Abstract: An advection-dispersion equation subjected to temporally and spatially dependent groundwater velocity, dispersion coefficient along with a time dependent pulse type input of time varying nature is solved for one dimensional semi-infinite porous medium. Input concentration is any continuous smooth function of time acts up to some finite time and then eliminated. Concentration gradient at other boundary domain is considered zero. Dispersion is linearly and squarely proportional to groundwater velocity in temporal and spatial measurement respectively. Initially, medium is uniformly polluted. Interpolation method is applied to reduce the input function into a polynomial. Using certain transformations the advection-dispersion equation is reduced to constant coefficient and freed from convective part then Laplace transform technique is applied to get the solution of advection-dispersion equation. Two different functions of input are discussed to understand the utility of the present study. Obtained result is demonstrated graphically with the help of numerical example.
Keywords: Summation; Advection; Dispersion; Porous Medium; Interpolation; Laplace Transformation.
How to cite this article:
R. R. Yadav and Joy Roy, One-Dimensional Solute Transport in a Heterogeneous Porous Media with Pulse Type Input Source, International Journal of Advances in Mathematics, Volume 2018, Number 6, Pages 35-51, 2018.