Embedded boundary methods (EBMs) for Computational Fluid Dynamics (CFD) and nonlinear fluid–structure interaction (FSI) – also known as immersed boundary methods, Cartesian methods, or fictitious domain methods – are the most robust methods for the solution of flow problems past obstacles that undergo large relative motions, significant deformations, large shape modifications, and/or surface topology changes. They can also introduce a high degree of automation in the task of grid generation and significant flexibility in the gridding of complex geometries. However, just like in the case of their counterpart body-fitted methods, their application to parametric flow computations at high Reynolds numbers remains today impractical in most engineering environments. For body-fitted CFD, the state of the art of projection-based model order reduction (PMOR) has significantly advanced during the last decade and demonstrated a remarkable success at reducing the dimensionality and wall-clock time of high Reynolds number models, while maintaining a desirable level of accuracy. For non-body-fitted CFD however, PMOR is still in its infancy, primarily because EBMs dynamically partition the computational fluid domain into real and ghost subdomains, which complicates the collection of solution snapshots and their compression into a reduced-order basis. In an attempt to fill this gap, this paper presents a robust computational framework for PMOR in the context of high Reynolds number flows and in the EBM setting of CFD/FSI (PMOR-EBM). The framework incorporates a hyperreduction approach based on the energy-conserving sampling and weighting (ECSW) method to accelerate the evaluation of the repeated projections arising in nonlinear implicit computations; and a piecewise-affine approach for constructing a nonlinear low-dimensional approximation of the solution to mitigate the Kolmogorov n-width barrier to the reducibility of transport models. The paper also assesses the performance of the proposed computational framework PMOR-EBM for two unsteady turbulent flow problems whose predictions necessitate or benefit from the application of an EBM; and two shape-parametric steady-state studies of the academic type but of relevance to design analysis and optimization.

中文翻译：

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CFD 和非线性 FSI 的嵌入式边界模型的基于投影的模型降阶


用于计算流体动力学 （CFD） 和非线性流固耦合 （FSI） 的嵌入式边界方法 （EBM） - 也称为浸没边界法、笛卡尔方法或虚构域方法，是解决通过经历较大相对运动、显著变形、大形状修改和/或表面拓扑变化的障碍物的流动问题的最可靠方法。它们还可以在网格生成任务中引入高度自动化，并在复杂几何形状的网格化中引入显着的灵活性。然而，就像它们的对应体拟合方法一样，它们在高雷诺数下的参数化流动计算中的应用在当今大多数工程环境中仍然不切实际。对于体拟合 CFD，基于投影的模型降阶 （PMOR） 的最新技术在过去十年中取得了显著进步，并在降低高雷诺数模型的维度和挂钟时间方面取得了显著成功，同时保持了理想的精度水平。然而，对于非体拟合 CFD，PMOR 仍处于起步阶段，主要是因为 EBM 将计算流体域动态划分为实数和虚影子域，这使得解快照的收集及其压缩为降阶基础变得复杂。为了填补这一空白，本文在高雷诺数流和 CFD/FSI （PMOR-EBM） 的 EBM 设置中提出了一个强大的 PMOR 计算框架。 该框架采用了基于节能采样和加权 （ECSW） 方法的超还原方法，以加速对非线性隐式计算中出现的重复投影的评估;以及一种分段仿射方法，用于构建解的非线性低维近似，以减轻 Kolmogorov n 宽度障碍对输运模型可归约性的阻碍。本文还评估了所提出的计算框架 PMOR-EBM 在两个非稳态湍流问题上的性能，这些问题的预测需要 EBM 的应用或从中受益;以及两项学术类型但与设计分析和优化相关的形状参数稳态研究。