Truncation error, dissipation and dispersion terms of fifth order WENO and of WCS for 1D conservation law

Abstract

In this paper, a derivation and a comparison of the truncation errors and the dissipation and dispersion terms of the fifth-order weighted essentially non-oscillatory scheme and of the weighted compact scheme are presented. The schemes are compared for smooth functions (by Fourier analysis), and near a shock.

Keywords:

• truncation error
• dissipation
• dispersion
• WENO
• compact scheme