Mathematical modeling of energy processes

Description: This discipline considers the issues of mathematical modeling in terms of problems of heat power engineering: mathematical models of energy processes, their forms, construction and simplification; methods and algorithms in systems with lumped parameters in static and dynamic systems; methods and algorithms in systems with dispersed parameters; solution of boundary value problems; methods and algorithms in geometric objects.

Amount of credits: 5

Пререквизиты:

• Theoretical basics of heat engineering

Course Workload:

Component: Component by selection

Cycle: Base disciplines

Goal

• to connect the general theoretical course of mathematics with its specific application in solving various problems of heat power engineering, to give a mathematical and methodological apparatus for applied research.

Objective

• To prepare doctoral studentfor the perception of theoretical issues in special courses and the conscious application in solving applied problems of methods and techniques that lead most quickly to reliable results. Students should have an idea about a number of basic tasks solved in the field of thermal power engineering: calculations of normal modes of operation of thermal equipment, research on the stability of its operation, optimization of modes according to the criterion of energy efficiency.

Learning outcome: knowledge and understanding

• Know the basic mathematical equations for solving energy problems, be able to carry out calculations to obtain results.

Learning outcome: applying knowledge and understanding

• Have the skills to formulate mathematical problems of energy processes, apply programming methods to solve the tasks, analyze the results in accordance with the boundary and initial conditions.

Learning outcome: formation of judgments

• Have the ability to substantiate a mathematical solution and simulate technological processes in the energy sector to solve industrial, practical and laboratory problems.

Learning outcome: communicative abilities

• Be able to analyze the modes of operation of heat engineering equipment based on mathematical methods, investigate the stability of its operation, process the results obtained and analyze the modes of operation of energy processes in a team.

Learning outcome: learning skills or learning abilities

• Possess the skills to determine the feasibility of research and processing the results obtained, use modern computing tools when conducting research based on mathematical and computer modeling of energy processes.

Teaching methods

In the conditions of credit technology of education, classes should be conducted mainly in active and creative forms. Among the effective pedagogical methods and technologies that contribute to the involvement of students in the search and management of knowledge, the acquisition of experience in independent problem solving, we should highlight: - technology of problem-based and project-based learning; - technologies of educational and research activities; - communication technologies (discussion, press conference, brainstorming, educational debates and other active forms and methods); - case method (situation analysis); - gaming technologies, within which students participate in business, role-playing, simulation games; - information and communication (including distance learning) technologies.

Topics of lectures

• Introduction
• Approximation of functions
• Approximation of functions of one variable
• Elements of probability theory and mathematical statistics
• Systems
• Control
• Optimization tasks
• Linear programming
• Nonlinear programming
• Analytical methods for finding the conditional and unconditional extremum of a function of several variables
• Numerical methods for finding the conditional extremum of a function of several variables
• Birneshe aynymaly funktsionalnyn shartty extremumyn tabudyn sandyk adisteri

Key reading

• Гордиевский И.Г. Критериальный анализ некоторых технико- экономических задач энергетики. - М.: Высшая школа, 2002.
• Волков Л.Т. Математические задачи энергетики. Типовые задачи: Учеб.пос. / -М.: Энергия, 2003.
• Трусов П.В. Введение в математическое моделирование. -М.: «Логос», 2004.
• Логинов, В.С. Примеры и задачи по тепломассообмену: Учебное пособие / В.С. Логинов, А.В. Крайнов, В.Е. Юхнов и др. - СПб.: Лань, 2019. - 256 c.

Further reading

• Уравнения в частных производных для инженеров: Перевод с английского. Шарма Дж.Н., Сингх К. - Изд.: «Техносфера», 2002.
• Оптимальные решения: Лекции по методам обработки измерений. Саврасов Ю.С. - Изд.: «Радио и связь», 2000. - 151 с.
• Рунова, Е.М. Примеры и задачи по тепломассообмену: Учебное пособие / Е.М. Рунова, С.А. Чжан и др. - СПб.: Лань, 2011. - 256 c.
• Пашков, Л. Т. Математические модели процессов в паровых котлах / Л. Т. Пашков. — Москва, Ижевск : Институт компьютерных исследований, 2019. — 208 c. — ISBN 978-5-4344-0716-8. https://www.iprbookshop.ru