LEAPS-MPS: Computational Methods for Many-Physics Problems Involving Multi-Material Flows

LEAPS-MPS：涉及多材料流的许多物理问题的计算方法

• 批准号: 2302080
• 负责人: Xianyi Zeng
• 金额: $ 24.57万
• 依托单位: Lehigh 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: 2023-04-15 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2302080&HistoricalAwards=false
• 关键词: LEAPS; MPS; Computational; Methods; Many

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). In recent years, physical and mechanical systems that contain more than two entities have become common in applications. Some examples include fuel mixing in a deforming engine chamber, wind and ocean waves impacting on offshore wind power generation systems, and heart blood flow simulations. Although there are many numerical methods that can be used individually, most do not work well with each other for solving challenges in these more complex situations. To this end, this project aims at developing a computational framework and software suite for the high-fidelity simulation of multi-material flows. Upon completion, this project will provide a powerful tool for studying the coupling between multi-material fluids and any number of structures. The project also involves collaboration in two related subjects – a computational method to capture under-resolved structural boundaries in fluid-structure interaction problems and a machine-learning based reduced order modeling of embedded flow computations to realize real-time flow predictions in complex environments. In carrying out the project, the PI will train two graduate students. In addition, the PI will improve two graduate courses for a new PhD program in Data Science at The University of Texas at El Paso to better prepare a majority Hispanic student body to solve data and computing related challenges. Furthermore, the project involves the organization of a new annual one-day workshop to promote a STEM-related career among young students from underrepresented groups and low-income families in the Borderplex region.The major component of the project is an efficient and reliable embedded boundary method on moving computational grids, called the ALE-EBM method. Traditionally, the interface between fluids and structures are tracked by mesh points and it necessarily causes the grid to move, a strategy commonly known as the Arbitrary Lagrangian-Eulerian or ALE methods, whereas the interface between two fluids are usually captured implicitly by various embedded boundary methods (EBM), due to its large deformation or topological changes. The two strategies, however, cannot be combined per se to enable computation of multi-fluid/structure interaction problems or multi-material shock hydrodynamics, as existing EBMs rely heavily on the assumption of a fixed grid. The new ALE-EBM method attempts to fill this gap by providing a proved methodology to perform embedded boundary computations on a computational grid that is allowed to move freely. In particular, the project includes: (1) analyzing multi-material Riemann problems to enforce various transmission conditions between materials while maintaining the physical relevance of the numerical solutions, (2) utilizing multiple level sets to capture the motion of multiple fluid sub-domains while preserving the signed distance meaning of each level set and conserving the mass of each fluid, (3) using a Nitsche-type method to capture adjacent structural boundary with a much smaller physical scale, and (4) a machine learning approach to achieve efficient reduced-order modeling computations of these problems.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.

该奖项的全部或部分资金均根据《2021 年美国救援计划法案》（公法 117-2）提供。 近年来，包含两个以上实体的物理和机械系统在应用中已变得很常见，其中包括燃料混合。变形的发动机舱、风和海浪对海上风力发电系统的影响以及心脏血流模拟虽然有许多数值方法可以单独使用，但大多数方法不能很好地相互配合来解决这些挑战。复杂的情况。为此，该项目旨在开发用于多材料流动高保真模拟的计算框架和软件套件。完成后，该项目将为研究多材料流体与任意数量结构之间的耦合提供强大的工具。该项目还涉及两个相关主题的合作——一种捕获流固耦合问题中未解决的结构边界的计算方法，以及一种基于机器学习的嵌入式流动计算降阶建模，以实现复杂环境中的实时流动预测。在实施该项目时，PI 将培训此外，PI 还将改进德克萨斯大学埃尔帕索分校数据科学新博士课程的两门研究生课程，以更好地为大多数西班牙裔学生解决数据和计算相关的挑战做好准备。涉及组织一个新的年度为期一天的研讨会，以促进来自 Borderplex 地区代表性不足群体和低收入家庭的年轻学生与 STEM 相关的职业生涯。该项目的主要组成部分是一种高效可靠的嵌入式边界方法，用于移动计算网格，称为 ALE-EBM传统上，流体和结构之间的界面由网格点跟踪，这必然会导致网格移动，这种策略通常称为任意拉格朗日-欧拉或 ALE 方法，而两种流体之间的界面通常由各种隐式捕获。然而，嵌入式边界方法（EBM）由于其大变形或拓扑变化，本身无法组合起来计算多流体/结构相互作用问题或多材料冲击流体动力学。现有的 EBM 在很大程度上依赖于固定网格的假设，新的 ALE-EBM 方法试图通过提供一种经过验证的方法来在允许自由移动的计算网格上执行嵌入式边界计算来填补这一空白。 ：（1）分析多材料黎曼问题以强制材料之间的各种传输条件，同时保持数值解的物理相关性，（2）利用多个水平集捕获多个流体子域的运动，同时保留符号距离含义每个水平集并保存每种流体的质量，（3）使用尼采型方法以更小的物理尺度捕获相邻结构边界，以及（4）机器学习方法来实现这些问题的高效降阶建模计算。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审查标准进行评估，被认为值得支持。

项目成果

Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

浅水双曲方程的嵌入域简化基模型的位移边界法

• DOI: 10.1016/j.cma.2022.115143
• 发表时间: 2022-08
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Zeng, Xianyi;Stabile, Giovanni;Karatzas, Efthymios N.;Scovazzi, Guglielmo;Rozza, Gianluigi
• 通讯作者: Rozza, Gianluigi

On the stability of explicit finite difference methods for advection–diffusion equations

平流扩散方程显式有限差分法的稳定性

• DOI: 10.1002/num.22897
• 发表时间: 2022-07
• 期刊: Numerical Methods for Partial Differential Equations
• 影响因子: 3.9
• 作者: Zeng, Xianyi;Hasan, Md Mahmudul
• 通讯作者: Hasan, Md Mahmudul

A central compact hybrid-variable method with spectral-like resolution: One-dimensional case

具有类谱分辨率的中心紧凑混合变量方法：一维情况

• DOI: 10.1016/j.cam.2022.114894
• 发表时间: 2023-03
• 期刊: Journal of Computational and Applied Mathematics
• 影响因子: 2.4
• 作者: Hasan, Md Mahmudul;Zeng, Xianyi
• 通讯作者: Zeng, Xianyi