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# Math. J. Interdiscip. Sci. ### Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM

Dipak J Prajapati and N B Desai

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https://doi.org/10.15415/mjis.2018.71003

## Volume 7, Number 1 (Sep-2018)

 KEYWORDS Advection, Dispersion, Convergence-control parameter, Discrete squared residual PUBLISHED DATE September, 2018 PUBLISHER The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications. ABSTRACT This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation. INTRODUCTION Solutions of advection-dispersion equation (ADE) may be used to predict the concentration of solutes in unsteady groundwater flow. Advection causes the contaminant plum to flow in the direction of groundwater water without any change in the shape. Dispersion of plum arises due to the variation in groundwater velocity. The heterogeneity of the porous medium is responsible for dispersion. The solute transport in heterogeneous aquifer is thus the combined process of advection and dispersion. The dispersion in the direction of groundwater flow is called longitudinal dispersion and the transverse dispersion is perpendicular to the groundwater flow direction. The ADE can be derived using Fick’s law and low of conservation of mass. Analytical solutions in one-dimensional problems through semi-infinite or finite porous media have been presented by several researchers: (Mazaheri et. al. 2013, Kumar et. al. 2010, Marino et al. 1974, Singh et al. 2008) etc. The objective of this work is to derive an approximate analytical solution of ADE with the help of Optimal Homotopy Analysis Method (OHAM). In this work, an approximate analytical solution of one-dimensional ADE in heterogeneous finite aquifer is derived for continuous time dependent input source concentration of increasing nature. Page(s) 15-20 URL http://dspace.chitkara.edu.in/jspui/bitstream/123456789/756/3/003_MJIS.pdf ISSN Print: 2278-9561, Online: 2278-957X DOI https://doi.org/10.15415/mjis.2018.71003 CONCLUSION The approximate analytical solution of advection-dispersion equation with variable coefficients is obtained by optimal homotopy analysis method with time-dependent input source concentration. The contaminant transport behaves as expected i.e. the concentration at a fixed time decreases as the distance increases and the concentration at a fixed position advances with time. The solution is useful as a preliminary predictive tool for simulating the solute migration in aquifer due to the release of a time-dependent source. REFERENCES Baxter M., Van Gorder R. A., Vajravelu K (2014). 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