Citation
Hou, Wei (2025) Fast Algorithms for Spanwise Periodic Incompressible External Flows: From Simulation to Analysis. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/eygj-k325. https://resolver.caltech.edu/CaltechTHESIS:03202025-173020131
Abstract
External flows over spanwise-homogeneous geometries are ubiquitous in science and engineering applications. In this thesis, we propose algorithms to simulate and analyze these flows using the lattice Green's function (LGF) approach. The LGF is the analytical inverse of a discrete elliptic operator that automatically incorporates exact far-field boundary conditions and minimizes computational expense by allowing snug computational regions encompassing only vortical flow regions. By combining LGFs with adaptive mesh refinement (AMR) and immersed boundary (IB) methods, we present two numerical algorithms specially designed for spanwise periodic incompressible external flows: one to directly solve the nonlinear equations of motion and one to compute stability and resolvent analyses.
For these algorithms, the LGFs of the screened Poisson equation must be computed at runtime. To enable efficient flow simulation and analysis algorithms, we propose a fast numerical algorithm to tabulate these LGFs. We derive convergence results for the algorithms and show that they are orders of magnitude faster than existing algorithms. Armed with the LGF for the screened Poisson equation, we further develop algorithms to solve the Navier-Stokes equations and associated linearized eigenvalue problems.
We present two applications of these algorithms. We perform simulations to validate the starting vortex theory proposed by Pullin and Sader (2021), and we perform stability analyses of flow past a rotating cylinder with a control cylinder in its wake.
Item Type: | Thesis (Dissertation (Ph.D.)) | |||||||||||||||
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Subject Keywords: | fluid mechanics, computational method, numerical analysis | |||||||||||||||
Degree Grantor: | California Institute of Technology | |||||||||||||||
Division: | Engineering and Applied Science | |||||||||||||||
Major Option: | Mechanical Engineering | |||||||||||||||
Minor Option: | Applied And Computational Mathematics | |||||||||||||||
Thesis Availability: | Public (worldwide access) | |||||||||||||||
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Defense Date: | 12 December 2024 | |||||||||||||||
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Record Number: | CaltechTHESIS:03202025-173020131 | |||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:03202025-173020131 | |||||||||||||||
DOI: | 10.7907/eygj-k325 | |||||||||||||||
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Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
ID Code: | 17083 | |||||||||||||||
Collection: | CaltechTHESIS | |||||||||||||||
Deposited By: | Wei Hou | |||||||||||||||
Deposited On: | 10 Apr 2025 23:45 | |||||||||||||||
Last Modified: | 17 Apr 2025 10:37 |
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