Date of Award

2014

Document Type

Thesis

First Advisor

Yamaleev, Nail

Abstract

It has been shown that the conventional 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme of Jiang and Shu degenerates to third order at points where the first and higher order derivatives of the solution become equal to zero. Recently, Yamaleev and Carpenter proposed new weight functions which drastically improve the accuracy of high-order WENO-type schemes and provide the design order of accuracy for smooth solutions with any number of vanishing derivatives, if their tuning parameters satisfy consistency constraints. The truncation error analysis reveals that the accuracy of the flux reconstruction provided by the new weight functions can be increased near strong discontinuities, thus improving the shock-capturing capabilities of the corresponding WENO scheme. Six different modifications of the weight functions of Yamaleev and Carpenter are proposed and analyzed for both smooth and discontinuous solutions. Our grid refinement studies for the linear advection equation show that the modified weight functions improve the non-oscillatory properties of the scheme, while retaining the intended design order of accuracy.

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