 # Numerical Methods in Continuum Mechanics

Elective courses registration form

Course 'Numerical Methods in Continuum Mechanics' is a successor of the course 'Engineering Numerical Methods'.

No of hours per week: 3  [2 + 1], one term   ECTS: 4

 Lecturer: Assistent:

Study: graduate study of mechanical engineering
Course: process and energy
Orientation: energy
Term: III term
Course type:
Field-related

Knowledge assessment:
continous [colloquy, programs]

Type of exercises:
Laboratory

Exam prerequisites:
Thermodynamics I, Fluid Mechanics I
Course Goal:
Introduce students to the numerical methods used in continuum mechanics, with an emphasis on numerical modelling of heat and mass transfer. The main objective of the course is to provide advanced knowledge necessary for the mathematical modelling of heat and mass transfer and numerical solutions which may serve for a better understanding of real processes in modern engineering systems.

Recommended literature:
1. S.V . Patankar, Numerical Heat Transfer and Fluid Flow, chap. 6, Hemisphere, Washington, D.C. and Mc Graw-Hill, New York,1985.
2. D.A. Anderson, J.C. Tanchill, R.H. Pletcher, Computational flud mechanic and heat transfer, Hemisphere, New York, 1984.
3. R.S. Hirsch, Numerical Computation of Internal and External Flows, vol. I i II, John Wiley and Sons, New York, Brisbone, Toronto, Singapour, 1991.

Exam dates

Week Lectures   Exercises

1. Introduction. Modelling problems in continuum mechanics.   The application of numerical methods in engineering systems.
2. Demonstration of commercial computer packages for control volume method.   Application of a commercial software package for control volume method.
3. Creation of geometry for a model. The generation of network control volume. Types of network control volumes.   Creating a model geometry using the network control volume. Examples of 2D mesh generation.
4. The generation of network control volumes in complex geometries.   Creating complex geometry models using the network control volume. Examples of automatically generating a 3D network.
5. Basic laws of continuum mechanics.   Basic laws of continuum mechanics and their applications.
6. The initial and boundary conditions.   Examples of applying the initial and boundary conditions in engineering systems using the software package for the control volume method. Setup in a computer package.
7. Numerical differentiation. Numerical integration.   Examples of numerical differentiation. Examples of numerical integration.
8. Control volume method.   Simple examples of application of control volumes for problems of heat and mass transfer.
9. Discretization of time. Explicit and implicit methods.   Application of explicit and implicit methods of solving.
10. Methods for solving systems of linear equations.   Solving systems of linear equations.
11. Modelling of turbulence. Demonstration of turbulence models. Fundamentals of turbulence.   Numerical simulation of heat and mass transfer in a simple example using the software package for the control volume method. Application of the k-epsilon turbulence model.
12. RANS turbulence modelling.   Numerical simulation of turbulent flow using the k-zeta f turbulence models.
13. Large eddies simulation - LES.   Numerical simulations of large eddies.
14. Critical review of the numerical methods, consistency, stability, convergence, efficiency, evaluation errors.   Comparison of different numerical methods to simple examples.
15. Numerical methods and computer.   Preparing for a class project.