Abstract
A comparative study of the performance of TVB (total variation bounded), TVD (total variation diminishing), and ENO (essentially non-oscillatory) schemes for the Euler equations was conducted. All the schemes are constructed by applying the characteristic flux difference splitting method to a modified flux which has either TVB, TVD, or ENO property. A third-order ENO scheme using reconstruction via primitive function approach is also described. Numerical results for one-dimensional and two-dimensional gasdynamic problems indicate that ENO scheme performs better than the other two while the TVB has the least satisfactory results. A modified eigenvalue approach is proposed to improve the TVB scheme. Results using this approach for TVD, TVB, and ENO schemes are also included.
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