CAREER: Tailored Entropy Stable Discretizations of Nonlinear Conservation Laws

职业：非线性守恒定律的定制熵稳定离散化

• 批准号: 1943186
• 负责人: Jesse Chan
• 金额: $ 44.99万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1943186&HistoricalAwards=false
• 关键词: CAREER; Tailored; Entropy; Stable; Discretizations

The simulation of fluid flow is foundational to many scientific fields, ranging from environmental and aerospace engineering to solar physics. However, next-generation modeling and analysis is computationally challenging using existing tools. Tailored numerical methods have the potential to address such limitations. For example, projection-based reduced order models decrease computational costs associated with many-query scenarios (such as engineering design or uncertainty quantification) by replacing a high fidelity model with a less expensive low-dimensional surrogate. Similarly, high order accurate schemes are particularly effective at resolving fine-scale features in transient vorticular flows. Unfortunately, when applied to the equations of fluid dynamics, these numerical methods experience non-physical instabilities which can cause simulations to fail unexpectedly. The goal of this project is to enable robust and efficient simulations using discretely "entropy stable" schemes. By building fundamental energetic principles directly into a discretization, entropy stable methods retain accuracy while inheriting verifiable properties which improve "out-of-the-box" robustness. Discretely entropy stable high order discretizations for nonlinear conservation laws have seen rapid development over the last 7 years. This project will extend this methodology to three areas where existing approaches are suboptimal or unavailable: (1) high order methods on non-conforming meshes, (2) high order physical-frame discretizations for domain boundaries with fine-scale features, and (3) reduced order modeling. Additionally, the PI will integrate aspects of the proposed research with an educational program aimed at promoting computational science and improving retention among college students and K-12 teachers. Specifically, the PI will (1) design and supervise senior capstone research projects for engineering undergraduates, and (2) organize a summer research program for K-12 teachers centered around numerical modeling and discovery-based learning. The summer research program will also provide graduate students with mentoring experience, and the PI will follow up by partnering with teachers to incorporate concepts from numerical computing into reusable classroom modules.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.

流体流动的模拟是许多科学领域的基础，从环境和航天工程到太阳物理。然而，使用现有工具进行下一代建模和分析在计算上具有挑战性。量身定制的数值方法有可能解决这些限制。例如，基于投影的降阶模型通过将高保真模型替换为更便宜的低维代理来降低与许多查询场景(例如工程设计或不确定性量化)相关联的计算成本。同样，高阶精度格式在解决瞬变涡流中的细尺度特征方面特别有效。不幸的是，当应用于流体动力学方程时，这些数值方法会遇到非物理不稳定性，这可能会导致模拟意外失败。该项目的目标是使用离散的“熵稳定”方案实现健壮和高效的模拟。通过直接将基本能量原理构建为离散化，熵稳定方法在继承可验证属性的同时保持准确性，这些属性提高了“开箱即用”的健壮性。离散熵稳定的非线性守恒律的高阶离散化在过去的7年中得到了迅速的发展。该项目将把这一方法扩展到现有方法次优或不可用的三个领域：(1)非协调网格上的高阶方法，(2)具有精细特征的区域边界的高阶物理框架离散化，以及(3)降阶建模。此外，PI将把拟议研究的各个方面与一项旨在促进计算科学和提高大学生和K-12教师保留率的教育计划相结合。具体地说，PI将(1)为工科本科生设计和监督高级顶峰研究项目，(2)为K-12教师组织以数值建模和基于发现的学习为中心的暑期研究项目。暑期研究项目还将为研究生提供指导经验，PI将与教师合作，将数值计算的概念纳入可重复使用的课堂模块。该奖项反映了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

High-order methods for hypersonic flows with strong shocks and real chemistry

• DOI: 10.1016/j.jcp.2023.112310
• 发表时间: 2022-11
• 期刊: J. Comput. Phys.
• 作者: A. Peyvan;K. Shukla;Jesse Chan;G. Karniadakis

Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics

理想磁流体动力学的熵稳定高斯配置方法

• DOI: 10.1016/j.jcp.2022.111851
• 发表时间: 2023
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Rueda-Ramírez, Andrés M.;Hindenlang, Florian J.;Chan, Jesse;Gassner, Gregor J.
• 通讯作者: Gassner, Gregor J.

Discrete Adjoint Computations for Relaxation Runge–Kutta Methods

松弛龙格 - 库塔方法的离散伴随计算

• DOI: 10.1007/s10915-023-02102-y
• 发表时间: 2023
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Bencomo, Mario J.;Chan, Jesse
• 通讯作者: Chan, Jesse

Provably stable flux reconstruction high-order methods on curvilinear elements

曲线元素上可证明稳定的通量重建高阶方法

• DOI: 10.1016/j.jcp.2022.111259
• 发表时间: 2022
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Cicchino, Alexander;Del Rey Fernández, David C.;Nadarajah, Siva;Chan, Jesse;Carpenter, Mark H.
• 通讯作者: Carpenter, Mark H.

Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes

熵稳定分部求和方案的雅可比矩阵的高效计算

• DOI: 10.1016/j.jcp.2021.110701
• 发表时间: 2022
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Chan, Jesse;Taylor, Christina G.
• 通讯作者: Taylor, Christina G.