Numerical algorithm for three-dimensional space fractional advection diffusion equation

3rd International Conference on Advances in Energy, Environment and Chemical Engineering

能源学;生态环境科学;化学工业

Hu, Jiahui^1,2 ; Wang, Jungang^1 ; Yuan, Zhanbin^1 ; Yang, Zongze^1 ; Nie, Yufeng^1

Research Center for Computational Science, Northwestern Polytechnical University, Xi'an

710129, China^1

College of Science, Henan University of Technology, Zhengzhou

450001, China^2

关键词: Crank-Nicolson scheme;    Difference operators;    Fractional advection-diffusions;    Fractional derivatives;    Numerical algorithms;    Predictor-corrector algorithm;    Three dimensional space;    Three-dimensional problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/69/1/012127/pdf
DOI  :  10.1088/1755-1315/69/1/012127

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Space fractional advection diffusion equations are better to describe anomalous diffusion phenomena because of non-locality of fractional derivatives, which causes people to confront great trouble in problem solving while enjoying the convenience from mathematical modelling, especially in high dimensional cases. In this paper, we solve the three-dimensional problem by the process of dimension by dimension, which can be achieved through a predictor-corrector algorithm. In time discretization, Crank-Nicolson scheme is adopted to match second-order difference operator of the space direction. Then, the efficiency of this method is demonstrated by some numerical examples finally.