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

被引：17
作者：
Cao, Wen [1 ]
Xu, Qinwu [2 ]
Zheng, Zhoushun [1 ]
机构：
[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Peoples R China
[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2017年
基金：
美国国家科学基金会; 中国博士后科学基金;
关键词：
fractional calculus; time-fractional Burgers' equation; shock wave; numerical simulation; DISCONTINUOUS GALERKIN METHODS; COLE-HOPF TRANSFORMATION; DIFFUSION-EQUATIONS; FICKS LAW; DIFFERENTIAL-EQUATIONS; DECOMPOSITION METHOD; NUMERICAL-SOLUTIONS; POROUS-MEDIA; DERIVATIVES; MODEL;
D O I：
10.1186/s13662-017-1398-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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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页数：14
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