Open AccessAnalysis of application and improvement of methods to solve discrete models of Boltzmann equation
Author(s) -
В. П. Жуков,
A.Ye. Barochkin,
A. N. Belyakov,
О. В. Сизова
Publication year - 2021
Publication title -
vestnik igèu
Language(s) - English
Resource type - Journals
ISSN - 2072-2672
DOI - 10.17588/2072-2672.2021.6.062-069
Subject(s) - markov chain , boltzmann equation , boltzmann constant , mathematics , computer science , boltzmann machine , statistical physics , markov process , quality (philosophy) , energy (signal processing) , mathematical optimization , statistics , physics , artificial intelligence , thermodynamics , quantum mechanics , artificial neural network
To describe technological systems using models of Markov chains and discrete models of the Boltzmann equation it is necessary to determine the probabilities of transition of a system from one state to another. An urgent topic of a scientific research is to improve the accuracy of solving the Boltzmann equation by making a reasonable choice of probabilities of transition and admissible areas of their application. The strategy to model and determine the probabilities of transitions is based on the finite volume method, the ratios of the theory of probability and the joint analysis of material and energy balances. Considering the ratios of the theory of probability, the authors have obtained the refined formula for the probabilities of transitions over the cells of the computational space of discrete models of the Boltzmann equations in case of the description of technological systems. Recommendations to choose the area of application of the model are presented. The computational analysis has showed a significant improvement of the quality of forecasting when we implement the proposed dependencies and recommendations. The relative error of calculating the energy of the system is reduced from 8,4 to 2,8 %. The presented calculated dependencies to determine the probabilities of transition and recommendations for their application can be used to simulate various technological processes and improve the quality of their description.