К вопросу математического моделирования процессов солепереноса в почве грунтах с учетом конвективного переноса

Abstract. The article is devoted to the questions of mathematical modeling of the motion of matter in porous inhomogeneous media as applied to the transfer of moisture and salts in soils. The need for mathematical modeling of such processes is determined both by the importance of the water and salt regime of the soil for agricultural production, and the effectiveness of mathematical modeling as a tool for understanding natural phenomena. For comparison, the heat conduction equations were chosen as a test example and graphical results were obtained. In contrast to the heat equation, the salt transfer equation contains members of low derivatives. To get rid of these terms, and bring this equation to the form of the heat equation, a change of variables was made. After that, to solve the problem, the methods proposed by the Samara Sobol are chosen. To solve the one-dimensional problem, the Picard method was used, and in each iteration, the resulting system of algebraic equations with a tridiagonal matrix is ​​solved by the sweep method. The important for the numerical modeling of estimates of the behavior of the free boundary for the nonlinear equation of salt transfer taking into account convective transfer is constructed. Numerical schemes of algorithms and program complexes for the specified tasks in the Matlab complex software have been developed.
Keyword. Salt mode, self-similar equation, convective transport, difference schemes.
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