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Course: Introduction to Modeling

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Course title Introduction to Modeling
Course code NTI/UM
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Lecturer(s)
  • Severýn Otto, doc. Ing. Ph.D.
Course content
Lectures: 1. Introduction. Concept of modelling, model-reality relationship. Types of models used in practice. Degrees of abstraction of models. 2. Partial differential equations (PDE). Definitions, examples, properties. Linear and nonlinear PDEs. Analytical solution of PDEs. 3. Equations of mathematical physics. Nabla and delta operators. Gradient, divergence and rotation operators - mathematical definition and physical examples. Types of PDEs of the 2nd order (elliptical, parabolic, hyperbolic). 4.,5. Overview of physical problems described by PDEs: Heat conduction, linear elasticity, electromagnetic field, Newtonian fluid flow, porous fluid flow, acoustics. Problem-specific PDEs (linear / nonlinear), typical boundary conditions. 6. Coupled problems: THM processes, piezoelectricity, poroelasticity, interaction of flow and fluid, aeroacoustics. 7. Problems of numerical solution of PDEs. Basic principles of approximation. Finite diference method. 8. Finite element method - basic principles, derivation, properties. 9. Other numerical methods - finite volumes method, meshless methods, LBM spectral methods. 10. Numerical linear algebra, methods of solving large sparse systems of linear algebraic equations produced by numerical methods for solving PDEs. 11. Input and output data of numerical methods, preparation of input data. Meshing, refinement, influence of mesh quality on results of modeling. 12. Tools for numerical modelling - libraries, general systems (Matlab, etc.), specialized tools (Ansys, Fluent, etc.). Postprocessing, visualization of results, visualization software tools. 13. Verification, validation and calibration of models, methods, tools. Use of optimization methods. Modelling with a high degree of uncertainty of input data. 14. Final summary. Questions of choice of suitable tools for modelling, available data, interpretation of results, degree of uncertainty of results. Seminars: Practising the topics covered in the lectures. In the second half of the semester, the creation of a simple numerical model and experiments with it.

Learning activities and teaching methods
Lecture, Practicum
  • Home preparation for classes - 40 hours per semester
  • Preparation for credit - 20 hours per semester
  • Preparation for exam - 34 hours per semester
  • Contacts hours - 56 hours per semester
Learning outcomes
The aim of the course is to acquaint students with the problems of numerical solution of partial differential equations (PDEs), especially in application for computer modelling of physical processes.

Prerequisites
Knowledge of the issue of solving ordinary differential equations and its numerical approximation. Basic knowledge of programming in a higher programming language.

Assessment methods and criteria
Combined examination

The credit is conditional on active participation in seminars, elaboration and defence of semester work. The exam is written and oral.
Recommended literature
  • Eriksson, K., Estep, D., Hansbo, P., Johnson, C. Computational Differential Equations. Cambridge, 1996. ISBN 0521563127.
  • Rektorys, K. Variační metody v inženýrských problémech a problémech matematické fyziky. Academia Praha, 1999.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Technical University of Liberec, date of update: 25.04.2024 23:50.