Introduction to Modelling of Multiphysics Problems

Introductory Course on Multiphysics Modelling (ICMM)

Tomasz G. Zieliński

NEW:

• new Slides (see 18)

Lecture Notes & Slides

0. Course Outline    notes / slides
1. Mathematical Preliminaries    notes / slides
2. Introduction to Partial Differential Equations    notes / slides
3. Exercises on Partial Differential Equations    notes / slides
4. Weigthed Residual Methods    notes / slides
5. Ritz Method    notes / slides
6. Introduction to Finite Element Method    notes / slides
7. Heat Transfer Problems    notes / slides
8. Galerkin Finite Element Model for Heat Transfer    notes / slides
9. Tutorials on Heat Transfer using COMSOL Multiphysics
10. Fundamentals of Linear Elasticity    notes / slides
11. Tutorials on Elasticity, Thermoelasticity, and model implementation using COMSOL Multiphysics PDE Interfaces    notes / slides
12. Fundamentals of Piezoelectricity    notes / slides
13. Tutorials on Piezoelectricity using COMSOL Multiphysics
14. Ideal Flow Theory and Basic Aerodynamics    notes / slides
15. Elementary Viscous Flow    notes / slides
16. Tutorials on Fluid-Structure Interaction (FSI) using COMSOL Multiphysics
17. Waves in Fluids    notes / slides
18. Basics of Multiscale Modelling: Tutorial on Porous Media Flow using COMSOL Multiphysics    slides
19. Fundamentals of Acoustics    notes / slides
20. Tutorials on Acoustics and Vibroacoustics using COMSOL Multiphysics
21. Bulk and Surface Acoustic Waves in Piezoelectric Media    notes / slides
22. Tutorials on Piezoelectric Surface Acoustic Waves using COMSOL Multiphysics

Thematic Quiz

Quiz - for the Introductory Course on Multiphysics Modelling (ICMM)

Course Outline

Introductory lectures:

1. General mathematical preliminaries
2. Basics of Partial Differential Equations (PDEs)
   • types and classifications
   • review of solution techniques
   • review of classic PDEs
3. Fundamentals of Finite Element Method (FEM)
   • Weighted Residual Methods
   • Ritz-Galerkin method
   • the equivalence of strong and weak formulations
   • various FEM issues (procedures, shape functions, etc.)

Problems to discuss:

4. Heat transfer
5. Linear elasticity
6. Thermo-elasticity (thermo-mechanical coupling)
7. Fluid dynamics (and the basics of aerodynamics)
8. Waves in fluids
9. Fluid-structure interaction
10. Acoustics and vibroacoustics (acoustic-structure interaction)
11. Piezoelectricity (electro-mechanical coupling)
12. Wave propagation in anisotropic media
13. Surface Acoustic Waves
14. Multi-scale modelling (example: transport in porous media)

For each problem, (all or some of) the following topics will be covered:

• derivation of the governing PDE (fundamental principles and constitutive laws, primary and secondary dependent variables)
• discussion of boundary conditions (from the physical and mathematical points of view)
• derivation of the weak formulation
• the Galerkin approximation (definitions and interpretations of the coefficient matrices)
• discussion of analogies and possible couplings to other problems

Short Course
(April-May 2019, October-November 2019, November-December 2021)