VIJAY P SINGH
Articles written in Journal of Earth System Science
Volume 128 Issue 8 December 2019 Article ID 0203 Research Article
In the present study, analytical solutions of the advection dispersion equation (ADE) with spatially dependent concave and convex dispersivity are obtained within the fractal and the Euclidean frameworks by using the extended Fourier series method. The dispersion coefficient is considered to be proportional to the nth power of a non-homogeneous quadratic spatial function, where the index n is considered to vary between 0 and 1.5 so that the spatial dependence of dispersivity remains within the limit to describe the heterogeneity in the fractal framework. Real values like n ¼ 0.5 and 1.5 are considered to delineate heterogeneity of the aquifer in the fractal framework, whereas integral values like n = 1 represent thesame in the Euclidean sense. A concave or convex variation is free from demanding a limiting value as in the case of linear variation, hence it is more appropriate in the ambience of many disciplines in which ADE is used. In this study, concentration at the source site remains uniform until the source is present and becomes zero once it is annihilated forever. The analytical solutions, validated through the respective numerical solutions, are obtained in the form of an extended Fourier series with only first five terms. They are convergent to the desired concentration pattern and are stable with the Peclet number. It has been possible because of the formulation of a new Sturm–Liouville problem with advective information. The analytical solutions obtained in this paper are novel.
Volume 129 All articles Published: 1 January 2020 Article ID 0001 Research Article
Groundwater contamination due to multiple sources occurring in mega cities was modelled. One constant source contamination was considered at the source boundary, whereas other sources may join in between at various locations at different times. Initially, the aquifer was contamination-free in mega cities and was subsequently contaminated by means of different sources in due course of time. One-dimensional ADE (Advection Dispersion Equation) for modelling groundwater contamination was used and solved analytically in the semi-infinite aquifer domain for a finite number of point sources. A numerical solution wasalso obtained for two sources to compare analytical solutions. Results were examined for different velocity profiles to show the maximum contaminant concentration level with distance. This may be helpful to model the maximum possible number of point sources of contamination (i.e., it represents approximately what happens in the field situation). Some remedial measures may be taken to overcome these kinds of contamination problems in mega cities by treating the sources so that recharge of the aquifer is not affected.
Volume 130, 2021
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