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Fast Algorithms for Spanwise Periodic Incompressible External Flows: From Simulation to Analysis

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.))
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)
Research Advisor(s):
  • Colonius, Tim
Thesis Committee:
  • Blanquart, Guillaume (chair)
  • Bae, H. Jane
  • Sader, John E.
  • Colonius, Tim
Defense Date:12 December 2024
Funders:
Funding AgencyGrant Number
The Boeing CompanyCT-BA-GTA-1
Air Force Office of Scientific Research (AFOSR)FA9550-18-1-0440
Office of Naval Research (ONR)N00014-16-1-2734
Record Number:CaltechTHESIS:03202025-173020131
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:03202025-173020131
DOI:10.7907/eygj-k325
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2403.03076DOIAdapted for Chapter 2
https://doi.org/10.1016/j.jcp.2024.113370DOIAdapted for Chapter 3
https://doi.org/10.2514/6.2023-3414DOIAdapted for Chapter 4
https://doi.org/10.1017/jfm.2024.515DOIAdapted for Chapter 5
ORCID:
AuthorORCID
Hou, Wei0000-0001-8023-6395
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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