Выходит 12 номеров в год
ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337
Indexed in
Optimal Control of Intensity of Water Point Sources in Unsaturated Porous Medium
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Краткое описание
Moisture transfer in an unsaturated porous medium with point sources, described by the Richards−Klute equation is a very complicated and unstable computational process. This can be explained by the fact that the physical process, described by this equation, is characterized by a large number of diverse parameters. For reduction of this complexity we propose the approach, based on the Kirchhoff transformation, which enables reduction of the quasilinear parabolic initial-boundary problem to a linear and dimensionless problem. In this paper a two-dimensional quasilinear problem of optimal control using point sources for a rectangular unsaturated porous medium with known initial conditions, fixed humidity at the bottom bound and the given target humidity, is considered. In this statement the problem is studied and solved for the first time. To solve the linear dimensionless optimal control problem on non-stationary moisture transport in an unsaturated porous medium obtained using the Kirchhoff transformation, the variation algorithm of identifying the optimal source power is used, which allows modeling the process under realistic assumptions. The correctness of linearized dimensionless problem of moisture transfer is proved. In particular, theorems of existence and uniqueness of the generalized solution are proven as well as the existence and the uniqueness of the optimal control of power of the immersed sources. Modelling of moisture transfer from an immersed source in a dry ground area is done. The results of numerical experiments showing high accuracy of the method are adduced. The proposed method allows solving the urgent problem of selection of the optimal parameter for a drip irrigation system and improvement of its efficiency.
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