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

基本信息

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

项目摘要

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，以解决各种重要的科学和工程应用中的部分微分方程，例如航空航天工程，半导体设备设计，天体物理学和生物学应用。即使有了当今的快速超级计算机，设计有效且可靠的算法仍然至关重要，以获取高精度可以提高这些设备的安全性和性能的这些应用的准确解决方案。这些算法将对这些应用中复杂解决方案结构的计算机模拟做出积极贡献。该项目将包括STEM中代表性不足群体的学生的劳动力开发。该项目旨在调查算法开发，分析和应用高阶数值方法的应用，包括不连续的Galerkin（DG）有限元方法和有限元差异和有限量差异和有限量加权。非振荡（WENO）方案。该算法将旨在求解线性和非线性对流的部分微分方程（PDE），强调结合的保留，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用于数值边界条件的逆宽松程序，具有移动边界和界面，数学特性和有效的求解器，用于前向后耦合的PDE系统，来自交通流量，高阶数值，用于歇斯底里的高阶数值方法订购拉格朗日方法，用于DG方案和其他空间离散化的高效且稳定的时间步变技术，高阶准确准确的限制性保护方案和应用程序，包括涉及高度非线性约束的问题以及一步Lax-Wendroff类型的时间隔离，与僵硬的源术语，僵硬的源术语，僵硬的问题，问题高阶DG方案用于固定双曲方程和辐射转移方程，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南，同时提高其准确性，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，以在现有算法中有效地应用这些新算法或新功能。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子和更广泛的影响来评估。审查标准。