title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐµÐ»ÑÐµÑÐ° ÑÐµÑÑÐ¸ÑÐ¾ÑÐ¸Ð¸ Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ ÑÑÐ¾Ð·Ð¸Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ SPH
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: Modelling of landform change through erosion by SPH method
Creators: name: Ð¥Ð°Ð¼ÑÐ¾ÐµÐ², ÐÐ»ÐµÐºÑÐ°Ð½Ð´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: 2024
Subjects: ÑÑÐ¾Ð·Ð¸Ñ
Ð³Ð¸Ð´ÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° ÑÐ³Ð»Ð°Ð¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ
Ð»Ð°Ð½Ð´ÑÐ°ÑÑ
Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ
erosion
smoothed particle hydrodynamics
landscape
optimisation

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ ÑÐµÐ»ÑÐµÑÐ° Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÑÐ¾Ð·Ð¸Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° Ð³Ð¸Ð´ÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¸ ÑÐ³Ð»Ð°Ð¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ (SPH). ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾Ð´ÑÐµÑÐºÐ¸Ð²Ð°ÐµÑ Ð°ÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÐ°Ð»Ð¸ÑÑÐ¸ÑÐ½Ð¾Ð³Ð¾ Ð»Ð°Ð½Ð´ÑÐ°ÑÑÐ° Ð² ÑÐ°ÐºÐ¸Ñ Ð¿ÑÐ¸Ð»Ð¾Ð¶ÐµÐ½Ð¸ÑÑ, ÐºÐ°Ðº ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð²Ð¸Ð´ÐµÐ¾Ð¸Ð³Ñ Ð¸ Ð³ÐµÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ. ÐÐµÑÐ¾Ð´ SPH Ð±ÑÐ» Ð²ÑÐ±ÑÐ°Ð½ Ð·Ð° ÐµÐ³Ð¾ ÑÐ¿Ð¾ÑÐ¾Ð±Ð½Ð¾ÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ»Ð¾Ð¶Ð½ÑÐµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð¼ÐµÐ¶Ð´Ñ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÑÑ Ð¸ ÑÐ²ÐµÑÐ´ÑÐ¼ ÑÐµÐ»Ð¾Ð¼ Ð±ÐµÐ· ÑÐ¸ÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐµÑÐºÐ¸. ÐÐ¾Ð´ÑÐ¾Ð±Ð½Ð¾ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ñ SPH, Ð²ÐºÐ»ÑÑÐ°Ñ Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ñ Ð¸ ÑÐ°ÑÑÐµÑ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸, Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ Ð²ÑÐ·ÐºÐ¾ÑÑÐ¸ ÑÐ°ÑÑÐ¸Ñ. ÐÐ½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ðµ Ð²Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÐ»ÐµÐ½Ð¾ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÑ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð². Ð­ÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð²ÐµÑÐµÐ½Ð° Ð½Ð° ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÑÐµÐ½Ð°ÑÐ¸ÑÑ, ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ð²Ð½ÑÑÑÐ¸ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÐµÐ¿Ð¸Ð¿ÐµÐ´Ð° Ð¸ Ð½Ð°Ð²Ð¾Ð´Ð½ÐµÐ½Ð¸Ðµ. Ð Ð·Ð°ÐºÐ»ÑÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð¼ ÑÐ°Ð·Ð´ÐµÐ»Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ¾Ð·Ð¸Ð¸, Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÑÑÐ¸Ðµ, ÐºÐ°Ðº Ð²Ð¾Ð´Ð½ÑÐ¹ Ð¿Ð¾ÑÐ¾Ðº Ð¼Ð¾Ð¶ÐµÑ Ð¸Ð·Ð¼ÐµÐ½ÑÑÑ Ð»Ð°Ð½Ð´ÑÐ°ÑÑÑ, Ð¿ÐµÑÐµÐ½Ð¾ÑÑ ÑÐ°ÑÑÐ¸ÑÑ Ð¿Ð¾ÑÐ²Ñ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¸Ð¼ÐµÑÑ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¿ÑÐ¸ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ð¸ ÑÐµÐ°Ð»Ð¸ÑÑÐ¸ÑÐ½ÑÑ Ð»Ð°Ð½Ð´ÑÐ°ÑÑÐ¾Ð² Ð´Ð»Ñ Ð²Ð¸Ð´ÐµÐ¾Ð¸Ð³Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð² Ð³ÐµÐ¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ñ Ð¸ Ð¸Ð½Ð¶ÐµÐ½ÐµÑÐ½ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸ÑÑ. ÐÑÐ´ÑÑÐ¸Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð³ÑÑ ÑÐ¾ÑÑÐµÐ´Ð¾ÑÐ¾ÑÐ¸ÑÑÑÑ Ð½Ð° ÑÐ¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¸ ÑÐ°ÑÑÐ¸ÑÐµÐ½Ð¸Ð¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° SPH Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¿ÑÐ¸ÑÐ¾Ð´Ð½ÑÑ Ð¸ ÑÐµÑÐ½Ð¾Ð³ÐµÐ½Ð½ÑÑ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð².
description: This paper deals with the modelling of terrain deformation by erosion using the Smoothed Particle Hydrodynamics (SPH) method. The study highlights the relevance of realistic landscape modelling in applications such as video game development and geological studies. The SPH method was chosen for its ability to model complex fluid-solid interactions without a fixed mesh. The principles of SPH are discussed in detail, including interpolation and calculation of particle density, pressure and viscosity. Considerable attention is paid to the computational optimisation. The effectiveness of the proposed algorithms has been tested on various scenarios such as fluid interaction inside a parallelepiped and flooding. In the final section, erosion modelling results are presented, demonstrating how water flow can modify landscapes by transporting soil particles. The results have practical applications in creating realistic landscapes for video games, as well as in geological and engineering studies. Future research may focus on improving optimisation algorithms and expanding the application of the SPH method for modelling various natural and anthropogenic processes.