Analytical Solution of Contaminant Transport Equation in River by Arbitrary variable coefficients using Generalized Integral Transform Technique

Document Type : Original Paper


1 Department of Water Structures, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran

2 *Department of Water Structures, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran

3 Sharif University of Technology


Contamination transport in the river is expressed using advection-dispersion-reaction partial differential equation (ADRE). There are a variety of analytical and numerical methods for solving the aforementioned equation. Analytical solutions such integral transforms are very powerful and useful tools in solving ADRE. In the present study, one-dimensional ADRE with space-dependent coefficients in river has been solved using generalized integral transform technique (GITT). Forward and inverse transformations are defined in GITT technique which using them in problem solving leads to generating time-dependent system of ordinary differential equations. Analytical solution verification was accomplished using the comparison of the results of mathematical models with analytical solutions and also numerically model based on finite differences method. To inspect the accuracy of models’ results, statistical indicators were calculated. Comparison of GITTs’ result with analytical solutions that used in verification and numerical solution implied high accuracy of the proposed solution. Also to show the importance of the application of variable coefficients in ADRE in river, the results of solving equation with constant and variable coefficients were compared. 


Main Subjects

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