A Spectral Study on the Dissipation and Dispersion of the WENO Schemes

Abstract

The dissipation and dispersion (spectral) properties of the nonlinear fifth order classical weighted essentially non-oscillatory finite difference scheme (WENO-JS5) and its improved version (WENO-Z5) using the approximate dispersion relation (ADR) (Pirozzoli in J Comput Phys 219:489–497, 2006) and the nonlinear spectral analysis (NSA) (Fauconnier et al. in J Comput Phys 228(6):1830–1861, 2009) are studied. Unlike the previous studies, the …