numerical solution

One of the main issues threatening hydraulic structures is the uplift pressure caused by the water flow in the porous media under the structures. Cut-off walls installed underneath a hydraulic structure can reduce the uplift pressure, by changing the water flow velocity, and as a result, the possibility of cracking and fracturing in the body of the structure. In this study, the effect of inclined cut-off walls with different angles of inclination (to the horizontal axis) underneath an irrigation canal (with laboratory dimensions) on the water flow velocity in the porous medium was investigated. The changes in the velocity due to the inclination were obtained using the Hydrus-2D numerical model. The velocity under the canal with no cut-off walls showed slight fluctuations, but increased owing to all the angles of inclination, reaching its maximum at the location of the cut-off walls. The most effective cut-off walls in increasing the velocity were the closest ones to the horizontal axis, i.e., those with angles of 15°, 30° and 165°, while the less effective angles were 90° and 120°, which were closer to the vertical line. The velocity just below the canal bottom increased with an increase in the angle, so that it changed by 18.05% and 209.45% due to the angles 15° and 165°, respectively. In fact, the cut-off walls performed better as they inclined from the earth’s surface to the canal bottom. In general, the angle of inclination should be selected based on the groundwater level, vulnerability of the walls and bottom of the canal, and economic considerations.

The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The flow velocity is considered temporally dependent in homogeneous media however, both spatially and temporally dependent is considered in heterogeneous porous media. First-order degradation term is taken into account to obtain a solution using Laplace Transformation Technique (LTT) for both the medium. The solute concentration distribution and breakthrough are depicted graphically. The effect of different transport parameters is studied through proposed analytical investigation. Advection-dispersion theory of contaminant mass transport in porous media is employed. Numerical solution is also obtained using Crank Nicholson method and compared with analytical result. Furthermore, accuracy of the result is discussed with root mean square error (RMSE) for both the medium. This study has developed a transport and prediction 2-D model that allows the early remediation and removal of possible pollutant in both the porous structures. The result may also be used as a preliminary predictive tool for groundwater resource and management.

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e. its semi-infinite part. Without losing any generality, one can consider that the aquifer is initially contamination-free. Thus, the current study explores variations of two-dimensional contaminant concentration with depth throughout the domain, showing them graphically. Non-point source problem, i.e. the line source problem, can be discussed by solving two-dimensional depth-dependent variable source problem, as x=0 is a 2D line. A new transformation has been used to transform the time-dependent ADE to one with constant coefficients, with Matlab (pdetool) being employed in order to solve the problem, numerically, using finite element method.

The rapid increase in technological innovations and utilizations have adversely affected the environment and consequently continued to constitute a threat to the future survival of human. To counter these assaults and the threats of further degradation of the environment and human health, the basic recommended approach for predicting the impact of the pollution and for the determination of the risk assessment strategies is through the use of mathematical models. Therefore, this work presents mathematical models for the prediction of the effects of combustion generated pollutants, such as Carbon-monoxide (CO) on human health. The developed coupled system of nonlinear partial differential equation for the ambient concentration of carbon mono-oxide in which the human subject was exposed to and the concentration of Carboxyhemoglobin (COHb) in the blood is solved numerically using Alternating-Direct Implicit (ADI) scheme. From the computations, the variables of the models show significant results in their variations and the standard error of the predicted results from the model range in between 0.5-0.85 for the different concentrations of ambient carbon monoxide. This established that the computed results show good agreement with available experimental data. Therefore, the model can be used as a means of controlling the effects of the pollutant on human health and the results will serve as a way of evaluating our technological injuries, effectively controlling our pollutants emissions and also as a tool for designing and developing better equipments and engines with lower carbon or pollutants emissions.