Open AccessAn Analytical Solution of Spatially Dependent One-Dimensional Advection-Dispersion Equation for a Varying Pulse Type Input Source
Author(s) -
Raja Ram Yadav,
Joy Sankar Deb Roy
Publication year - 2020
Publication title -
advances in modelling and analysis. a, general mathematical and computer tools
Language(s) - English
Resource type - Journals
ISSN - 1258-5769
DOI - 10.18280/ama_a.571-402
Subject(s) - dispersion (optics) , laplace transform , advection , exponent , mathematical analysis , mathematics , constant (computer programming) , porous medium , mechanics , physics , chemistry , porosity , thermodynamics , optics , linguistics , philosophy , computer science , programming language , organic chemistry
In present study, solution of advection-dispersion equation is obtained to determine concentration distribution of solute introduced from a varying pulse type point source in one-dimensional heterogeneous semi-infinite porous medium. Heterogeneity of the medium gives rise to space dependent groundwater velocity, dispersion coefficient and retardation factor. Groundwater velocity is some exponent ξ to a linear function of space. The dispersion and retardation factor are also exponents of same linear function with exponents (ξ+1) and (ξ-1), respectively, where ξ takes the value 0 or 1. At one end of the domain, a time dependent varying nature source, which involves step-size increasing function of time, acts along the flow up to a certain time the n eliminated while concentration gradient is considered zero at the other end of the domain. Initially, medium is uniformly polluted. Firstly, the advection-dispersion equation is reduced into constant coefficients by using certain transformations and then Laplace Integral Transformation Technique is utilized to get the solution. The obtained result is illustrated with numerical examples to study the effect of various parameters.