A space-time fully decoupled wavelet Galerkin method for solving two-dimensional Burgers’ equations

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• 关键词：Space&ndash ; time fully decoupled formulation ; Wavelet Galerkin method ; Burgers&rsquo ; equations ; High Reynolds number ; Mixed explicit&ndash ; implicit scheme
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：72
• 期：12
• 页码：2908-2919
• 全文大小：1351 K
• 卷排序：72

文摘

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.