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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。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普遍。一些例子包括在变形的发动机室内混合燃料，风和海浪影响海上风力发电系统以及心脏血流模拟。尽管有许多数值方法可以单独使用，但大多数方法在这些更复杂的情况下彼此之间的效果并不好。为此，该项目旨在开发一个计算框架和软件套件，以进行多物质流的高保真模拟。完成后，该项目将为研究多物质流体与任意数量的结构之间的耦合提供强大的工具。该项目还涉及在两个相关主题中的协作 - 一种计算方法，用于捕获流体结构交互问题中解决不足的结构边界，以及基于机器学习的基于机器学习的嵌入式流量计算的减少订单建模，以实现复杂环境中的实时流量预测。在执行该项目时，PI将培训两名研究生。此外，PI将在德克萨斯大学埃尔帕索分校的数据科学新博士学位课程中改善两个研究生课程，以更好地准备大多数西班牙裔学生团体，以解决数据和计算相关的挑战。此外，该项目涉及组织新的一日一日研讨会，以促进Borderplex地区中代表性不足的群体和低收入家庭的年轻学生中与STEM相关的职业。该项目的主要组成部分是一种有效且可靠的嵌入式边界方法，用于移动计算网格，称为ALE-EBM方法。传统上，流体和结构之间的界面通过网格点跟踪，它一定会导致电网移动，这种策略通常被称为任意的拉格朗日 - 欧拉或ALE方法，而两种流体之间的界面通常由于其各种嵌入式边界方法（EBM）而隐含地捕获。但是，这两种策略本身不能结合起来，以便计算多流体/结构相互作用问题或多物质冲击流体动力学，因为现有的EBM在很大程度上依赖于固定网格的假设。新的ALE-EBM方法试图通过在允许自由移动的计算网格上执行嵌入式边界计算的方法来填补这一空白。特别是，该项目包括：（1）分析多物质的黎曼问题，以在维持数值解决方案的物理相关性之间在材料之间执行各种传输条件，（2）利用多个级别的集合来捕获多个流体亚域运动的运动，同时使用每个级别的范围内捕获每个级别的范围，并保留每个级别的质量，并保留了a n secter a n see n see-n se，（3） - （3）较小的物理规模，以及（4）一种机器学习方法，以实现这些问题的有效降低订购建模计算。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响来审查标准，被认为是通过评估来获得的支持。

项目成果

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

• DOI: 10.1016/j.cam.2022.114894
• 发表时间: 2022-10
• 期刊: J. Comput. Appl. Math.
• 作者: M. K. Hasan;Xianyi Zeng

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

• DOI: 10.1002/num.22897
• 发表时间: 2020-06
• 期刊: Numerical Methods for Partial Differential Equations
• 影响因子: 3.9
• 作者: Xianyi Zeng;M. K. Hasan

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
• 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