Moving Polygon Methods for Incompressible Fluid Dynamics

Chartrand, Chris

Publication:
Moving Polygon Methods for Incompressible Fluid Dynamics

dc.contributor.advisor	Blair PErot
dc.contributor.advisor	David Schmidt
dc.contributor.advisor	Jon G. McGowan
dc.contributor.advisor	Hans Johnston
dc.contributor.author	Chartrand, Chris
dc.contributor.department	University of Massachusetts Amherst
dc.date	2024-03-27T18:28:29.000
dc.date.accessioned	2024-04-26T15:51:07Z
dc.date.available	2024-04-26T15:51:07Z
dc.date.submitted	February
dc.date.submitted	2022
dc.description.abstract	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.
dc.description.degree	Doctor of Philosophy (PhD)
dc.description.department	Mechanical Engineering
dc.identifier.doi	https://doi.org/10.7275/26841056
dc.identifier.orcid	https://orcid.org/0000-0003-2446-0186
dc.identifier.uri	https://hdl.handle.net/20.500.14394/18767
dc.relation.url	https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=3501&context=dissertations_2&unstamped=1
dc.source.status	published
dc.subject	Polygons Mimetic Methods CFD incompressible Fluids
dc.subject	Aerodynamics and Fluid Mechanics
dc.subject	Discrete Mathematics and Combinatorics
dc.subject	Fluid Dynamics
dc.subject	Numerical Analysis and Scientific Computing
dc.title	Moving Polygon Methods for Incompressible Fluid Dynamics
dc.type	openaccess
dc.type	article
dc.type	dissertation
digcom.contributor.author	isAuthorOfPublication\|email:ccchartrand@gmail.com\|institution:University of Massachusetts Amherst\|Chartrand, Chris
digcom.identifier	dissertations_2/2438
digcom.identifier.contextkey	26841056
digcom.identifier.submissionpath	dissertations_2/2438
dspace.entity.type	Publication