title: ÐÑÐµÐ½ÐºÐ° ÐºÐ°ÑÐµÑÑÐ²Ð° Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð´Ð²ÑÐ¼ÐµÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð³Ð»ÑÐ±Ð¾ÐºÐ¸Ð¼Ð¸ ÑÐ²ÐµÑÑÐ¾ÑÐ½ÑÐ¼Ð¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐ¼Ð¸ ÑÐµÑÑÐ¼Ð¸
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: Estimation of quality ofprediction of characteristics of two-dimensional flows by deep convolutionalneural networks
Creators: name: ÐÐ°ÑÐ°Ð½Ð¾Ð², ÐÐ°ÑÐ¸Ð»Ð¸Ð¹
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: 2023
Subjects: ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ðµ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ðµ
Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
ÐºÑÑÐ»Ð¾Ð²Ð¾Ð¹ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ
Ansys Fluent
Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ
Python
TensorFlow
Ð³Ð»ÑÐ±Ð¾ÐºÐ¸Ðµ ÑÐ²ÑÑÑÐ¾ÑÐ½ÑÐµ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸
Ð¿Ð°ÑÐ°Ð»Ð»ÐµÐ»ÑÐ½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹
numerical simulation
laminar flow
two-dimensional flow
airfoil
machine learning
deep convolutional neural networks
parallel model training

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°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¼ÐµÑÐ¾Ð´Ð¸Ðº Ð¸ Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐµÐ¹ Ð¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð³Ð»ÑÐ±Ð¾ÐºÐ¸Ñ ÑÐ²ÑÑÑÐ¾ÑÐ½ÑÑ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÑ ÑÐµÑÐµÐ¹ Ð´Ð»Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð´Ð²ÑÐ¼ÐµÑÐ½ÑÑ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÑ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÑÐ¾ÑÐ°Ð±Ð¾ÑÐºÐ° Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐ½ÑÑ Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ¾Ð², Ð¾ÑÐ²ÐµÑÐ°ÑÑÐ¸Ñ Ð²Ð¾Ð¿ÑÐ¾ÑÑ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÑÐ²ÑÑÑÐ¾ÑÐ½ÑÑ Ð¸ÑÐºÑÑÑÑÐ²ÐµÐ½Ð½ÑÑ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÑ ÑÐµÑÐµÐ¹ Ðº Ð·Ð°Ð´Ð°ÑÐ°Ð¼ Ð¸Ð· Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÐ¸ Ð¸ Ð³Ð°Ð·Ð°, Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ Ð±Ð°Ð·Ð¸ÑÑÑÑÐ¸ÑÑÑ Ð½Ð° Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð°Ð²ÑÐ¾ÐºÐ¾Ð´Ð¸ÑÐ¾Ð²ÑÐ¸ÐºÐ¾Ð². 2. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð½Ð° ÑÐ·ÑÐºÐµ Python Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¾ÑÐºÑÑÑÐ¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ TensorFlow Ð¸ Ð´ÑÑÐ³Ð¸Ñ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐº Ð½Ð°Ð±Ð¾ÑÐ° Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÐµÐ¹ Ñ ÑÐ°Ð·Ð½ÑÐ¼Ð¸ Ð°ÑÑÐ¸ÑÐµÐºÑÑÑÐ°Ð¼Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾Ð³Ð¾ ÑÐ¾Ð¿ÑÑÑÑÐ²ÑÑÑÐµÐ³Ð¾ ÐºÐ¾Ð´Ð°. 3. ÐÐ¾Ð´Ð³Ð¾ÑÐ¾Ð²ÐºÐ° ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð´Ð»Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð»Ð°Ð¼Ð¸Ð½Ð°ÑÐ½Ð¾Ð¼ Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ð¸ ÐºÑÑÐ»Ð¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð±Ð°Ð·Ð¾Ð²Ð¾Ð¹ ÑÐ°ÑÑÐµÑÐ½Ð¾Ð¹ ÑÐµÑÐºÐ¸, ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð¸ÑÑÑÑÐ¸Ñ ÑÐºÑÐ¸Ð¿ÑÐ¾Ð² Ð¸ ÑÑÐ¸Ð»Ð¸Ñ Ð´Ð»Ñ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¼Ð°ÑÑÐ¾Ð²ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð² Ð¿Ð°ÐºÐµÑÐµ ANSYS Fluent, Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ð¸ Ð¸ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿Ð¾Ð»ÐµÐ¹ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½ Ð² Ð¿Ð°ÐºÐµÑÐµ Tecplot 360. 4. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÑ ÑÑÐµÐ´ÑÑÐ² Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ ÑÐµÑÐ¸Ð¸ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð¾Ð±ÑÐµÐºÐ°Ð½Ð¸Ñ ÐºÑÑÐ»Ð¾Ð²Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÑÐ¸Ð»Ñ Ð´Ð»Ñ ÑÐ°Ð·Ð½ÑÑ ÑÐ³Ð»Ð¾Ð² Ð°ÑÐ°ÐºÐ¸ Ð² ÑÐµÐ»ÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ Ð½Ð°Ð±Ð¾ÑÐ¾Ð² Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÐµÐ¹ (ÐºÐ°ÑÑÐ¸Ð½ Ð¿Ð¾Ð»ÐµÐ¹ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½). 5. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ·ÑÐºÐ° Python Ð¸ Ð´Ð¾Ð¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÑ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐº, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ñ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐ°ÑÑ Ð½Ð°Ð±Ð¾Ñ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ Ð´Ð°ÑÐ°ÑÐµÑÐ°, Ð¿ÑÐ¸Ð³Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð´Ð»Ñ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÐµÐ¹. 6. ÐÑÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÑ Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÐµÐ¹ Ð½Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð½Ð°Ð±Ð¾ÑÐ°Ñ Ð´Ð°Ð½Ð½ÑÑ. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÐºÐ°ÑÐµÑÑÐ²Ð° Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÐ¹ÑÐ¾ÑÐµÑÑÑ ÑÐµÑÐµÐ½Ð¸Ñ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼Ð¾Ð³Ð¾ ÑÐ¸Ð¿Ð°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÑ Ð²ÑÐµ Ð²ÑÑÐµÐ¿ÐµÑÐµÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð±ÑÐ»Ð¸ ÑÑÐ¿ÐµÑÐ½Ð¾ ÑÐµÑÐµÐ½Ñ, Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ Ð¾ÑÐ¸Ð³Ð¸Ð½Ð°Ð»ÑÐ½ÑÐ¹ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð» Ð¸ Ð¾Ð¿ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ Ð² Ð±ÑÐ´ÑÑÐ¸Ñ ÑÐ°Ð±Ð¾ÑÐ°Ñ Ð¿Ð¾ ÑÐµÐ¼Ð°ÑÐ¸ÐºÐµ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð² Ð¾Ð±ÑÑÐ¶Ð´Ð°ÐµÐ¼Ð¾Ð¹ Ð¿ÑÐµÐ´Ð¼ÐµÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸.
description: This work is devoted to research and development of methods and study of possibilities and efficiency of deep convolutional neural networks for prediction of characteristics of two-dimensional stationary laminar flows. The objectives of the research were: 1. Review of literary sources covering the issues of practical application of convolutional artificial neural networks to the problems from the field of fluid and gas mechanics, including those based on the use of autoencoders. 2. Development in Python using the open-source library TensorFlow and other libraries of a set of neural networks with different architectures, as well as the necessary accompanying code. 3. Preparing a computational statement for the problem of laminar flow over the airfoil in a two-dimensional formulation, the construction of the base computational grid, the development of automated scripts and utilities for the ANSYS Fluent bulk parametric calculations, interpolation, and visualization of the fields of values in the Tecplot 360 package. 4. Using the developed automation tools, to conduct a series of calculations of laminar flow over the airfoil for different angles of attack to obtain data sets for training neural networks (pictures of fields of values). 5. Development of programs using the Python language and additional libraries to process the data set to obtain a dataset suitable for neural network training. 6. Development of training methods for the developed neural networks on the obtained datasets. Training and quality analysis of neural network prediction of the flow of the type considered. As a result of the work all the above tasks have been successfully solved, and the original material and experience can be used in future works on the application of machine learning methods in the discussed subject area.