Committee Chair

Anderson, W. Kyle

Committee Member

Kapadia, Sagar; Wang, Li; Sreenivas, Kidambi

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 this research a stabilized finite element approach is utilized in the development of a high-order flow solver for compressible turbulent flows. The Reynolds averaged Navier-Stokes (RANS) equations and modified Spalart-Almaras (SA) turbulence model are discretized using the streamline/upwind Petrov-Galerkin (SUPG) scheme. A fully implicit methodology is used to obtain steady state solutions or to drive unsteady problems at each time step. Order of accuracy is assessed for inviscid and viscous flows in two and three dimensions via the method of manufactured solutions. Proper treatment of curved surface geometries is of vital importance in high-order methods, especially when high aspect ratio elements are used in viscous flow regions. In two dimensions, analytic surface representations are used to ensure proper surface point placement, and an algebraic mesh smoothing procedure is applied to prevent invalid elements in high aspect ratio meshes. In dealing with complex three-dimensional geometries, high-order curved surfaces are generated via a Computational Analysis PRogramming Interface (CAPRI), while the interior meshes are deformed through a linear elasticity solver. In addition, the effects of curved elements on solution accuracy are evaluated. Finally, several test cases in two and three dimensions are presented and compared with benchmark results and/or experimental data.

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

12-2013

Subject

Navier-Stokes equations

Keyword

Finite elements; CFD; Navier-Stokes; Streamline/upwind Petrov-Galerkin (SUPG); Turbulence; Higher order methods

Discipline

Applied Mathematics | Computational Engineering

Document Type

Doctoral dissertations

Extent

xii, 95 leaves

Language

English

Rights

Under copyright.

License

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

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