A stabilized finite element dynamic overset method for the Navier-Stokes equations

Author

Chao Liu, University of Tennessee at ChattanoogaFollow

Committee Chair

Newman, James C., III

Committee Member

Sreenivas, Kidambi; Anderson, W. Kyle; Matthews, John V., III

Department

Dept. of Computational Engineering

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

In terms of mesh resolution requirements, higher-order finite element discretization methods offer a more economic means of obtaining accurate simulations and/or to resolve physics at scales not possible with lower-order schemes. For simulations that may have large relative motion between multiple bodies, overset grid methods have demonstrated distinct advantages over mesh movement strategies. Combining these approaches offers the ability to accurately resolve the flow phenomena and interaction that may occur during unsteady moving boundary simulations. Additionally, overset grid techniques when utilized within a finite element setting mitigate many of the difficulties encountered in finite volume implementations. This research presents the development of an overset grid methodology for use within a streamline/upwind Petrov-Galerkin formulation for unsteady, viscous, moving boundary simulations. A novel hole cutting procedure based on solutions to Poisson equation is introduced and compared to existing techniques. A MPI-based parallel three-dimensional overset grid assembly framework is developed. Order of accuracy is examined via the method of manufactured solutions. The potential benefits of using Adaptive Mesh Refinement (AMR) in overset grid simulations are explored by combining the overset method with an AMR approach. The importance of considering linearization due to the overset boundaries within the preconditioning is studied. Numerical experiments are performed comparing an ILU(k) preconditioner with two proposed modifications referred to as “triangular inter-grid ILU(k)” and “Jacobi inter-grid ILU(k)”. The efficiency gains observed from the proposed modifications are also applicable to general parallel simulations on distributed memory machines, regardless of whether an overset grid approach is used. Overset grid results are presented for several inviscid and viscous, steady-state and time-dependent moving boundary simulations with linear, quadratic, and cubic elements.

Acknowledgments

First and foremost, I would like to express my sincere gratitude to my advisor Dr. James C. Newman III for his support and encouragement, not only for my work, but also for my life. His dedication to his students and to his work is what impresses me most. I would also like to thank Dr. W. Kyle Anderson, who has given me tremendous guidance. His dedication to his work has always inspired me. I owe a debt of gratitude to Dr. Timothy Swafford and the entire SimCenter faculty and staff for providing an open and friendly environment during my research. Additionally, I would like to thank Bezhad Reza Ahrabi for being a supportive colleague and a great friend.

Degree

Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.

Date

5-2016

Subject

Navier-Stokes equations -- Numerical solutions; Unsteady flow (Aerodynamics)

Keyword

Computational fluid dynamics; High-order method; Finite element method; Overset grid; Hole cutting; Moving boundary simulation

Discipline

Computational Engineering

Document Type

Doctoral dissertations

DCMI Type

Text

Extent

xiii, 99 leaves

Language

English

Rights

https://rightsstatements.org/page/InC/1.0/?language=en

License

http://creativecommons.org/licenses/by-nd/3.0/

Recommended Citation

Liu, Chao, "A stabilized finite element dynamic overset method for the Navier-Stokes equations" (2016). Masters Theses and Doctoral Dissertations.
https://scholar.utc.edu/theses/458