Study of 2D contaminant transport with depth varying input source in a groundwater reservoir

Abstract

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 contaminant enters into 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.

The space between us: Modeling spatial heterogeneity in synthetic microbial consortia dynamics

“…Combined with a growing number of experimental approaches for designing consortia with specific spatial arrangements, including optogenic, seeding, and other approaches ( 20 , 22 , 23 , 24 ), modulating consortium dynamics through spatial organization is becoming more practical. Since the underlying numerical scheme used to solve our reaction-diffusion equation model has routinely been applied in higher dimensions ( 39 , 40 , 41 , 42 ), our framework is well suited to interrogate the effects of the more complex spatial organizations implemented by these experimental methods ( 23 , 43 , 44 , 45 ). Through enabling these investigations into the impact of spatial organization on microbial consortium dynamics, we hope that our modeling framework helps advance the understanding of these systems and supports the development of new applications involving them.…”

A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

“…On the other hand, implicit methods work with the whole system matrix, thus they can be extremely slow with huge memory usage when the number of cells is large. Still, these methods are typically used for solving these kinds of equations, see for example [10][11][12][13][14][15][16].…”

Aquifer-wide estimation of longitudinal dispersivity by the combination of empirical equations, inverse solution, and aquifer zoning methods

“…Simulation of groundwater quality could be considered an appropriate tool for aquifer management and planning (Ansarifar et al 2020a, b). Typically, the governing equation (the related partial differential equations) is used to predict contaminant dispersion's spatial and temporal distribution in an aquifer (Singh et al 2021).…”