Dimensionality Reduction of Embedded Boundary Models for Problems with Large Shape Changes

Abstract

Embedded (or immersed) boundary methods for computational fluid dynamics (CFD) and fluid-structure interaction are Eulerian methods that operate on non body-fitted fluid meshes in which discrete representations of obstacle surfaces are embedded. They introduce a high degree of automation in the task of mesh generation and significant flexibility in the meshing of complex geometries. They are also the most robust solution methods for flow problems past obstacles that undergo large motions, deformations, shape changes, and/or topological changes. Hence, they are attractive for fluid-structure interaction and multidisciplinary design analysis and optimization, where they eliminate the need for remeshing and therefore avoid the pitfalls of transferring information from one CFD mesh to another. However, embedded boundary methods complicate the collection and compression of solution snapshots because they dynamically partition the fluid domain into real and fictitious subdomains, challenging the construction of projection-based reduced-order models. Consequently, they hamper the acceleration of the solution of computationally intensive problems such as shape and multidisciplinary optimization problems by these types of physics-based surrogate models. For all these reasons, this paper presents, illustrates, and demonstrates a robust computational framework for constructing projection-based reduced-order embedded boundary models and hyperreducing them to achieve near-real-time performance.