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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

1

Institution of the Russian Academy of Sciences Dorodnicyn Computing Centre

of RAS, Moscow, 119333, Russia

2

Bauman 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-

Keywords:

the steepest descent method, the objective function, the optimal control prob-

lem, a method of fast automatic differentiation.

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