Date of Award

Spring 11-13-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Aerospace Engineering Sciences

First Advisor

Kenneth E. Jansen

Second Advisor

John Farnsworth

Third Advisor

John Evans

Fourth Advisor

Peter Hamlington

Fifth Advisor

Brian Argrow

Abstract

Computational modeling of incompressible two-phase flows requires an efficient means of tracking the interface between phases. An ideal method would directly provide information about the interface's location and curvature, would be strictly volume conserving, and would work for parallel computing on unstructured meshes. For incompressible two-phase flows, there are several popular interface tracking schemes, but each has significant shortcomings. For example, while level set schemes directly provide the location and curvature of the interface, they do not strictly conserve volume. Conversely, volume of fluid methods strictly conserve volume, but they do not directly provide the interface's location or curvature. Coupled level set volume of fluid (CLSVOF) methods mitigate some of the weaknesses of both level set and volume of fluid methods while preserving many of their strengths, but CLSVOF methods face challenges yet to be resolved for unstructured meshes.

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This work first examines the challenges in implementing a CLSVOF method on unstructured meshes for parallel computing. It does not present a complete CLSVOF method, but it lays the foundation and makes recommendations for future work. This work also examines several variations of level set methods to develop an understanding of the trade-offs inherent in the methods (e.g., preservation of curvature versus volume conservation, and computational cost versus volume conservation). The developments of this work are implemented in Parallel Hierarchic Adaptive Stabilized Transient Analysis (PHASTA) software, a proven finite element flow solver, and the level set variations are tested on several canonical problems.

This work also examines the use of interface-based adaptive mesh refinement (AMR) to improve interface tracking and volume conservation. Proximity to the interface and/or the curvature of the level set field can be used to define areas of mesh refinement, thereby reducing the discretization errors near the interface without incurring unmanageable computational expense. This approach to AMR is demonstrated on a dam break problem and an annular flow simulation. It is also paired with the level set variations to offer a more complete picture of the options available.

Available for download on Wednesday, November 13, 2019

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