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.

引用

页数：14

共 50 条

[41] Two-dimensional axisymmetric stresses exerted by instantaneous pulses and sources of diffusion in an infinite space in a case of time-fractional diffusion equation
Povstenko, Y. Z.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2007, 44 (7-8) : 2324 - 2348
[42] An analytical solution for two and three dimensional nonlinear Burgers' equation
Gao, Q.
Zou, M. Y.
APPLIED MATHEMATICAL MODELLING, 2017, 45 : 255 - 270
[43] An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate
Abbaszadeh, Mostafa
Dehghan, Mehdi
NUMERICAL ALGORITHMS, 2017, 75 (01) : 173 - 211
[44] Haar Wavelet Method for Solving Two-Dimensional Burgers' Equation
Wang, Miaomiao
Zhao, Fengqun
PROCEEDINGS OF THE 2011 2ND INTERNATIONAL CONGRESS ON COMPUTER APPLICATIONS AND COMPUTATIONAL SCIENCE, VOL 2, 2012, 145 : 381 - 387
[45] A robust numerical solution to a time-fractional Black-Scholes equation
Nuugulu, S. M.
Gideon, F.
Patidar, K. C.
ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
[46] NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION
Prakash, Amit
Kumar, Manoj
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2019, 9 (03): : 446 - 454
[47] Numerical Solution of Time Fractional Burgers Equation by Cubic B-spline Finite Elements
Esen, Alaattin
Tasbozan, Orkun
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (03) : 1325 - 1337
[48] A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation
Ezz-Eldien, S. S.
Doha, E. H.
Wang, Y.
Cai, W.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 91
[49] A Fast Second-Order ADI Finite Difference Scheme for the Two-Dimensional Time-Fractional Cattaneo Equation with Spatially Variable Coefficients
Nong, Lijuan
Yi, Qian
Chen, An
FRACTAL AND FRACTIONAL, 2024, 8 (08)
[50] Discrete Chebyshev polynomials for the numerical solution of stochastic fractional two-dimensional Sobolev equation
Heydari, M. H.
Zhagharian, Sh.
Razzaghi, M.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 130

← 1 2 3 4 5 →