Spectral analysis of nonlinear finite difference discretizations. (English) Zbl 1262.65099

Fauconnier, Dieter; Dick, Erik

J. Comput. Appl. Math. 246, 113-121 (2013).

Summary: 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 the authors [J. Comput. Phys 230, No. 12, 4488–4518 (2011; Zbl 1416.76174)] 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.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20	Finite difference methods applied to problems in fluid mechanics

Keywords:

nonlinear spectral analysis; nonlinear discretizations; TVD; WENO

Citations:

Zbl 1416.76174