Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

被引：37
作者：
Liu, Q. [1 ]
Liu, F. [2 ,3 ]
Turner, I. [2 ]
Anh, V. [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Peoples R China
来源：
IMA JOURNAL OF APPLIED MATHEMATICS | 2009年 / 74卷 / 02期
基金：
美国国家科学基金会; 中国国家自然科学基金; 澳大利亚研究理事会;
关键词：
seepage flow; fractional derivative; fractional alternating direction implicit scheme; modified Douglas scheme; stability and convergence; Richardson extrapolation; FINITE-DIFFERENCE METHODS; DIFFUSION EQUATION; APPROXIMATION;
D O I：
10.1093/imamat/hxn044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSF-UM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.
引用
收藏
页码：201 / 229
页数：29
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