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Total Approximation Method for an Equation Describing Droplet Breakup and Freezing in Convective Clouds

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Abstract

A locally one-dimensional scheme for a general parabolic equation in a \(p\)-dimensional parallelepiped is considered. A special nonlocal integral source is added to the considered equation to describe droplet breakup and freezing in convective clouds. An a priori estimate for the solution of the locally one-dimensional scheme is obtained, and its convergence is proved.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-31-90094.

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Authors and Affiliations

  1. Institute of Computer Science and Problems of Regional Management, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, 360051, Nalchik, Russia

    B. A. Ashabokov

  2. Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, 360051, Nalchik, Russia

    A. Kh. Khibiev & M. Kh. Shkhanukov-Lafishev

Authors
  1. B. A. Ashabokov
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  2. A. Kh. Khibiev
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  3. M. Kh. Shkhanukov-Lafishev
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Corresponding author

Correspondence to A. Kh. Khibiev.

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Translated by I. Ruzanova

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Ashabokov, B.A., Khibiev, A.K. & Shkhanukov-Lafishev, M.K. Total Approximation Method for an Equation Describing Droplet Breakup and Freezing in Convective Clouds. Comput. Math. and Math. Phys. 60, 1518–1527 (2020). https://doi.org/10.1134/S0965542520090055

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  • DOI: https://doi.org/10.1134/S0965542520090055

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