High Order Methods for Kinetic Transport Models

动力学输运模型的高阶方法

• 批准号: 1913072
• 负责人: Fengyan Li
• 金额: $ 27.5万
• 依托单位: Rensselaer Polytechnic Institute
• 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: 2019-08-15 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913072&HistoricalAwards=false
• 关键词: Order; Methods; Kinetic; Transport; Models

Accurate, robust and efficient simulations of kinetic transport models are of fundamental importance to many applications in physics and engineering, such as rarefied gas dynamics, plasma physics, nuclear and biomedical engineering, and network dynamics. While fluid models often provide lower dimensional approximations, they are valid only when the systems are closed to their equilibria, and therefore kinetic transport models are necessary to account for a wider range of phenomena, including those displaying multiple scales in space and/or time or those involving particles from multiple energy groups. This project aims at advancing computational tools of high order accuracy for time-dependent multi-scale kinetic transport models, both algorithmically and mathematically.Kinetic transport equations are mathematical descriptions of the transport of particles such as neutrons, photons, molecules as well as their interaction with a host medium or among themselves, and they arise in a broad range of applications. The numerical challenges lie in the high dimensionality of the phase space, small scales, multiple scales in space (and even in time), nonlinear interactions, collision operators with multi-fold integrals, as well as the conservation or positivity property of the solutions. The objective of this project is therefore to take important steps in the understanding and simulations of the time-dependent multi-scale kinetic transport models, with the aim of: 1) providing accurate deterministic simulation tools with excellent stability to the kinetic transport community, and 2) developing novel analytical and numerical techniques to address some challenges related to accurate multi-scale kinetic transport simulations. The longer term goal is to develop algorithms robustly simulating more realistic kinetic models with high resolution and good efficiency.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.

准确、稳健和高效的动力学输运模型的模拟对于稀薄气体动力学、等离子体物理、核和生物医学工程以及网络动力学等许多物理和工程应用具有重要意义。虽然流体模型通常提供低维近似，但它们只有在系统接近其平衡时才有效，因此需要动力学输运模型来解释更广泛的现象，包括在空间和/或时间上显示多个尺度的现象或涉及来自多个能量组的粒子的现象。该项目的目标是在算法和数学上为含时多尺度动力学输运模型提供高精度的计算工具。动力学输运方程是对粒子输运的数学描述，如中子、光子、分子以及它们与宿主介质或它们之间的相互作用，它们出现在广泛的应用中。数值挑战在于相空间的高维、小尺度、空间(甚至时间)的多尺度、非线性相互作用、具有多重积分的碰撞算子以及解的守恒性或正性。因此，本项目的目标是在理解和模拟与时间相关的多尺度动力学输运模型方面采取重要步骤，目的是：1)向动力学输运界提供具有良好稳定性的精确确定性模拟工具；2)开发新的分析和数值技术，以解决与准确的多尺度动力学输运模拟有关的一些挑战。更长期的目标是开发算法，以高分辨率和良好的效率稳健地模拟更现实的动力学模型。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling

• DOI: 10.1016/j.jcp.2020.109485
• 发表时间: 2020-08
• 期刊: J. Comput. Phys.
• 作者: Zhichao Peng;Yingda Cheng;Jing-Mei Qiu;Fengyan Li

Energy Stable SBP-FDTD Methods for Maxwell–Duffing Models in Nonlinear Photonics

非线性光子学中麦克斯韦杜芬模型的能量稳定 SBP-FDTD 方法

• DOI: 10.1109/jmmct.2019.2959587
• 发表时间: 2019
• 期刊: IEEE Journal on Multiscale and Multiphysics Computational Techniques
• 影响因子: 2.3
• 作者: Appelo, Daniel;Bokil, Vrushali A.;Cheng, Yingda;Li, Fengyan
• 通讯作者: Li, Fengyan

Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property

• DOI: 10.1137/20m1336503
• 发表时间: 2020-05
• 期刊: ArXiv
• 作者: Zhichao Peng;Yingda Cheng;Jing-Mei Qiu;Fengyan Li

A Reduced Basis Method for Radiative Transfer Equation

• DOI: 10.1007/s10915-022-01782-2
• 发表时间: 2021-03
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Zhichao Peng;Yanlai Chen;Yingda Cheng;Fengyan Li

Asymptotic preserving IMEX-DG-S schemes for linear kinetic transport equations based on Schur complement

• DOI: 10.1137/20m134486x
• 发表时间: 2020-06
• 期刊: SIAM J. Sci. Comput.
• 作者: Zhichao Peng;Fengyan Li