Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals

This work is devoted to the construction of a locally one-dimensional difference scheme for calculating the first boundary value problem for a general parabolic equation for the mass distribution function of ice particles. The functions are introduced such that and give at each point at time the con...

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Главные авторы:	Khibiev, A. H., Хибиев, А. Х.
Формат:	Статья
Язык:	English
Опубликовано:	Pleiades Publishing 2025
Темы:	Approximation error Stability Difference scheme Convergence of the scheme Boundary value problem
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/30362
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record_format	dspace
spelling	ir-123456789-303622025-04-02T11:51:54Z Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals Khibiev, A. H. Хибиев, А. Х. Approximation error Stability Difference scheme Convergence of the scheme Boundary value problem This work is devoted to the construction of a locally one-dimensional difference scheme for calculating the first boundary value problem for a general parabolic equation for the mass distribution function of ice particles. The functions are introduced such that and give at each point at time the concentration of cloud droplets and ice particles, respectively, whose mass is in the range from to The equation is written with respect to the function ; the function (the droplet mass distribution function) is given in the equation. The equation is part of a system of integro-differential equations for the mass distribution functions of droplets and ice particles describing microphysical processes in convective clouds against the background of a given thermohydrodynamics. A locally one-dimensional difference scheme for a general parabolic equation in a ‑dimensional parallelepiped is constructed by the method of total approximation. To describe the interaction of droplets and crystals, nonlocal (nonlinear) integral sources are included in the equation. Using energy inequalities, an a priori estimate is obtained, from which follows the stability and convergence of the difference scheme. The results of the work will be used to build a model of microphysical processes in mixed convective clouds, which will be used to conduct research in topical areas such as the study of the role of the system properties of clouds in the formation of their microstructural characteristics and the development of technology for managing precipitation processes in convective clouds by introducing particles of ice-forming reagents. 2025-04-02T11:50:20Z 2025-04-02T11:50:20Z 2024 Статья Ashabokov B.A., Khibiev A.K., Shkhanukov-Lafishev M.K. Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals // Theoretical Foundations of Chemical Engineering. - 2024. - 58 (5). - pp. 1745 - 1751. - DOI: 10.1134/S0040579525600457 https://dspace.ncfu.ru/handle/123456789/30362 en Theoretical Foundations of Chemical Engineering application/pdf application/pdf Pleiades Publishing
institution	СКФУ
collection	Репозиторий
language	English
topic	Approximation error Stability Difference scheme Convergence of the scheme Boundary value problem
spellingShingle	Approximation error Stability Difference scheme Convergence of the scheme Boundary value problem Khibiev, A. H. Хибиев, А. Х. Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
description	This work is devoted to the construction of a locally one-dimensional difference scheme for calculating the first boundary value problem for a general parabolic equation for the mass distribution function of ice particles. The functions are introduced such that and give at each point at time the concentration of cloud droplets and ice particles, respectively, whose mass is in the range from to The equation is written with respect to the function ; the function (the droplet mass distribution function) is given in the equation. The equation is part of a system of integro-differential equations for the mass distribution functions of droplets and ice particles describing microphysical processes in convective clouds against the background of a given thermohydrodynamics. A locally one-dimensional difference scheme for a general parabolic equation in a ‑dimensional parallelepiped is constructed by the method of total approximation. To describe the interaction of droplets and crystals, nonlocal (nonlinear) integral sources are included in the equation. Using energy inequalities, an a priori estimate is obtained, from which follows the stability and convergence of the difference scheme. The results of the work will be used to build a model of microphysical processes in mixed convective clouds, which will be used to conduct research in topical areas such as the study of the role of the system properties of clouds in the formation of their microstructural characteristics and the development of technology for managing precipitation processes in convective clouds by introducing particles of ice-forming reagents.
format	Статья
author	Khibiev, A. H. Хибиев, А. Х.
author_facet	Khibiev, A. H. Хибиев, А. Х.
author_sort	Khibiev, A. H.
title	Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
title_short	Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
title_full	Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
title_fullStr	Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
title_full_unstemmed	Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals
title_sort	locally one-dimensional scheme for the distribution function equation by ice particle masses considering the interaction of droplets and crystals
publisher	Pleiades Publishing
publishDate	2025
url	https://dspace.ncfu.ru/handle/123456789/30362
work_keys_str_mv	AT khibievah locallyonedimensionalschemeforthedistributionfunctionequationbyiceparticlemassesconsideringtheinteractionofdropletsandcrystals AT hibievah locallyonedimensionalschemeforthedistributionfunctionequationbyiceparticlemassesconsideringtheinteractionofdropletsandcrystals
_version_	1842245545427468288

Locally One-Dimensional Scheme for the Distribution Function Equation by Ice Particle Masses Considering the Interaction of Droplets and Crystals

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