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

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。近年来，包含两个以上实体的物理和机械系统在应用中变得普遍。一些例子包括变形发动机舱内的燃料混合，风和海浪对海上风力发电系统的影响，以及心脏血流模拟。尽管有许多数值方法可以单独使用，但在解决这些更复杂的情况下的挑战时，大多数方法都不能很好地相互配合。为此，本项目旨在开发一个计算框架和软件套件，用于高保真地模拟多物质流动。该项目完成后，将为研究多材料流体与任意数量结构之间的耦合提供强有力的工具。该项目还涉及两个相关课题的合作，一个是在流固耦合问题中捕捉未解结构边界的计算方法，另一个是基于机器学习的嵌入式流计算的降阶建模，以实现复杂环境中的实时流预测。在实施该项目时，PI将培训两名研究生。此外，PI还将改进德克萨斯大学埃尔帕索分校（University of Texas at El Paso）数据科学新博士项目的两门研究生课程，以更好地为拉美裔学生群体解决数据和计算相关挑战做好准备。此外，该项目还涉及组织一个新的为期一天的年度研讨会，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从事与stem相关的职业。该项目的主要组成部分是一种高效可靠的移动计算网格嵌入式边界方法，称为ALE-EBM方法。传统上，流体和结构之间的界面是由网格点跟踪的，它必然导致网格移动，这种策略通常被称为任意拉格朗日-欧拉或ALE方法，而两种流体之间的界面通常由各种嵌入边界方法（EBM）隐式捕获，因为它的大变形或拓扑变化。然而，这两种策略本身不能结合起来计算多流体/结构相互作用问题或多材料激波流体动力学，因为现有的EBMs严重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填补这一空白，该方法可以在允许自由移动的计算网格上执行嵌入式边界计算。具体而言，该项目包括：(1)分析多材料黎曼问题，在保持数值解的物理相关性的同时，执行材料之间的各种传输条件；(2)利用多个水平集捕获多个流体子域的运动，同时保留每个水平集的符号距离意义并保留每个流体的质量；(3)使用nitsche型方法以更小的物理尺度捕获相邻结构边界。(4)采用机器学习方法对这些问题进行高效的降阶建模计算。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.