Moving Polygon Methods for Incompressible Fluid Dynamics

Author

Chris Chartrand, University of Massachusetts AmherstFollow

Author ORCID Identifier

https://orcid.org/0000-0003-2446-0186

AccessType

Open Access Dissertation

Document Type

dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mechanical Engineering

Year Degree Awarded

2022

Month Degree Awarded

February

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

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.

DOI

https://doi.org/10.7275/26841056

Recommended Citation

Chartrand, Chris, "Moving Polygon Methods for Incompressible Fluid Dynamics" (2022). Doctoral Dissertations. 2438.
https://doi.org/10.7275/26841056 https://scholarworks.umass.edu/dissertations_2/2438