• Naveen Kumar

      Articles written in Journal of Earth System Science

    • Analytical solutions of one-dimensional advection–diffusion equation with variable coefficients in a finite domain

      Atul Kumar Dilip Kumar Jaiswal Naveen Kumar

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      Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the finite domain.This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity.The input condition is considered continuous of uniform and of increasing nature both.The analytical solutions are obtained by using Laplace transformation technique.In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.

    • One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

      Sanjay K Yadav Atul Kumar Dilip K Jaiswal Naveen Kumar

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      The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

    • Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

      Abhishek Sanskrityayn Naveen Kumar

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      Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.

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