Using wavelets to solve the Burgers equation: A comparative study

1 December 1992

journal article
Published by American Physical Society (APS) in Physical Review A

Vol. 46 (12) , 7953-7958
https://doi.org/10.1103/physreva.46.7953

Abstract

The Burgers equation is solved for Reynolds numbers ≲8000 in a representation using coarse-scale scaling functions and a subset of the wavelets at finer scales of resolution. Situations are studied in which the solution develops a shocklike discontinuity. Extra wavelets are kept for several levels of higher resolution in the neighborhood of this discontinuity. Algorithms are presented for the calculation of matrix elements of first- and second-derivative operators and a useful product operation in this truncated wavelet basis. The time evolution of the system is followed using an implicit time-stepping computer code. An adaptive algorithm is presented which allows the code to follow a moving shock front in a system with periodic boundary conditions.

Keywords

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