THREE-DIMENSIONAL HAUSDORFF DERIVATIVE DIFFUSION MODEL FOR ISOTROPIC/ANISOTROPIC FRACTAL POROUS MEDIA

被引：19

作者：

Cai, Wei ^{[1
]}

Chen, Wen ^{[2
]}

Wang, Fajie ^{[2
]}

机构：

[1] Hohai Univ, Coll Mech & Elect Engn, State Key Lab Hydrol Water Resources & Hydraul En, Changzhou, Peoples R China

[2] Hohai Univ, Coll Mech & Mat, Inst Soft Matter Mech, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing, Jiangsu, Peoples R China

来源：

THERMAL SCIENCE | 2018年 / 22卷

基金：

中国国家自然科学基金;

关键词：

anomalous diffusion; Hausdorff derivative; fundamental solution; Hausdorfffractal distance; FRACTIONAL DIFFUSION; ANOMALOUS DIFFUSION; TRANSPORT; EQUATION;

D O I：

10.2298/TSCI170630265C

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorfffractal distance and the fundamental solution. The concept of the Hausdorfffractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to I. The fundamental solution of the 3-D Hausdorff fractal derivative diffusion equation is proposed on the basis of the Hausdorfffractal distance. With the help of the properties of the Hausdorff derivative, the Huasdorff diffusion model is also found to be a kind of time-space dependent convection-diffusion equation underlying the anomalous diffusion behavior.

引用

页码：S1 / S6

页数：6