Galerkin modelling of the Burgers equation using harmonic wavelets

Journal article

In this paper we present a wavelet Galerkin approximation of the one-dimensional Burgers equation using complex harmonic wavelets. We derive exact expressions for the connection coefficients for the linear dissipation and nonlinear advection terms. A large reduction in the number of space-scale nonlinear modes is obtained by exploiting the band-limited spectra and localisation properties of harmonic wavelets. We discuss the advantages and disadvantages of implementing harmonic wavelets as opposed to the more standard choice of wavelets basis, highlighting the relevance to shell models of turbulence. © 1997 Elsevier Science B.V.

Authors: Muniandy, S; Moroz, I

• Publication status: Published
• Journal: PHYSICS LETTERS A
• Volume: 235
• Issue: 4
• Pages: 352-356
• Publication date: 1997-11-10
• DOI: 10.1016/S0375-9601(97)00639-7
• ISSN: 0375-9601
• Language: English
• Keywords: multiscale processes; wavelets; Galerkin method