Development of Adaptive Sparse Grid Discontinuous Galerkin Methods for Multiscale Kinetic Simulations in Plasmas

等离子体多尺度动力学模拟的自适应稀疏网格间断伽辽金方法的发展

• 批准号: 2404521
• 负责人: Yingda Cheng
• 金额: $ 20万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-12-15 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2404521&HistoricalAwards=false
• 关键词: Development; Adaptive; Sparse; Grid; Discontinuous

This project aims at designing efficient numerical schemes for simulating complex plasma phenomena. Plasma is a state of matter similar to gas in which a certain portion of the particles is ionized. Understanding the complex behaviors of plasmas has led to important advances in areas ranging from space physics, fusion energy, to high-power microwave generation and large scale particle accelerators. There is strong need for laying out mathematical and algorithmic foundations for the design of efficient numerical methods so that we can advance basic research in plasma simulations. The algorithms developed in this project have the potential to provide high fidelity simulations in plasma physics with manageable computational cost and will have applications and impacts in multiscale simulations in fusion devices. The principal investigator (PI) will organize special events at professional meetings and workshops to promote the participation of female researchers. This project provides research training opportunities for graduate students. The objective of the project is to make significant advances on the design and analysis of a class of numerical methods called adaptive sparse grid (aSG) discontinuous Galerkin (DG) methods. The methods incorporate high order accurate DG solver that excels at transport simulations and the dimension reduction technique by aSG approach. The aim of this proposal is to advance the algorithmic foundations of the schemes for time-dependent PDEs, and push them onto the broader arena of multiscale simulations and applications for fusion science. The PI will investigate several fundamental issues including the analysis of CFL conditions, development of multiscale time stepping, postprocessing and hybrid aSG schemes. For a class of multiscale kinetic problems bridging kinetic and fluid models, by utilizing the multiresolution offered in the aSG-DG framework, the research will take advantage of both multiscale simulation tools and multiresolution on hierarchically defined meshes to achieve acceleration in computations. The schemes will be applied to simulations of runaway electrons in tokamak devices.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.

该项目旨在设计有效的数值方案来模拟复杂的等离子体现象。等离子体是一种类似于气体的物质状态，其中一部分粒子被电离。 了解等离子体的复杂行为已经在空间物理、聚变能、高功率微波发生和大型粒子加速器等领域带来了重要进展。 迫切需要为有效数值方法的设计奠定数学和算法基础，以便我们能够推进等离子体模拟的基础研究。该项目开发的算法有潜力以可管理的计算成本提供等离子体物理的高保真度模拟，并将在聚变装置的多尺度模拟中产生应用和影响。首席研究员（PI）将在专业会议和研讨会上组织特别活动，以促进女性研究人员的参与。该项目为研究生提供研究培训机会。该项目的目标是在一类称为自适应稀疏网格（aSG）不连续伽辽金（DG）方法的数值方法的设计和分析方面取得重大进展。该方法结合了擅长传输模拟的高阶精确 DG 求解器和 aSG 方法的降维技术。该提案的目的是推进瞬态偏微分方程方案的算法基础，并将其推向更广泛的多尺度模拟和融合科学应用领域。 PI 将研究几个基本问​​题，包括 CFL 条件分析、多尺度时间步进、后处理和混合 aSG 方案的开发。对于一类连接动力学和流体模型的多尺度动力学问题，通过利用 aSG-DG 框架中提供的多分辨率，该研究将利用多尺度模拟工具和分层定义网格的多分辨率来实现计算加速。该计划将应用于托卡马克装置中失控电子的模拟。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。