Abstract
In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method of lines approach, the partial differential equation governing the contaminant transport in groundwater is converted into time-dependent ordinary differential equations. After this transformation, the time-integration of this system is realized by using an adaptive Runge–Kutta formula. In order to test the accuracy of the proposed method, four numerical examples were solved and the obtained results compared with various analytical and numerical solutions given in the literature. It is proven that the proposed method is faster and more reliable than other methods referenced herein and is a good alternative for simulation of contaminant transport problems as a result of these comparisons.
Highlights
Groundwater is one of the most important resources in the world
A new method of line approach based on B-spline functions is proposed for accurate simulation of two-dimensional contaminant transport problems
After the approximation of spatial derivatives, the partial differential equation representing the contaminant transport problem was converted to a time-dependent ordinary differential equation at each grid point
Summary
Groundwater is one of the most important resources in the world. This resource is used as clean water in many different fields such as domestic, industrial and agricultural. The need for clean water is increasing with the increase in the world population and the development of industrial and agricultural technologies. Both the quantity and the quality of groundwater are very important, because contaminated groundwater loses its intended use. In such cases, remediation works should be carried out for contaminated groundwater. Remediation works should be carried out for contaminated groundwater In these studies, modeling of contaminant transport in the relevant region is very important as it will provide an analysis of the current situation and provide information about the future status of the current pollution [1]
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