Модель фильтрации сквозь однородную пористую среду

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Модель фильтрации сквозь однородную пористую среду
Инженерный журнал: наука и инновации # 9·2016 11
Filtration model through a homogeneous porous medium
© A.A. Gurchenkov 1,2, M.V. Nosov 1
1Institution of the Russian Academy of Sciences Dorodnicyn Computing Centre
of RAS, Moscow, 119333, Russia
2Bauman Moscow State Technical University, Moscow, 105005, Russia
The study considers a model of vertical water transfer in soil; describes the water trans-
fer process by one-dimensional nonlinear parabolic equation. The diffusion coefficient
and the soil hydraulic conductivity included in the equation is calculated by van Genuch-
ten formulas widely used in practice. An important model component is the evaporation
from the soil surface. The study formulates the problem of determining evaporation as an
optimal problem — the one, in which the phase variables are the soil moisture values at
different depths, and control is the desired evaporation. The mean-square soil moisture
values deviation from some prescribed values derived from calculations based on the
hydrological models is the objective function. We solve the numerical optimization by the
steepest descent method; the objective function gradient is calculated using the fast au-
tomatic differentiation method (FAD).
Keywords: the steepest descent method, the objective function, the optimal control prob-
lem, a method of fast automatic differentiation.
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