices for energy and medical applications. In addition, radiation is used as an experimental tool to explore the basic structure of materials. Improved mathematical algorithms and analysis of radiation transport equations will enable important advances in these areas. More generally, these equations serve as a mathematical prototype for a variety of kinetic models that are used to describe dilute gases, plasmas, and multiphase flows. They also demonstrate the fundamental multi-scale nature of driven-dissipative systems. Historically, radiation transport equations have been a driver for many fundamental developments in basic numerical methods research. That trend will continue with this project. On the education side, this project will support and train a student for a career in computational mathematics. This includes support for travel to attend conferences and workshops in order to share research and provide networking opportunities. This grant will support 1 graduate student per year for 3 years.This project seeks to address one of the fundamental challenges in the kinetic description of radiation: the onset of ray effects in the discrete ordinates approximation of the radiation transport equation. The approach proposed here is based on the use of filters, which smooth the mathematical solution of these equations in a specified manner, in order to improve the fidelity of numerical solutions computed with under-resolved meshes. The project will advance numerical methods for radiation transport equations and, more generally, for kinetic equations and complex multi-physics systems. It will enable to the development of spectral approximation techniques and the synthesis of such techniques into the solution of large scale equations. It will introduce analysis tools to better understand and improve the accuracy of numerical approximation that are under-resolved, and it will establish connections with other types of filtering and sub-scale modeling approaches that are currently used in the simulation of fluids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

辐射是许多物理过程以及能源和医疗应用设备操作中能量交换的基本机制。此外，辐射被用作探索材料基本结构的实验工具。改进的数学算法和对辐射输运方程的分析将使这些领域取得重要进展。更一般地说，这些方程作为用于描述稀释气体、等离子体和多相流的各种动力学模型的数学原型。它们还证明了驱动耗散系统的基本多尺度性质。从历史上看，辐射输运方程一直是基本数值方法研究中许多基本发展的驱动力。这一趋势将在该项目中继续下去。在教育方面，该项目将支持和培训学生从事计算数学。这包括为参加会议和讲习班提供差旅支助，以便分享研究成果和提供建立联系的机会。该项目旨在解决辐射动力学描述中的一个基本挑战：辐射输运方程离散坐标近似中射线效应的开始。这里提出的方法是基于使用的过滤器，平滑这些方程的数学解以指定的方式，以提高与欠解析网格计算的数值解的保真度。该项目将推进辐射传输方程的数值方法，更一般地说，动力学方程和复杂的多物理系统。它将使谱近似技术的发展和这种技术的合成到大规模方程的解决方案。它将引入分析工具，以更好地理解和提高数值近似的准确性，这是欠解决，它将建立与其他类型的过滤和子尺度建模方法，目前在流体模拟中使用的连接。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。