Numerical simulation of unsteady underground water filtration in a porous medium
Abstract
The problem of the process of unsteady underground water filtration in a porous medium considered in the paper is an urgent one. It is related to design and developmentof hydraulic structures, regulation of groundwater runoff, flooding, salinization and waterlogging; all these cause great damage to the national economy. For the developmentof a mathematical model of the process, the research associated with this problem is analyzed in detail in this paper and a mathematical apparatus for studying and predictingchanges in the groundwater level during the process of filtering in porous media is proposed. To construct a mathematical model of the process, Darcy’s law is used and thesource of infiltration (rain, watering) and evaporation is taken into account. The task in the study is considered at various boundary and internal conditions. Since the process isdescribed by a nonlinear differential equation in partial derivatives, an analytical solution is difficult to obtain. To solve it a numerical algorithm based on a finite-difference schemehas been developed; an iterative scheme is used for nonlinear terms, its convergence is checked. Various locally-one-dimensional schemes were constructed for solving boundaryproblems of filtering in simply connected and multiply connected regions. The resulting system of a tridiagonal algebraic equation is solved by the sweep method. To illustratethe developed schemes, several examples of problem solving are given and the results of numerical experiments on computers are analyzed in detail; the conclusions are drawnthat the heterogeneity of the aquifer significantly affects the change in the groundwater level during the filtration process. It is found that the weight scheme is the most appropriateto solve the problems of groundwater filtration in multiply connected filtering regions.