title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐµÑÑÑÐ¾ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ¾Ð»ÑÑÐ¼Ð°Ð½Ð° Ð¸ ÐµÐ³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð´Ð»Ñ ÑÐ°ÑÑÑÑÐ° Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ LES
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: The implementation of the method of lattice Boltzmann equations and its application for the calculation of some turbulent flows based on LES
Creators: name: ÐÐ°Ð±ÐµÐ»Ð»Ð¾, ÐÐ¾Ð½ÑÑÐ°Ð½ÑÐ¸Ð½
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: Ð¼ÐµÑÐ¾Ð´ ÑÐµÑÐµÑÐ¾ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ¾Ð»ÑÑÐ¼Ð°Ð½Ð°
ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ
Ð²ÑÑÐ¾ÐºÐ¾Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð¸ÑÐµÐ»ÑÐ½ÑÐµ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ
lattice Boltzmann method
turbulent flows
high-performance computing

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐµÑÐµÑÐ¾ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ¾Ð»ÑÑÐ¼Ð°Ð½Ð° (LBM) Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð½ÐµÑÐ¶Ð¸Ð¼Ð°ÐµÐ¼Ð¾Ð¹ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ LES-Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾ÑÐµÐ½ÐºÐ¸ ÐµÐ³Ð¾ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð² ÐºÐ¾Ð½ÑÐµÐºÑÑÐµ Ð²ÑÑÐ¾ÐºÐ¾Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð¸ÑÐµÐ»ÑÐ½ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: â¢ Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐµÑÐµÑÐ¾ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÐÐ¾Ð»ÑÑÐ¼Ð°Ð½Ð° Ð² Ð²Ð¸Ð´Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐµ Fortran. â¢ ÐÑÐµÐ½ÐºÐ° ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»Ð¸Ð·Ð°ÑÐ¸Ð¸ LBM Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ OpenMP Ð¸ MPI. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¾Ð´Ð½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð° Ð¿Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ LB Ð¸ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ Ð¾Ð±ÑÐµÐ¼Ð¾Ð² (FVM). â¢ ÐÐ¿ÑÐ¾Ð±Ð°ÑÐ¸Ñ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½Ð° Ð·Ð°Ð´Ð°ÑÐ°Ñ Ð¾ ÑÐ°ÑÐ¿Ð°Ð´Ðµ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð³Ð¾ Ð²Ð¸ÑÑÑ Ð¢ÐµÐ¹Ð»Ð¾ÑÐ°-ÐÑÐ¸Ð½Ð°, Ð²ÑÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ð¸ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¸Ð·Ð¾ÑÑÐ¾Ð¿Ð½Ð¾Ð¹ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ Ð¸ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ð¸ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð¿Ð¾Ð´ ÑÐ³Ð»Ð¾Ð¼ Ð°ÑÐ°ÐºÐ¸ Ð² 45 Ð³ÑÐ°Ð´ÑÑÐ¾Ð². Ð Ð°ÑÑÐµÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»Ð¸ÑÑ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ ÐºÐ»Ð°ÑÑÐµÑÐ° ÑÐµÐºÑÐ¸Ð¸ "ÐÐ¸Ð´ÑÐ¾Ð°ÑÑÐ¾Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°, Ð³Ð¾ÑÐµÐ½Ð¸Ðµ Ð¸ ÑÐµÐ¿Ð»Ð¾Ð¾Ð±Ð¼ÐµÐ½" ÐÑÑÑÐµÐ¹ ÑÐºÐ¾Ð»Ñ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð¾Ð¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¸ Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ¸Ð·Ð¸ÐºÐ¸ Ð¡ÐÐ±ÐÐ£. ÐÑÐ¼ÐµÑÐµÐ½Ñ Ð²ÑÑÐ¾ÐºÐ¸Ðµ ÑÑÐµÐ±Ð¾Ð²Ð°Ð½Ð¸Ñ LBM Ðº Ð¾Ð±ÑÐµÐ¼Ñ Ð¸ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ ÑÐ°Ð±Ð¾ÑÑ Ñ Ð¿Ð°Ð¼ÑÑÑÑ, ÑÑÐ¾ Ð´ÐµÐ»Ð°ÐµÑ OpenMP-Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»Ð¸Ð·Ð°ÑÐ¸Ñ Ð½ÐµÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð¹. ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾Ð¹ Ð¿Ð°Ð¼ÑÑÐ¸, Ð½Ð°Ð¿ÑÐ¾ÑÐ¸Ð², Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÑÐµÑ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ðµ ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ðµ. ÐÑÐµÐ¼Ñ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¾Ð´Ð½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð° Ð¿Ð¾ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð² LBM Ð½Ð° Ð¿Ð¾ÑÑÐ´Ð¾Ðº Ð¼ÐµÐ½ÑÑÐµ, ÑÐµÐ¼ Ð² FVM. ÐÐ¾Ð»ÑÑÐµÐ½Ð¾ ÑÐ¾ÑÐ¾ÑÐµÐµ ÑÐ¾Ð²Ð¿Ð°Ð´ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñ Ð¾ ÑÐ°ÑÐ¿Ð°Ð´Ðµ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð³Ð¾ Ð²Ð¸ÑÑÑ Ð¢ÐµÐ¹Ð»Ð¾ÑÐ°-ÐÑÐ¸Ð½Ð° Ð¸ Ð²ÑÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ð¸ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¸Ð·Ð¾ÑÑÐ¾Ð¿Ð½Ð¾Ð¹ ÑÑÑÐ±ÑÐ»ÐµÐ½ÑÐ½Ð¾ÑÑÐ¸. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð± Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ° Ð´Ð»Ñ FVM Ð¸ LBM Ð¿Ð¾ÐºÐ°Ð·Ð°Ð»Ð¾ Ð½ÐµÐ¿ÑÐ¸Ð³Ð¾Ð´Ð½Ð¾ÑÑÑ Ð¿Ð¾ÑÐ»ÐµÐ´Ð½ÐµÐ³Ð¾ Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð´Ð¾Ð±Ð½Ð¾Ð³Ð¾ ÑÐ¾Ð´Ð° Ð·Ð°Ð´Ð°Ñ Ð¿Ð¾ Ð¿ÑÐ¸ÑÐ¸Ð½Ðµ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½ÑÑ ÑÐ°ÑÑÐµÑÐ½ÑÑ ÑÐµÑÐ¾Ðº Ð¸ Ð¾ÑÑÑÑÑÑÐ²Ð¸Ñ Ð½ÐµÐ¾ÑÑÐ°Ð¶Ð°ÑÑÐ¸Ñ Ð²ÑÑÐ¾Ð´Ð½ÑÑ Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹, ÑÑÐ¾ Ð¿ÑÐµÐ´ÑÑÐ²Ð»ÑÐµÑ Ð²ÑÑÐ¾ÐºÐ¸Ðµ ÑÑÐµÐ±Ð¾Ð²Ð°Ð½Ð¸Ñ Ðº Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼ ÑÐµÑÑÑÑÐ°Ð¼, Ð² Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ Ðº Ð¿Ð°Ð¼ÑÑÐ¸.
description: This work is devoted to the study of the applicability of the lattice Boltzmann equations (LBM) method for modeling turbulent incompressible fluid flows using the LES model, as well as evaluating its effectiveness in the context of high-performance computing. Tasks that were solved during the work: â¢ Implementation of the lattice Boltzmann method in the Fortran program. â¢ Evaluating the effectiveness of LBM parallelization using OpenMP and MPI. Comparison of the execution of a single step in time by the LB method and finite volumes (FVM). â¢ Approbation of the proposed model on the problems of the decay of a three-dimensional Taylor-Green vortex, degeneration of homogeneous isotropic turbulence and flow around a square cylinder at an angle of attack of 45 degrees. The calculations were carried out using the computing cluster of the section "Hydroaerodynamics, gorenje and heat Transfer" of the Higher School of Applied Mathematics and Computational Physics of SPbPU. LBMs high requirements for the volume and speed of working with memory are noted, which makes OpenMP parallelization ineffective. The use of distributed memory, on the contrary, demonstrates almost linear acceleration. The execution time of a single time step in LBM is an order of magnitude less than in FVM. The results are in good agreement with the literature data for the problems of the decay of a three-dimensional Taylor-Green vortex and the degeneracy of homogeneous isotropic turbulence. A comparison of solutions to the cylinder flow problem for FVM and LBM showed the unsuitability of the latter for solving such problems due to homogeneous computational grids and the absence of non-reflective output boundary conditions, which places high demands on computing resources, especially memory.