Temporal Multi-Scale Simulation Tools Kinetic Plasma Equations
时态多尺度模拟工具动力学等离子体方程
基本信息
- 批准号:1115709
- 负责人:
- 金额:$ 20万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-10-01 至 2015-09-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this work the PI and his student consider the development of novel methods for problems in kinetic transport. The goal is to develop methods that are capable of bridging multiple time scales. For instance, many problems in plasma physics, such as modeling edge plasma problems in fusion systems, can exhibit behavior which is consistent with both diffusion dominated transport as well as collisionless flow in the same problem at the same time. Generally speaking, this class of problems can be summarized as hyperbolic systems with stiff relaxation terms. Typically the stiff relaxation term can be nondimensionalized, leading to a scaling constant out in front of the relaxation term of the form 1/d. In the problems of interest, as d approaches zero, the system transitions from hyperbolic to parabolic. One approach to such problems is to use domain decomposition methods coupled with appropriate models for the various physical behaviors. However, a major difficulty with this approach is defining the boundary conditions for the two way coupling between the domains. The approach taken in this work is to develop numerical methods for the kinetic systems which can recover the correct limiting behavior in the limit of the system becoming collision dominated. The particular class of methods we focus on here are referred to as Asymptotic Preserving (AP) methods. The goal in designing an AP method is to develop time stepping strategies that maintain their order of accuracy for any d. In particular, as d approaches zero, the AP method should recover a consistent discretization for the limiting behavior. However, developing AP methods which are high order have proven difficult to construct. Further, for a range of important test problems, the CFL for the AP method is restricted to time steps less than the square of the spatial discretization. In this work, the PI and his student investigate a new method based on a pseudo upwinding method inside of the AP framework, which gives rise to a method which has a convergence rate independent of d with an apparent CFL of the time step proportional to the spatial discretization. Further, the PI proposes a novel method for lifting low order AP methods to high order based on integral deferred correction, a defect correction methodology developed by the PI and his collaborators. The approach is generalizable to a wide class of kinetic equations with stiff relaxation terms. A large number of important problems in science are characterized by multiple length scales. This includes studying the aerodynamics of spacecraft launch and reentry, the characterization of micro/nano mechanical systems and the study of charge particle transport, such as disassociated electrons and ions, in plasma lighting, micro chip design, and clean energy systems of the future, such as fusion, to name a few. In these examples, on the smallest scales, the individual atoms which make up the gas can be thought of as billiard balls bouncing around, each billiard ball having its own speed and direction. The gas molecules collide with each other, as well as the boundaries of obstacles in the flow, exchanging energy and momentum with each other as well as the environment. On this scale the system is well characterized by models know as kinetic equations, which describe the behavior of the gas from a probabilistic perspective. Kinetic equations account for time scales of individual atoms colliding with each other. On the largest length scales, the gas exhibits collective behavior such as wind, which we think of as having a single speed. As the density of a gas changes from low density to high density, the system behavior changes from individual particles to a collective average behavior. This transition happens in many systems, one interesting example is the reentry of a spacecraft, where at high altitude the atmosphere is a very low density gas and at ground level the atmosphere is 20 orders of magnitude higher in density. At low densities, these systems exhibit effects only described by kinetic models. At high densities, the systems exhibit collective behavior described my much simpler models. The critical kinetic time scale, described by inter-particle collisions, scales as one over the density. The importance of this work is to develop a new class of simulation tools that can handle the very stiff time scales associated with systems that undergo this very sharp transition in densities that can efficiently simulate both the rarified and dense gas regimes, as well as the transition in density. This framework will allow for the simulation of problems previously outside the scope of standard kinetic solvers, allowing the solvers to recover the correct limiting behavior with orders of magnitude increase in efficiency over existing methods.
在这项工作中,PI和他的学生考虑发展新的方法来解决动力学运输问题。 目标是开发能够连接多个时间尺度的方法。 例如,在等离子体物理学中的许多问题,例如在聚变系统中对边缘等离子体问题进行建模,可以表现出与扩散主导的输运以及同时在同一问题中的无碰撞流动相一致的行为。 一般来说,这类问题可以归结为具有刚性松弛项的双曲型方程组。 通常,刚性松弛项可以无量纲化,导致在形式为1/d的松弛项之前的缩放常数。 在感兴趣的问题中,当d接近零时,系统从双曲线过渡到抛物线。解决这些问题的一种方法是使用区域分解方法,结合各种物理行为的适当模型。 然而,这种方法的一个主要困难是定义域之间的双向耦合的边界条件。 在这项工作中采取的方法是发展的动力学系统,可以恢复正确的限制行为的限制系统成为碰撞为主的数值方法。 我们在这里关注的特定类别的方法被称为渐近保持(AP)方法。 设计AP方法的目标是开发时间步进策略,以保持其对任何数据的准确性。 特别是,当d接近零时,AP方法应该恢复极限行为的一致离散化。 然而,开发高阶AP方法已被证明难以构建。 此外,对于一系列重要的测试问题,AP方法的CFL被限制为小于空间离散化平方的时间步长。 在这项工作中,PI和他的学生研究了一种基于AP框架内的伪迎风方法的新方法,该方法产生了一种具有独立于d的收敛速度的方法,其时间步长的表观CFL与空间离散成比例。 此外,PI提出了一种基于积分延迟校正的将低阶AP方法提升到高阶的新方法,这是PI及其合作者开发的一种缺陷校正方法。 该方法是推广到广泛的一类动力学方程的刚性松弛项。科学中的许多重要问题都具有多重长度尺度的特征。 这包括研究航天器发射和再入的空气动力学,微/纳米机械系统的表征和电荷粒子传输的研究,如分离的电子和离子,等离子体照明,微芯片设计和未来的清洁能源系统,如聚变,仅举几例。 在这些例子中,在最小的尺度上,组成气体的单个原子可以被认为是四处弹跳的台球,每个台球都有自己的速度和方向。 气体分子相互碰撞,以及流动中障碍物的边界,相互交换能量和动量以及环境。 在这个尺度上,该系统的特征在于被称为动力学方程的模型,该模型从概率的角度描述了气体的行为。 动力学方程解释了单个原子相互碰撞的时间尺度。 在最大的长度尺度上,气体表现出集体行为,例如风,我们认为它具有单一的速度。 当气体的密度从低密度变为高密度时,系统行为从单个颗粒变为集体平均行为。 这种转变发生在许多系统中,一个有趣的例子是航天器的再入,在高空大气层是一种非常低密度的气体,而在地面大气层的密度要高出20个数量级。 在低密度下,这些系统表现出仅由动力学模型描述的效应。 在高密度下,系统表现出集体行为,描述了我更简单的模型。 由粒子间碰撞描述的临界动力学时间尺度,与密度成比例。 这项工作的重要性是开发一类新的模拟工具,可以处理与经历这种非常急剧的密度过渡的系统相关的非常严格的时间尺度,可以有效地模拟稀薄和稠密的气体状态,以及密度的过渡。 该框架将允许模拟以前标准动力学求解器范围之外的问题,允许求解器恢复正确的限制行为,其效率比现有方法提高了几个数量级。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Andrew Christlieb其他文献
A semi-Lagrangian adaptive-rank (SLAR) method for linear advection and nonlinear Vlasov-Poisson system
一种用于线性平流和非线性弗拉索夫 - 泊松系统的半拉格朗日自适应秩(SLAR)方法
- DOI:
10.1016/j.jcp.2025.113970 - 发表时间:
2025-07-01 - 期刊:
- 影响因子:3.800
- 作者:
Nanyi Zheng;Daniel Hayes;Andrew Christlieb;Jing-Mei Qiu - 通讯作者:
Jing-Mei Qiu
Andrew Christlieb的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Andrew Christlieb', 18)}}的其他基金
Collaborative Research: HDR DSC: Increasing Accessibility through Building Alternative Data Science Pathways
合作研究:HDR DSC:通过构建替代数据科学途径提高可访问性
- 批准号:
2123260 - 财政年份:2021
- 资助金额:
$ 20万 - 项目类别:
Continuing Grant
A Data-driven Approach to Multiscale Methods for ScalableTransport in Neutron Star Mergers and Complex Plasmas
中子星合并和复杂等离子体中可扩展传输的数据驱动多尺度方法
- 批准号:
2008004 - 财政年份:2020
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Implicit Multi-Scale Plasma Simulations Using Low Cost Matrix-Free Methods for Partial Differential Equations
使用低成本无矩阵方法进行偏微分方程的隐式多尺度等离子体模拟
- 批准号:
1912183 - 财政年份:2019
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
A Practical Approach to Rothe's Method: Method of Lines Transpose
罗特方法的实用方法:直线转置法
- 批准号:
1418804 - 财政年份:2014
- 资助金额:
$ 20万 - 项目类别:
Continuing Grant
Systematic Lagrangian Methods for Transport Problems
传输问题的系统拉格朗日方法
- 批准号:
0811175 - 财政年份:2008
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
相似国自然基金
面向宽带毫米波天线阵的大规模多尺度高效算法研究
- 批准号:QN25F010031
- 批准年份:2025
- 资助金额:0.0 万元
- 项目类别:省市级项目
多源融合的北斗规模化应用系统基座关键技术研究
- 批准号:2025JJ70057
- 批准年份:2025
- 资助金额:0.0 万元
- 项目类别:省市级项目
面向大规模多视图数据的粒球聚类研究
- 批准号:
- 批准年份:2025
- 资助金额:0.0 万元
- 项目类别:省市级项目
大规模诊疗数据的时空多模态哈希学习方法
- 批准号:2025JJ40057
- 批准年份:2025
- 资助金额:0.0 万元
- 项目类别:省市级项目
基于Douglas-Rachford分裂法的大规模
多智能体协同决策与控制方法研究
- 批准号:
- 批准年份:2025
- 资助金额:10.0 万元
- 项目类别:省市级项目
基于多功能超构表面的大规模多通道封
装天线阵列研究
- 批准号:
- 批准年份:2025
- 资助金额:10.0 万元
- 项目类别:省市级项目
大规模匹配市场中的多臂赌博机算法研究
- 批准号:
- 批准年份:2025
- 资助金额:10.0 万元
- 项目类别:省市级项目
面向并行计算的大规模多视图聚类算法及其应用研究
- 批准号:
- 批准年份:2025
- 资助金额:0.0 万元
- 项目类别:省市级项目
大规模复杂约束优化问题的多智能体协同求解理论研究
- 批准号:
- 批准年份:2024
- 资助金额:0.0 万元
- 项目类别:省市级项目
面向大规模未知环境探索的异构多机器人多源数据融合与协同感知关键技术研究
- 批准号:
- 批准年份:2024
- 资助金额:15.0 万元
- 项目类别:省市级项目
相似海外基金
Collaborative Research: ECO-CBET: Multi-scale design of liquid hydrogen carriers for spatio-temporal balancing of renewable energy systems
合作研究:ECO-CBET:用于可再生能源系统时空平衡的液氢载体的多尺度设计
- 批准号:
2318618 - 财政年份:2023
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Collaborative Research: ECO-CBET: Multi-scale design of liquid hydrogen carriers for spatio-temporal balancing of renewable energy systems
合作研究:ECO-CBET:用于可再生能源系统时空平衡的液氢载体的多尺度设计
- 批准号:
2318619 - 财政年份:2023
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Collaborative Research: ECO-CBET: Multi-scale design of liquid hydrogen carriers for spatio-temporal balancing of renewable energy systems
合作研究:ECO-CBET:用于可再生能源系统时空平衡的液氢载体的多尺度设计
- 批准号:
2318617 - 财政年份:2023
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Collaborative Research: ECO-CBET: Multi-scale design of liquid hydrogen carriers for spatio-temporal balancing of renewable energy systems
合作研究:ECO-CBET:用于可再生能源系统时空平衡的液氢载体的多尺度设计
- 批准号:
2318616 - 财政年份:2023
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Biomechanics of muscle after rotator cuff tear: Multi-scale assessment of spatial and temporal effects
肩袖撕裂后肌肉的生物力学:空间和时间影响的多尺度评估
- 批准号:
10556219 - 财政年份:2023
- 资助金额:
$ 20万 - 项目类别:
Analysing GNSS network data for deformation monitoring in multi-scale, multi-temporal civil engineering applications
分析 GNSS 网络数据以进行多尺度、多时态土木工程应用中的变形监测
- 批准号:
2763649 - 财政年份:2022
- 资助金额:
$ 20万 - 项目类别:
Studentship
Methodology for Multi Time-Scale Nonlinear Dynamical Spatio-Temporal Statistical Models
多时间尺度非线性动态时空统计模型方法
- 批准号:
1811745 - 财政年份:2018
- 资助金额:
$ 20万 - 项目类别:
Continuing Grant
Collaborative Research: Multi-Scale, Multi-Rate Spatio-Temporal Optimal Control with Application to Airborne Wind Energy Systems
合作研究:多尺度、多速率时空最优控制及其在机载风能系统中的应用
- 批准号:
1709767 - 财政年份:2017
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Collaborative Research: Multi-scale validation of earthquake source parameters to resolve any spatial, temporal or magnitude-dependent variability at Parkfield, CA
合作研究:对加利福尼亚州帕克菲尔德的地震源参数进行多尺度验证,以解决任何空间、时间或震级相关的变化
- 批准号:
1547071 - 财政年份:2016
- 资助金额:
$ 20万 - 项目类别:
Standard Grant
Collaborative Research: Multi-scale validation of earthquake source parameters to resolve any spatial, temporal or magnitude-dependent variability at Parkfield, CA
合作研究:对加利福尼亚州帕克菲尔德的地震源参数进行多尺度验证,以解决任何空间、时间或震级相关的变化
- 批准号:
1547083 - 财政年份:2016
- 资助金额:
$ 20万 - 项目类别:
Continuing Grant