Math. J. Interdiscip. Sci.

Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM

Dipak J Prajapati and N B Desai

  • Download PDF
  • DOI Number

Advection, Dispersion, Convergence-control parameter, Discrete squared residual

PUBLISHED DATE September 6, 2018
PUBLISHER The Author(s) 2018. This article is published with open access at

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.

Page(s) 15-20
ISSN Print: 2278-9561, Online: 2278-957X
  • Mathew Baxter, Robert A. Van Gorder, Kuppalapalle Vajravelu. On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem, Numerical Algorithms, 66(2) 269–298 (2014).
  • Pintu Das, Sultana Begam, Mritunjay Kumar Singh. Mathematical modeling of groundwater contamination with varying velocity field, Journal of Hydrology and Hydromechanics, 65(2) 192–204 (2017).
  • Atul Kumar, Dilip Kumar Jaiswal, Naveen Kumar. Analytical solutions to one-dimensional advection diffusion equation with variable coefficients in semi-infinite media, Journal of Hydrology, 380(3-4), 330–337 (2010).
  • Shijun Liao. An optimal homotopy analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., 15, 2003–2016 (2010).
  • Miguel A. Marino. Distribution of contaminants in porous media flow, Water Resources Research, 10(5) (1974).
  • M. Mazaheri, J. M. V. Samani, H. M. V. Samani. Analytical solution to one-dimensional advectiondiffusion equation with several point sources through arbitrary time-dependent emission rate patterns, J. Agr. Sci. Tech., 15, 1231–1245 (2013).
  • Dipak J. Prajapati, N. B. Desai. The solution of immiscible fluid flow by means of optimal homotopy analysis method, International Journal of Computer and Mathematical Sciences, 4(8) (2015).
  • Dipak J. Prajapati, N. B. Desai. Application of the basic optimal homotopy analysis method to fingering phenomenon, Global Journal of Pure and Applied Mathematics, 12(3), 2011–2022 (2016).
  • Dipak J. Prajapati, N. B. Desai, Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fuid effect, Kalpa Publications in Computing, 2, 85–94 (2017).
  • Dipak J. Prajapati, N. B. Desai. Approximate analytical solution for the fingero-imbibition phenomenon by optimal homotopy analysis method, International Journal of Computational and Applied Mathematics, 12(3), 751–761 (2017).
  • Dipak J. Prajapati, N. B. Desai. Analytic analysis for oil Recovery during cocurrent imbibition in inclined homogeneous porous medium, International Journal on Recent and Innovation Trends in Computing and Communication, 5(7), 189–194 (2017).
  • Dipak J. Prajapati, N. B. Desai. Mathematical investigation of counter-current imbibition phenomenon in heterogeneous porous medium, PRAJNA - Journal of Pure and Applied Sciences, 24-25 38–46 (2017).
  • Mritunjay Kumar Singh, Premlata Singh, Vijay P. Singh. Analytical solution for solute transport along and against time dependent source concentration in homogeneous finite aquifers, Advances in Theoretical and Applied Mechanics, 3(3), 99–119 (2010).
  • Mritunjay Kumar Singh, Nav Kumar Mahato, Premlata Singh. Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer, Journal of Earth System Science, 117(6) 945–949 (2008).
  • A. E. Scheidegger. General theory of dispersion in porous media, Journal of Geophysical Research, 66(10) 3273–3278 (1961).
  • Moujin Xu, Yoram Eckstein. Statistical analysis of the relationships between dispersivity and other physical properties of porous media. Hydrogeology Journal, 5(4) 4–20 (1997).