Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers

被引：0
作者：
Wen Cao
Qinwu Xu
Zhoushun Zheng
机构：
[1] Central South University,School of Mathematics and Statistics
[2] Nanjing University,Department of Mathematics
来源：
Advances in Difference Equations | / 2017卷
关键词：
fractional calculus; time-fractional Burgers’ equation; shock wave; numerical simulation; 26A33; 34A08;
D O I：
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摘要：
Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerkin method to spatial variables and a finite difference scheme to temporal variables. The corresponding numerical analysis is also presented. Several numerical tests are carried out to demonstrate the theoretical analysis and we present a shock wave phenomenon of the new Burgers model.
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