title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¸ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ Ð² Ð¿Ð°ÐºÐµÑÐµ OpenFOAM
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Implementation and verification of the shallow water model using OpenFOAM software
Creators: name: ÐÐ¾Ð¿Ð¾Ð², ÐÐ»Ð°Ð´Ð¸Ð¼Ð¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ
OpenFOAM
Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ Ð¾Ð±ÑÑÐ¼Ð¾Ð²
ÑÐ¾ÑÐ¼ÑÐ»Ð° ÐÐ°Ð½Ð½Ð¸Ð½Ð³Ð°
Ð¿Ð¾Ð»Ð¾Ð³Ð¸Ð¹ Ð±ÐµÑÐµÐ³
shallow water equations
finite volume method
Manning formula
sloping beach

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¿Ð°ÐºÐµÑÐ° OpenFOAM Ð±ÑÐ» ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ ÑÐµÑÐ°ÑÐµÐ»Ñ Ð´Ð»Ñ ÑÐ¸ÑÑÐµÐ¼Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÑÐ½Ð½ÑÐµ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ:
 1. ÐÑÐ²Ð¾Ð´ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ Ð¸Ð· ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð­Ð¹Ð»ÐµÑÐ°.
 2. Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿Ð°ÐºÐµÑÐ° OpenFOAM.
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 4. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÑÐµÐ¼ Ð½Ð° ÑÐ°Ð±Ð¾ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°.
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 6. Ð Ð°ÑÑÑÑ Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð½Ð°ÑÐµÐºÐ°Ð½Ð¸Ñ Ð½Ð° Â«Ð½ÐµÑÐ¾Ð²Ð½ÑÐ¹Â» Ð±ÐµÑÐµÐ³.
 ÐÑÑÐ¾Ð´Ð½ÑÐ¹ ÐºÐ¾Ð´ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾Ð»Ð²ÐµÑÐ° Ð±ÑÐ» Ð½Ð°Ð¿Ð¸ÑÐ°Ð½ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐ¾ÑÑÐ¾Ð¹ Ð¸ÑÐµÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÑÐµÐ¼Ñ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð¼ÐµÐ»ÐºÐ¾Ð¹ Ð²Ð¾Ð´Ñ Ñ ÐºÐ¾ÑÑÐµÐºÑÐ¸ÐµÐ¹ Ð²ÑÑÐ¾ÑÑ. ÐÐ»Ñ Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ¾Ð»Ð²ÐµÑÐ° Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð°ÑÑ Ð·Ð°Ð´Ð°ÑÐ° Ð½Ð°ÑÐµÐºÐ°Ð½Ð¸Ñ Ð²Ð¾Ð»Ð½Ñ Ð½Ð° Ð¿Ð¾Ð»Ð¾Ð³Ð¸Ð¹ Ð±ÐµÑÐµÐ³. ÐÑÐ»Ð¾ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¹ ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÑÐµÐ¼ Ð½Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ. ÐÑÐ»Ð° Ð¿ÑÐ¾ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¿Ð¾Ð¿ÑÐ°Ð²ÐºÐ° Ð½Ð° ÑÐ¸Ð»Ñ ÑÑÐµÐ½Ð¸Ñ Ð¿Ð¾ ÐÐ°Ð½Ð½Ð¸Ð½Ð³Ñ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ ÑÐ¾Ð»Ð²ÐµÑ Ð±ÑÐ» Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½ Ð´Ð»Ñ ÑÐµÑÑÐ¾Ð²Ð¾Ð³Ð¾ ÑÐ°ÑÑÑÑÐ° Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ Ð½ÐµÑÐ¾Ð²Ð½Ð¾Ð³Ð¾ Ð±ÐµÑÐµÐ³Ð°.
description: In this paper, using the OpenFOAM software package, a solver for the shallow water equations was implemented. 
 Tasks solved in the course of this work:
 1. Derivation of shallow water equations from Euler equations.
 2. Implementation of a numerical algorithm for solving shallow water equations using OpenFOAM software.
 3. Verification of the developed solution with problem of the flow around the sloping beach.
 4. Investigation on the effect of used numerical schemes.
 5. Testing of the developed solution using two-dimensional problem of the flow around the beach with the complex shape.
 The source code of the developed solver was written based on a simple iterative scheme for solving shallow water equations with height correction. For verification of the solver problem of the flow around the sloping beach was used. Research on convergence of the resulting numerical solution was conducted. Effect of used numerical schemes was investigated. Method correction using Manning formula was tested. For the test case of the derived solver was chosen two-dimensional problem of the flow around the beach with the complex shape.