A Concept to Eliminate the Meshing Bottleneck During the Design and Analysis of Fluid Systems

许多对美国经济、国防和国民健康至关重要的系统的正常功能依赖于流体流动（即液体或气体的流动）。这种系统的例子包括商用和军用飞机、汽车发动机、风力涡轮机和心脏泵。流体系统的特点是不直观的物理，这使得它们特别难以设计。在缺乏实验数据和工程经验的非常规流体系统的概念设计过程中，这一困难尤为突出。原则上，工程师可以使用数值模拟来分析创新的流体系统，但高保真度模拟在概念设计中的应用有限。为什么?流动模拟通常依赖于网格，网格将流体所占据的区域划分为许多较小的体积，而为复杂的几何形状生成高质量的网格仍然是一个耗时的、人工循环的过程。本研究将探索一种全新的方法来缓解网格瓶颈，从而改善流体系统的设计过程。项目成果将包括新的算法和算法的原型实现，这些算法将在在线存储库中提供。本课题将研究一种新的浸入式边界方法及其在设计优化中的应用。关键的观点是将浸入边界法作为一个逆问题。这个想法是在几何内部引入一个物体力，或表面通量，它就像一个控制变量来施加边界条件。该控制的最优值是通过求解一个偏微分方程约束逆问题来确定的。由于计算网格不需要符合几何形状，因此这种方法对概念设计期间的流体系统分析具有吸引力。此外，与大多数浸入式边界方法不同，本项目的方法保持准确，并与高阶离散化兼容。为了评估该概念的潜力，该项目将调查几个关键问题：在可选的反问题公式中，哪一个是最好的？这个问题应该如何规范化？如何有效地求解逆问题？当应用于不完美的CAD几何形状时，该概念的鲁棒性和准确性如何？如何将该方法用于推进形状优化算法？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。

The proper function of many systems vital to the United States' economy, defense, and national health depend on fluid flow (i.e., the flow of a liquid or gas). Examples of such systems include commercial and military aircraft, automobile engines, wind turbines, and heart pumps. Fluid systems are characterized by unintuitive physics, which makes them exceptionally difficult to design. This difficulty is particularly acute during the conceptual design of unconventional fluid systems, for which experimental data and engineering experience is lacking. In principle, engineers could use numerical simulations to analyze innovative fluid systems, but high-fidelity simulations have found limited use during conceptual design. Why? Flow simulations typically rely on meshes, which divide the region occupied by the fluid into many smaller volumes, and generating high-quality meshes for complex geometries remains a time-consuming, human-in-the-loop process. This research will investigate a fundamentally new approach to mitigate the meshing bottleneck and thereby improve the fluid system design process. Project outcomes will include novel algorithms and prototype implementations of the algorithms that will be made available in an online repository. The research project will study a novel immersed-boundary method and its application to design optimization. The key insight is to frame the immersed-boundary method as an inverse problem. The idea is to introduce a body force, or surface flux, interior to the geometry that acts like a control variable to impose the boundary conditions. The optimal value for this control is determined by solving a partial-differential-equation constrained inverse problem. This approach is attractive for the analysis of fluid systems during conceptual design, because the computational mesh does not need to conform to the geometry. Furthermore, unlike most immersed-boundary methods, this project's approach remains accurate and is compatible with high-order discretizations. To assess the potential of the concept, the project will investigate several critical questions: among alternative inverse-problem formulations, which one is the best? How should the problem be regularized? How do we solve the inverse problem efficiently? How robust and accurate is the concept when applied to imperfect CAD geometries? And, how can the method be used to advance shape optimization 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.