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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mechanical Engineering

Year Degree Awarded


Month Degree Awarded


First Advisor

Blair PErot

Second Advisor

David Schmidt

Third Advisor

Jon G. McGowan

Fourth Advisor

Hans Johnston

Subject Categories

Aerodynamics and Fluid Mechanics | Discrete Mathematics and Combinatorics | Fluid Dynamics | Numerical Analysis and Scientific Computing


Hybrid particle-mesh numerical approaches are proposed to solve incompressible fluid flows. The methods discussed in this work consist of a collection of particles each wrapped in their own polygon mesh cell, which then move through the domain as the flow evolves. Variables such as pressure, velocity, mass, and momentum are located either on the mesh or on the particles themselves, depending on the specific algorithm described, and each will be shown to have its own advantages and disadvantages. This work explores what is required to obtain local conservation of mass, momentum, and convergence for the velocity and pressure in a particle-mesh CFD simulation method. Current particle methods are explored and analyzed for their benefits and deficiencies, and newly developed methods are described with results and analysis.

A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, so a generalization of Voronoi polygon meshes is formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method's ability to simulate various physical scenarios is shown. The advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps.


bubble_high_res.mkv (19334 kB)
Rising bubble – high resolution

bubble_low_res.mkv (12151 kB)
Rising bubble – low resolution

dam_break_low_res.mkv (5213 kB)
Dam break – low resolution

dam_break_high_res.mkv (5060 kB)
Dam break – high resolution

LO_0.022.mkv (10596 kB)
Lamb Oseen Vortex

raft_high_res.mkv (54815 kB)
Floating raft – high resolution

raft_low_res.mkv (29964 kB)
Floating raft – low resolution

raft_zoom.mkv (103520 kB)
Floating raft – high resolution zoom

raft-render.mkv (7995 kB)
Floating raft – high resolution rendered

slosh.0.01.mkv (12263 kB)
Sloshing wave – dx = 0.01

slosh.0.02.mkv (13143 kB)
Sloshing wave – dx = 0.02

slosh.0.0027.mkv (11765 kB)
Sloshing wave – dx = 0.0027

slosh.0.0055.mkv (11391 kB)
Sloshing wave – dx = 0.0055

MP_2D_tor_ref_0.32_0.01_crop.avi.mp4 (8518 kB)
Torsion Flow over cylinder – Re=0.64

MP_2D_tor_ref_32_crop.avi.mp4 (4286 kB)
Torsion Flow over cylinder – Re=64

MP_2D_vor_ref_0.32_0.01_crop.avi.mp4 (8878 kB)
Voronoi Flow over cylinder – Re=0.64

MP_2D_vor_ref_32_crop.avi.mp4 (4670 kB)
Voronoi Flow over cylinder – Re=64

voronoi.avi.mp4 (19111 kB)
Voronoi Reconnection

colors.0.01.mkv (24898 kB)
Taylor Green Vortex mixing – dx = 0.01

colors.0.02.mkv (39093 kB)
Taylor Green Vortex mixing – dx = 0.02

colors.0.0027.mkv (84260 kB)
Taylor Green Vortex mixing – dx = 0.0027

colors.0.0055.mkv (37818 kB)
Taylor Green Vortex mixing – dx = 0.0055

velocity_viridis.0.01.mkv (3204 kB)
Taylor Green Vortex velocity – dx = 0.01

velocity_viridis.0.02.mkv (5085 kB)
Taylor Green Vortex velocity – dx = 0.02

velocity_viridis.0.0027.mkv (2198 kB)
Taylor Green Vortex velocity – dx = 0.0027

velocity_viridis.0.0055.mkv (3033 kB)
Taylor Green Vortex velocity – dx = 0.0055