Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Shilt_Dissertation_vF.pdf (26.84 MB)

ETD Abstract Container

Abstract Header

High-Resolution Computational Fluid Dynamics using Enriched Finite Elements

Shilt, Troy P
http://rave.ohiolink.edu/etdc/view?acc_num=osu1636449813015831

Abstract Details

2021, Doctor of Philosophy, Ohio State University, Aero/Astro Engineering.
Computational fluid dynamics provides quantitative insights that complement physical experiments and enable cheaper and faster design/analysis processes. However, problems of interest tend to be highly complex, manifesting multiple physical processes over a broad range of spatial and temporal scales. The consequence of this is the desire for fluid simulations spanning many temporal and spatial scales. Here, relevant physical phenomena include steep gradients – due to shock waves, boundary layers, and laminar to turbulent boundary layer transition – and the broadband response of turbulence. Despite continual advancement in computing power, tractable analysis of problems involving such phenomena depends upon parallel advancements in the efficiency of numerical solution strategies. In these contexts, the overarching goal of this research is to assess the numerical solution of fluid dynamic problems using an enriched finite element framework. Through an enrichment process, this framework enables the expansion of the approximation space associated with more traditional finite element methods to non-polynomials. Non-polynomial approximation spaces better enable solution-tailored approximations that can significantly reduce computational costs. For example, previous works applying enriched finite elements in other disciplines have resulted in highly efficient numerical simulation of problems containing steep gradients, discontinuities, and singularities. Application of enriched finite elements for fluid dynamics problems is nontrivial due to numerical challenges: (1) restrictions on allowable velocity-pressure discretization for the solution of incompressible flows and (2) non-physical spurious oscillations in numerical solutions for advection dominated problems. Therefore, an enriched finite element method must address these challenges. For applying enriched finite elements to fluid dynamics, this research focuses on (1) addressing the aforementioned numerical challenges and (2) obtaining high-accuracy numerical solutions using solution-tailored enrichments. In the presented methodology, stability and high-accuracy solutions are interlinked. Specifically, solution-tailored enrichments typically result in stable and high-accuracy solutions that capture relevant features more efficiently regarding status quo methods; Results demonstrate this for the numerical solution of the governing equations of an elastic medium, creeping flow, the advection-diffusion equation, and the Burgers’ equation.
Jack McNamara (Advisor)
Patrick O'Hara (Committee Member)
Armando Duarte (Committee Member)
Datta Gaitonde (Committee Member)
Jen-Ping Chen (Committee Member)
168 p.
Aerospace Engineering; Engineering; Fluid Dynamics; Mechanical Engineering
Finite elements, GFEM, XFEM, fluid dynamics, advection-diffusion equation, Burgers' equation, Navier-Stokes equation

Recommended Citations

Citations

  • Shilt, T. P. (2021). High-Resolution Computational Fluid Dynamics using Enriched Finite Elements [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1636449813015831

    APA Style (7th edition)

  • Shilt, Troy. High-Resolution Computational Fluid Dynamics using Enriched Finite Elements. 2021. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1636449813015831.

    MLA Style (8th edition)

  • Shilt, Troy. "High-Resolution Computational Fluid Dynamics using Enriched Finite Elements." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1636449813015831

    Chicago Manual of Style (17th edition)

osu1636449813015831
46
© 2021, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.