Non-linear mathematical model to predict the changes in underground water level and salt concentration

Abstract An urgent problem related to the process of change in underground water level and mineral salt transfer in soils is solved in the paper. The problem is described by a system of partial differential equations and the corresponding initial, internal and boundary conditions of various kinds. To derive a mathematical model of the process under consideration, a detailed review of scientific papers devoted to various aspects and software of the object of study is given. To conduct a comprehensive study of the process of filtration and change in salt regime of groundwater, mathematical models and an effective numerical algorithm are proposed taking into account external sources and evaporation. Since the process is described by a nonlinear system of partial differential equations, it is difficult to obtain an analytical solution. To solve it, a numerical algorithm based on a finite-difference scheme is developed, and an iterative scheme is used for nonlinear terms, the convergence of the iterative method is checked. In the conclusion of the paper it is shown that the developed mathematical apparatus can significantly reduce the volume of field experiments on monitoring and predicting the level of groundwater and salt concentration and minimize expensive and resource-intensive experimental work.

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