Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows.
In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-ε and k-ω turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flow. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter.
Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flow. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence.
In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined "asymptotic geometry," is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening strategy in order to qualitatively improve strand grid mesh quality.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-5745 |
| Date | 01 May 2016 |
| Creators | Tong, Oisin |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). |
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