Rakesh Singh - Academia.edu (original) (raw)

Papers by Rakesh Singh

Contaminant transport in a soil formation is described by advection dispersion equation. In this ... more Contaminant transport in a soil formation is described by advection dispersion equation. In this study, a horizontal and transversal contaminant transport along transient groundwater flow under non-linear sorption is solved numerically to examine the contaminant distribution profiles in finite soil media. The horizontal and transversal pore-water seepage velocities are defined as varying exponentially with time. Dispersion is considered directly proportional to the first power of the pore-water velocity. Axial input sources varying exponentially with time are assigned along the two-dimensional coordinate axes. For approximating the governing solute transport equation into algebraic equations, Crank-Nicolson (CN) and alternating direction implicit (ADI) methods are used. Both the numerical solutions are illustrated graphically with the help of computer software for various hydrological input data. In a special case, the numerical solutions are also compared with an approximate solution obtained by PDEtool. The comparison is performed with the help of contour plots. The CN method gives more accurate result than ADI method for the present model problem.

In this study, a one-dimensional non-linear advection-dispersion equation subject to spatial-temp... more In this study, a one-dimensional non-linear advection-dispersion equation subject to spatial-temporal dependent advection and dispersion coefficients is solved for a heterogeneous groundwater system. The non-linearity of the governing equation is based on the Freundlich and Langmuir sorption isotherms. The groundwater flow is considered to vary exponentially with time. Also, a generalized theory of the dispersion coefficient is used for extensive study of the model problem. The approximate solutions of the model problem are obtained in a semi-infinite and finite heterogeneous media by employing the Crank-Nicolson scheme. The exact solutions are obtained in both domains by the Laplace transform technique subject to linear sorption isotherm and non-transient flow conditions. Further, various graphical solutions are obtained using MATLAB scripts to examine the contaminant transport behaviour. For quantitative evaluation of the proposed model, a root mean square (RMS) error is computed. Overall, the results show that RMS error of the approximate solutions with respect to the exact solutions is within acceptable limits (less than 5%) for different combinations of discretization parameters. The robustness of the proposed model suggests its better suitability for modelling groundwater transport phenomena under the consideration of a non-linear sorption isotherm.

This study deals with a two-dimensional (2D) contaminant transport problem subject to depth varyi... more This study deals with a two-dimensional (2D) contaminant transport problem subject to depth varying input source in a finite homogeneous groundwater reservoir. A depth varying input source at the upstream boundary is assumed as the location of disposal site of the pollutant from where the contaminant enters the soil medium and ultimately to the groundwater reservoir. At the extreme boundary of the flow site, the concentration gradient of the contaminant is assumed to be zero. Contaminant dispersion is considered along the horizontal and vertical directions of the groundwater flow. The governing transport equation is the advection-dispersion equation (ADE) associated with linear sorption and first-order biological degradation. The ADE is solved analytically by adopting Laplace transform method. Crank-Nicolson scheme is also adopted for the numerical simulation of the modelled problem. In the graphical comparison of the analytical and numerical solutions, the numerical solution follows very closely with the analytical solution. Also, Root Mean Square (RMS) error and CPU run time are obtained to account for the performance of the numerical solution.

Groundwater pollution is a one of the major problems of our environment caused by various sources... more Groundwater pollution is a one of the major problems of our environment caused by various sources such as industries, pesticides, fertilizers, and mining activities. Convection-dispersion equation (CDE) is employed to model the transport of groundwater contamination mathematically, but it can be challenging due to complex geometries and hydrogeological characteristics. Moreover, for several realistic scenarios, the input contaminant source might be located at an intermediate location of the domain, leading to dispersion in forward and backward directions from the source point. Few previous works in this context have been approached analytically and limited to the one-dimensional (1D) assumption of the medium. In this study, a pollutant dispersion with an intermediate time-dependent point source is modelled mathematically. The forwardbackward pollutant distribution in a two-dimensional (2D) semi-infinite transient groundwater flow field is investigated. The concentration gradients are taken as zero across the final boundaries of the domain. The effect of off-diagonal dispersion is included in the model equation. The impact of various hydrological input parameters, such as dispersion, porosity, distribution coefficient, decay parameter, etc., on the pollutant transport is examined graphically. The proposed transport model problem is solved numerically and analytically using the Crank-Nicolson (CN) method, and Laplace transform technique (LTT), respectively. The accuracy of the proposed numerical method is evaluated by comparing it with the analytical solution using graphical and statistical measures. The obtained numerical solution of the 2D model problem shows a good agreement with the analytical solution. This may interest researchers working in surface water and vadose zone hydrology areas.

Forward-backward solute dispersion with an intermediate point source in one-dimensional semi-infi... more Forward-backward solute dispersion with an intermediate point source in one-dimensional semi-infinite homogeneous porous media is studied in this paper. Solute transport under sorption conditions, firstorder decay and zero-order production terms are included. The first type of boundary condition is taken as a constant point source at an intermediate point from where forward and backward solute dispersion is examined. The Laplace transform method is adopted to solve the governing equation analytically. All the analytical results are obtained in graphical form to investigate the forward-backward solute transport in porous media for various hydrological input data. The graphical nature of the analytical solution is compared with numerical data taken from existing literature and similar results are obtained. Also, numerical solution of the governing equation is obtained by the Crank-Nicolson finite difference scheme and validated with the analytical solution, which demonstrates good agreement between them. Accuracy of the solution is also observed by using RMSE.

In recent decades, the pollution of Earth sub-surface natural water has been a major problem thro... more In recent decades, the pollution of Earth sub-surface natural water has been a major problem throughout the world. It is polluted either naturally or by anthropogenic activities of human beings. Day by day quality of groundwater is cautiously deteriorating; as a result it became unfit for human beings. Once the groundwater become polluted, it is very difficult, time consuming and expensive to clean it up. Mathematical model plays important role to study about the solute or pollutant transport in aquifer. To study groundwater pollution, groundwater modelling is very helpful as it enables engineers or researchers to better understand complex systems, predict their behaviour, optimize designs and strategies, assess risks, and develop innovative solutions to address environmental and geotechnical challenges. In grigoundwater system, the solute dispersion and groundwater seepage velocity play a major role in solute transportation. Many researchers and scientists analyzed the relationship between these two crucial processes in the classical model of advection-diffusion equation (ADE). Freeze & Cherry (1979) found that dispersion correlates with the n th power of the seepage velocity with the exponent typically falling between Article Info

Hydrological Sciences Journal, 2020

Forward-backward solute dispersion with an intermediate point source in onedimensional semi-infin... more Forward-backward solute dispersion with an intermediate point source in onedimensional semi-infinite homogeneous porous media is studied in this paper. Solute transport under sorption condition, first-order decay and zero-order production terms are included. The first type boundary condition is taken as a constant point source at an intermediate point from where forward and backward solute dispersion is examined. The Laplace transform method is adopted to solve the governing equation analytically. All the analytical results are obtained in graphical form to investigate the forward-backward solute transport in porous media for various hydrological input data. The graphical nature of the analytical solution is compared with numerical data taken from existing literature and similar results are obtained. Also, numerical solution of the governing equation is obtained by Crank-Nicolson finite difference scheme and validated with the analytical solution, which demonstrated good agreement between them. Accuracy of the solution is also observed by using RMSE.

Hydrological Sciences Journal, 2020