Date of Award:

5-1-2014

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mechanical and Aerospace Engineering

Advisor/Chair:

Aaron J. Katz

Abstract

This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it \corrects" the ux terms of an established numerical method, cancelling various error terms in the uxes and making the method higher-order. In this work, this change is made to a traditionally second-order nite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the uxes are introduced to the method. Gradi- ents are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruc- tion, a derivative of the high-order Discontinuous Galerkin and Spectral Dierence methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the eect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.

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