High Order Schemes: Bound Preserving, Moving Boundary, Stochastic Effects and Efficient Time Discretization

高阶方案：保界、移动边界、随机效应和高效时间离散化

• 批准号: 2309249
• 负责人: Chi-Wang Shu
• 金额: $ 40万
• 依托单位: Brown 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: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309249&HistoricalAwards=false
• 关键词: Order; Schemes; Bound; Preserving; Moving

The project aims to develop efficient and high-precision numerical methods for solving partial differential equations in various important scientific and engineering applications, such as aerospace engineering, semiconductor device design, astrophysics, and biological applications. Even with today's fast supercomputers, it is still essential to design efficient and reliable algorithms to obtain accurate solutions to these applications where high precision can improve the safety and performance of those devices. These algorithms will make positive contributions to computer simulations of the complicated solution structure in these applications. The project will include workforce development for students from underrepresented groups in STEM.The project aims to investigate algorithm development, analysis, and application of high-order numerical methods, including discontinuous Galerkin (DG) finite element methods and finite difference and finite volume weighted essentially non-oscillatory (WENO) schemes. The algorithms will be designed to solve linear and nonlinear convection-dominated partial differential equations (PDEs), emphasizing bound preserving, moving boundary, stochastic effects and efficient time discretization. Topics of the research investigations will include an inverse Lax-Wendroff procedure for numerical boundary conditions with moving boundaries and interfaces, mathematical properties and efficient solvers for forward-backward coupled PDE systems from traffic flow modeling, high order numerical methods for hysteretic flows, robust high order Lagrangian methods, efficient and stable time-stepping techniques for DG schemes and other spatial discretizations, high order accurate bound-preserving schemes and applications including problems involving highly nonlinear constraints and one step Lax-Wendroff type time discretizations, problems with stiff source terms, high order DG schemes for stationary hyperbolic equations and radiative transfer equations, oscillation-free DG methods, and numerical solutions of stochastic differential equations. The research will provide guidelines for the algorithms' applicability and limitations while enhancing their accuracy, stability, and robustness. The research will include collaborations with engineers and other applied scientists to enable the efficient application of these new algorithms or new features in existing algorithms.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.

该项目旨在开发高效、高精度的数值方法，用于求解各种重要科学和工程应用中的偏微分方程，例如航空航天工程、半导体器件设计、天体物理学和生物应用。即使拥有当今快速的超级计算机，设计高效可靠的算法以获得这些应用的准确解决方案仍然至关重要，其中高精度可以提高这些设备的安全性和性能。这些算法将为这些应用中复杂解结构的计算机模拟做出积极的贡献。该项目将包括针对 STEM 中代表性不足群体的学生的劳动力发展。该项目旨在研究算法开发、分析和高阶数值方法的应用，包括不连续伽辽金 (DG) 有限元方法以及有限差分和有限体积加权本质上非振荡（WENO）方案。该算法旨在求解线性和非线性对流主导的偏微分方程（PDE），强调边界保持、移动边界、随机效应和有效的时间离散化。研究调查的主题将包括具有移动边界和界面的数值边界条件的逆 Lax-Wendroff 过程、交通流建模中的前向-后向耦合偏微分方程系统的数学特性和高效求解器、滞回流的高阶数值方法、稳健的高阶数值方法。阶拉格朗日方法、DG 方案和其他空间离散化的高效稳定时间步进技术、高阶精确保界方案和应用，包括涉及高度非线性约束和一步的问题Lax-Wendroff 型时间离散化、刚性源项问题、平稳双曲方程和辐射传递方程的高阶 DG 格式、无振荡 DG 方法以及随机微分方程的数值解。该研究将为算法的适用性和局限性提供指导，同时提高算法的准确性、稳定性和鲁棒性。该研究将包括与工程师和其他应用科学家的合作，以实现这些新算法或现有算法中的新功能的有效应用。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进行评估，被认为值得支持审查标准。

项目成果

High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics

三温辐射流体动力学高阶保守拉格朗日格式

• DOI: 10.1016/j.jcp.2023.112595
• 发表时间: 2024-01
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Cheng, Juan;Lei, Nuo;Shu, Chi
• 通讯作者: Shu, Chi

Approximated decompositions for computational continuum mechanics

计算连续介质力学的近似分解

• DOI: 10.1016/j.jcp.2023.112576
• 发表时间: 2023-10-01
• 期刊: J. Comput. Phys.
• 作者: Rafael B. de R. Borges;Flávio C. Colman;Nicholas D. P. da Silva;Gabriela Wessling Oening Dicati;J. Gubaua;Chi
• 通讯作者: Chi