Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 72, Issue 12, Pages 2908-2919Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.10.016
Keywords
Space-time fully decoupled formulation; Wavelet Galerkin method; Burgers' equations; High Reynolds number; Mixed explicit-implicit scheme
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Funding
- National Natural Science Foundation of China [11421062, 11502103]
- Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment [GZ15115]
- Fundamental Research Funds for the Central Universities [lzujbky-2015-178]
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A space-time fully decoupled formulation for solving two-dimensional Burgers' equations is proposed based on the Coiflet-type wavelet sampling approximation for a function defined on a bounded interval. By applying a wavelet Galerkin approach for spatial discretization, nonlinear partial differential equations are first transformed into a system of ordinary differential equations, in which all matrices are completely independent of time and never need to be updated in the time integration. Finally, the mixed explicit-implicit scheme is employed to solve the resulting semi-discretization system. By numerically studying three widely considered test problems, results demonstrate that the proposed method has a much better accuracy and a faster convergence rate than many existing numerical methods. Most importantly, the study also indicates that the present wavelet method is capable of solving the two-dimensional Burgers' equation at high Reynolds numbers. (C) 2016 Elsevier Ltd. All rights reserved.
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