scholarly journals Analytical simulation of two dimensional advection dispersion equation of contaminant transport

2017 ◽  
Vol 21 (5) ◽  
pp. 827
Author(s):  
A.T. Cole ◽  
A Abdulrahim ◽  
R.O. Olayiwola ◽  
M.D. Shehu
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Two Dimensional ◽  
Advection Dispersion ◽  
Analytical Simulation

Numerical treatment for solving two-dimensional space-fractional advection–dispersion equation using meshless method

2018 ◽  
Vol 32 (06) ◽  
pp. 1850073 ◽  
Author(s):  
Rongjun Cheng ◽  
Fengxin Sun ◽  
Qi Wei ◽  
Jufeng Wang
Keyword(s):  
Dispersion Equation ◽  
Convergence Rates ◽  
Dimensional Space ◽  
Energy Functional ◽  
Least Square ◽  
Approximation Schemes ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Moving Least Square ◽  
Advection Dispersion

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

scholarly journals Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

2013 ◽  
Vol 61 (2) ◽  
pp. 146-160 ◽  
Author(s):  
Martinus Th. van Genuchten ◽  
Feike J. Leij ◽  
Todd H. Skaggs ◽  
Nobuo Toride ◽  
Scott A. Bradford ◽  
...  
Keyword(s):  
Surface Water ◽  
Dispersion Equation ◽  
Contaminant Transport ◽  
Analytical Solutions ◽  
Decay Chain ◽  
Transport Processes ◽  
Dispersive Transport ◽  
Chain Reactions ◽  
Surface Water Hydrology ◽  
Advection Dispersion

Abstract Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective- dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.

scholarly journals Exact Analytical Solutions for Contaminant Transport in Rivers

2013 ◽  
Vol 61 (3) ◽  
pp. 250-259 ◽  
Author(s):  
Martinus Th. van Genuchten ◽  
Feike J. Leij ◽  
Todd H. Skaggs ◽  
Nobuo Toride ◽  
Scott A. Bradford ◽  
...  
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Analytical Solutions ◽  
Hyporheic Zone ◽  
Decay Chain ◽  
Transport Processes ◽  
Dispersive Transport ◽  
Chain Reactions ◽  
First Order ◽  
Advection Dispersion

Abstract Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advectivedispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.

scholarly journals Subordinated advection-dispersion equation for contaminant transport

2001 ◽  
Vol 37 (6) ◽  
pp. 1543-1550 ◽  
Author(s):  
Boris Baeumer ◽  
David A. Benson ◽  
Mark M. Meerschaert ◽  
Stephen W. Wheatcraft
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Advection Dispersion

A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation

2015 ◽  
Vol 8 (1) ◽  
pp. 166-186 ◽  
Author(s):  
Guofei Pang ◽  
Wen Chen ◽  
Kam Yim Sze
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Comparative Study ◽  
Dispersion Equation ◽  
Dimensional Space ◽  
Finite Difference Methods ◽  
Rectangular Domain ◽  
Two Dimensional ◽  
Element Analysis ◽  
Advection Dispersion

AbstractThe paper makes a comparative study of the finite element method (FEM) and the finite difference method (FDM) for two-dimensional fractional advection-dispersion equation (FADE) which has recently been considered a promising tool in modeling non-Fickian solute transport in groundwater. Due to the non-local property of integro-differential operator of the space-fractional derivative, numerical solution of FADE is very challenging and little has been reported in literature, especially for high-dimensional case. In order to effectively apply the FEM and the FDM to the FADE on a rectangular domain, a backward-distance algorithm is presented to extend the triangular elements to generic polygon elements in the finite element analysis, and a variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the FEM compares favorably with the FDM in terms of accuracy and convergence rate whereas the latter enjoys less computational effort.

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