Spectral analysis of nonlinear finite difference discretizations

• Autores: D. Fauconnier, E. Dick
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 246, Nº 1, 2013, págs. 113-121
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.11.004
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• Resumen

  • The objective of the present work is to provide a theoretical analysis of the spectral properties of a selection of nonlinear finite difference schemes. The Nonlinear Spectral Analysis (NSA) of Fauconnier and Dick (2011) [6] is applied in order to study the statistical behavior of the modified wavenumber of TVD schemes in combination with five common limiter functions and also the 5th-order WENO scheme, for a large set of synthetic scalar fields with prescribed energy spectrum and random phase. The theoretical observations are verified numerically for the linear propagation of a broadband wave.