EMBEDDED BOUNDARY METHODS WITH STABILITY, ACCURACY, AND SMOOTHNESS GUARANTEES FOR MULTIDISCIPLINARY DESIGN, ANALYSIS AND OPTIMIZATION
Abstract
In the context of CFD and fluid-structure interaction (FSI), embedded boundary methods (EBMs) are Eulerian methods that operate on non body-fitted fluid meshes in which discrete representations of obstacle surfaces are embedded. They are attractive for numerous reasons. They introduce a high degree of automation in the task of mesh generation and a 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. Such problems arise in FSI and multidisciplinary design, analysis and optimization (MDAO). However, EBMs typically generate discrete events that are sources of roughness and spurious oscillations in the flow results computed at an embedded, discrete, boundary surface or in its vicinity. At best, such numerical flaws are sufficiently small not to affect the quality of the computations. However, they inhibit differentiation with respect to any evolution of the embedded surface. Therefore, they hinder the application of EBMs to the gradient-based solution of aerodynamic shape optimization problems, where they are pressingly needed to avoid remeshing and the pitfalls of transferring numerical results from one CFD mesh to another. Furthermore, EBMs complicate the collection and compression of solution snapshots because they partition the fluid domain into real and fictitious subdomains and require adaptive mesh refinement for tracking boundary layers and flow features. Hence, they challenge the construction of nonlinear, projection-based reduced-order models.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010286
Entities
People
- Charbel Farhat
Organizations
- Air Force Office of Scientific Research
- Stanford University
- United States Air Force