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Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

Citation

Liska, Sebastian (2016) Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9ZC80TG. http://resolver.caltech.edu/CaltechTHESIS:04062016-223108239

Abstract

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:incompressible viscous flow; unbounded domain; lattice Green's function; immersed boundary method; fast multipole method; difference equation; parallel computing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Awards:Rolf D. Buhler Memorial Award in Aeronautics, 2009.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Colonius, Timothy E.
Thesis Committee:
  • Blanquart, Guillaume (chair)
  • Colonius, Timothy E.
  • Meiron, Daniel I.
  • Leonard, Anthony
Defense Date:24 March 2016
Record Number:CaltechTHESIS:04062016-223108239
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:04062016-223108239
DOI:10.7907/Z9ZC80TG
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2014.07.048DOIArticle adapted for ch. 2
http://arxiv.org/abs/1601.00035arXivArticle adapted for ch. 3
http://arxiv.org/abs/1604.01814arXivArticle adapted for ch. 4
http://arxiv.org/abs/1603.02306arXivArticle's scientific contributions used for the work included in ch. 4
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9658
Collection:CaltechTHESIS
Deposited By: Sebastian Liska Cabrera
Deposited On:25 Apr 2016 18:40
Last Modified:18 May 2017 18:13

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