Micro-Macro Decomposition Numerical Schemes for Multiscale Simulation of Plasma

等离子体多尺度模拟的微观-宏观分解数值方案

• 批准号: 1620128
• 负责人: James Rossmanith
• 金额: $ 19.6万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620128&HistoricalAwards=false
• 关键词: Micro; Macro; Decomposition; Numerical; Schemes

Plasma physics is the study of the dynamics of ionized gases. Because plasma, often referred to as the fourth state of matter, is the most abundant form of ordinary matter in the universe, there exist many important application problems for which an understanding of the plasma dynamics is critical. Some examples of these applications include understanding the dynamics of stars, the affect of the solar wind on the Earth's magnetosphere, the dynamics of magnetically confined fusion devices, and the dynamics of laser-plasma devices that could be used in medical imaging applications. The objective of this research is to develop highly accurate and efficient computational tools for simulating the dynamics of the electrons (negatively charged particles) and the ions (positively charged particles) that constitute the plasma of interest. This research aims to develop novel computational techniques based on novel multiscale methods that divide the underlying equations into macroscopic (large scale phenomena) and microscopic (small scale phenomena), and couple these scales in some appropriate manner. These methods will be implemented in computer code that will take advantage of modern parallel computer architectures. The resulting methods and codes will be used to simulate various application problems in order to verify and validate the approach.The primary objective of this research is to develop accurate and efficient computational methods for solving nonlinear differential equations used to model plasma dynamics. The goal is to solve a class of multiscale models of plasma using a novel micro-macro decomposition approach. The idea behind the micro-macro decomposition is to start with a general enough model that contains the coupled dynamics of macroscopic and microscopic phenomena, to then write this model into two parts with appropriate coupling terms, and finally to apply potentially different numerical techniques to each part in order to optimize efficiency. The specific schemes that will be used in this research are based on high-order discontinuous Galerkin finite element methods with novel time-stepping strategies to achieve computational efficiency. This research will develop new computational tools for simulating plasma dynamics. In particular, new micro-macro decomposition techniques will be designed and implemented that allow for the efficient numerical solution of multi-species plasma systems. New strategies will be developed to adaptively turn on and off the microscopic solvers. As part of the research project, novel computational methods and software will be produced that in the future could be applied to a wide range of both laboratory and astrophysical plasma problems. The software developed will be made freely available on the web as part of the DoGPack software project.

血浆物理学是对电离气体动力学的研究。由于血浆通常被称为物质的第四个状态，是宇宙中最丰富的普通物质形式，因此存在许多重要的应用问题，对等离子体动力学的理解至关重要。这些应用的一些示例包括了解恒星的动力学，太阳风在地球磁层上的影响，磁性限制的融合设备的动力学以及可用于医疗成像应用中的激光等E设备的动力学。这项研究的目的是开发高度准确，有效的计算工具来模拟电子（带负电荷的粒子）和构成构成感兴趣等离子体的离子（带正电荷的粒子）的动力学。这项研究旨在基于新型的多尺度方法开发新的计算技术，该方法将基础方程分为宏观（大规模现象）和微观（小规模现象），并以某种适当的方式仔细缩小这些量表。这些方法将在计算机代码中实现，以利用现代的并行计算机架构。最终的方法和代码将用于模拟各种应用问题，以验证和验证方法。本研究的主要目的是开发用于求解用于模拟等离子动力学的非线性微分方程的准确有效的计算方法。目的是使用一种新型的微麦克罗分解方法来解决一类血浆的多尺度模型。微麦克罗分解背后的想法是从一个足够的通用模型开始，该模型包含宏观和显微镜现象的耦合动力学，然后将此模型写入两个具有适当耦合术语的部分，最后将潜在的不同数值技术应用于每个部分部分是为了优化效率。这项研究中将使用的特定方案基于具有新颖的时间步变策略以实现计算效率的高阶不连续的galerkin有限元方法。这项研究将开发用于模拟等离子体动态的新计算工具。特别是，将设计和实施新的微型麦克罗分解技术，以有效地对多种物种等离子体系统进行数值解决方案。将制定新的策略来自适应打开和关闭微观求解器。作为研究项目的一部分，将生产出新的计算方法和软件，即将来可以应用于实验室和天体物理等血浆问题。开发的软件将作为Dogpack软件项目的一部分在网络上免费提供。