Fractional vector calculus for fractional advection-dispersion

被引：145

作者：

Meerschaert, Mark M. ^{[1
]}

Mortensen, Jeff

Wheatcraft, Stephen W.

机构：

[1] Univ Otago, Dept Math & Stat, Dunedin 9001, New Zealand

[2] Univ Nevada, Dept Math & Stat, Reno, NV 89557 USA

[3] Univ Nevada, Dept Geol Sci, Reno, NV 89557 USA

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2006年 / 367卷

基金：

美国国家科学基金会;

关键词：

functional derivatives; advection-dispersion equation; porous media flow; transport;

D O I：

10.1016/j.physa.2005.11.015

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：181 / 190

页数：10

共 46 条

[1]

[Anonymous], 2002, FRACT CALC APPL ANAL

[2]

ARENDT W, 2001, MONOGRAPHYS MATH

[3] Subordinated advection-dispersion equation for contaminant transport [J].

Baeumer, B ;

Benson, DA ;

Meerschaert, MM ;

Wheatcraft, SW .

WATER RESOURCES RESEARCH, 2001, 37 (06) :1543-1550

[4] From continuous time random walks to the fractional Fokker-Planck equation [J].

Barkai, E ;

Metzler, R ;

Klafter, J .

PHYSICAL REVIEW E, 2000, 61 (01) :132-138

[5] Fractional Fokker-Planck equation, solution, and application [J].

Barkai, E .

PHYSICAL REVIEW E, 2001, 63 (04)

[6]

Bear J., 1972, Dynamics of Fluids in Porous Media

[7] The fractional-order governing equation of Levy motion [J].

Benson, DA ;

Wheatcraft, SW ;

Meerschaert, MM .

WATER RESOURCES RESEARCH, 2000, 36 (06) :1413-1423

[8] Application of a fractional advection-dispersion equation [J].

Benson, DA ;

Wheatcraft, SW ;

Meerschaert, MM .

WATER RESOURCES RESEARCH, 2000, 36 (06) :1403-1412

[9] Fractional dispersion, Levy motion, and the MADE tracer tests [J].

Benson, DA ;

Schumer, R ;

Meerschaert, MM ;

Wheatcraft, SW .

TRANSPORT IN POROUS MEDIA, 2001, 42 (1-2) :211-240

[10] Physical pictures of transport in heterogeneous media: Advection-dispersion, random-walk, and fractional derivative formulations [J].

Berkowitz, B ;

Klafter, J ;

Metzler, R ;

Scher, H .

WATER RESOURCES RESEARCH, 2002, 38 (10)

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