ORCID Identifier(s)

0000-0002-2052-9396

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Chaoqun Liu

Abstract

The Weighted Upwinding Compact Scheme in this dissertation has been constructed due to dissipation and dispersion analysis at each stencil. The new scheme is applied to many one-dimensional typical problems involving discontinuities and shock waves, and it maintains a 7th order of accuracy in smooth areas. Additionally, when using the technology of decoupling the system of WUCS, the global dependency problem of the compact scheme is transferred to a local dependency problem in shock regions. As a result of the decoupling method, the shocks are captured sharply with fewer points compared to the related schemes. Furthermore, high order, high resolution, and non-oscillation are achieved. In future work, there will be an effort to apply the new scheme to the 2-D and 3-D Navier-Stokes equations and to multi-dimensional flows with shock-turbulence interaction.

Keywords

WUCS, Weighted Upwinding Compact Scheme

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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