Numerical analysis of transport processes 2

Course guarantor:

Lecturer:

Tutor:

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Department of Mechanics

Synopsis:

Numerical analysis of transport processes 2 introduces the most popular numerical methods for solving stationary and non-stationary heat and moisture transfer in porous media. It covers the finite difference method, finite volume method, boundary element method, and finite element method. The main attention is paid to the finite element method. The main principles are discussed, e.g., Galerkin's method, spatial and time discretization, various types of finite elements and approximation functions, and numerical integration. Students will practice simple benchmarks and computer implementation.

Requirements:

No prerequisites.

Syllabus of lectures:

1. Introduction to FEM, transport processes

2. Galerkin method, weighted residual method - 1D heat conduction problem, steady state (FEM)

3. 2D heat conduction problem, steady state (FEM)

4. Aproximation functions and numerical integration - Gauss quadrature (FEM)

5. Finite elements - types, approx. functions (FEM)

6. Non-stationary 1D heat conduction problem (FEM)

7. Coupled non-stationary heat and moisture transfer (FEM) - solution of Künzel and Kiessl coupled model

8. Numerical Aspects of FEM

9. Introduction to the Finite Volume Method

10. Finite Difference Method

11. Introduction to the Boundary Element Method

12. Test

13. Reserve

Syllabus of tutorials:

1. Introduction, Introduction to Programming - Matlab, Octave, Excel; Semester project

2. Localization, conductivity matrix (FEM)

3. 1D heat conduction problem, steady state (FEM)

4. 2D heat conduction problem, steady state (FEM)

5. 2D heat conduction problem, steady state (FEM)

6. Non-stationary 1D heat conduction problem (FEM)

7. Non-stationary 1D heat conduction problem (FEM)

8. - 12. Non-stationary 1D heat conduction problem - computer code in Matlab, Octave

13. Reserve

Study Objective:

Students will be able to apply their knowledge of the finite element method to practical problems of heat and moisture transfer. The output of the course is a short PC program based on the finite element method. This program will be used to simulate heat transfer throughout an external wall of a real building.

Study materials:

1. Z. Bittnar - J. Šejnoha: Numerické metody mechaniky I a II, ČVUT Praha, 1992

2. K. Rektorys a spol.: Přehled užité matematiky I a II, vydavatelství Prometheus, s.r.o., 1995

3. K. Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky, Akademie věd České republiky, 1999

4. R. Černý: Transportní procesy (skriptum), ČVUT Praha, 1993

5. R. Černý: Řešení transportních procesů na počítači (skriptum), ČVUT Praha, 1997

6. O. C. Zienkewicz and R. L. Taylor: The Finite Element Method, Volume 1, The Basis, Fifth Edition, Butterworth-Heinemann, 2000

7. R. W. Lewis, B. Schrefler: The Finite Element Method in the Static and Dynamic Deformation and Consolidaion of Porous Media, Second Edition, John Wiley and Sons Ltd, 2000

8. H. M. Künzel - K. Kiessl: Calculation of Heat and Moisture Transfer in Eposed Buliding Componets, Int. J. Heat Mass Transfer, 40, 159-167, 1997

9. T. Krejčí, T. Nový, L. Sehnoutek and J. Šejnoha: Structure - Subsoil Interaction in view of Transport Processes inPorous Media, CTU Reports 1 Volume 5, 2001

Note:

Further information:

https://mech.fsv.cvut.cz/~krejci/vyuka/NTP2/ntp2.html

No time-table has been prepared for this course

The course is a part of the following study plans: