Advanced Numerical Methods in Coupled Multiphysics Problems
Code  Completion  Credits  Range  Language 

D32PNM  ZK  2P  Czech 
 Garant předmětu:
 Jaroslav Kruis
 Lecturer:
 Jaroslav Kruis
 Tutor:
 Jaroslav Kruis
 Supervisor:
 Department of Mechanics
 Synopsis:

The aim of the course is to solve coupled multiphysics problems, e.g. thermoelasticity, coupled heat and moisture transfer, thermohydromechanical problem, electordiffusion, etc. First, the balance equations together with constitutive laws will be summarized for selected coupled multiphysics problems. Discretization in space and time (GalerkinBubnov method, GalerkinPetrov method, generalized trapezoidal rule, etc.) will follow. Solution of systems of linear algebraic equations obtained after discretization (the use of symmetry and sparsity, direct methods, iterative methods). Solution of systems of nonlinear algebraic equations (NewtonRaphson method, the arclength method). Utilization of parallel computers for solution of large problems based on domain decomposition methods.
 Requirements:

Elementary knowledge of ordinary and partial differential equations and theory of continuum.
 Syllabus of lectures:

1. Summary of theory of continuum medium (strain, stress, heat flux, etc.).
2. Description of pore space in porous material.
3. Viscous flow, Hagen law, capillary effects.
4. Basic balance equations.
5. Basic constitutive laws (Hook's law, Fourier's law, Darcy's law, Fick's law).
6. Coupled heat and moisture transport.
7. Coupled mechanicsmoisture transport with influence of temperature.
8. Transport of chlorides.
9. GalerkinBubnov method for diffusion problems.
10. GalerkinPetrov method for diffusionadvection problem.
11. Integration in time (generalized trapezoidal rule).
12. Systems of nonlinear algebraic equations, NewtonRaphson method.
13. Introduction of methods for solution of systems of linear algebraic equations.
 Syllabus of tutorials:

1. Summary of theory of continuum medium (strain, stress, heat flux, etc.).
2. Description of pore space in porous material.
3. Viscous flow, Hagen law, capillary effects.
4. Basic balance equations.
5. Basic constitutive laws (Hook's law, Fourier's law, Darcy's law, Fick's law).
6. Coupled heat and moisture transport.
7. Coupled mechanicsmoisture transport with influence of temperature.
8. Transport of chlorides.
9. GalerkinBubnov method for diffusion problems.
10. GalerkinPetrov method for diffusionadvection problem.
11. Integration in time (generalized trapezoidal rule).
12. Systems of nonlinear algebraic equations, NewtonRaphson method.
13. Introduction of methods for solution of systems of linear algebraic equations.
 Study Objective:

Students will be introduced into multiphysics problems and their numerical solution based on the finite element method.
 Study materials:

R.W. Lewis, B.A. Schrefler: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. John Wiley & Sons, 2000, Chichester, England.
O.C. Zienkiewicz, R.L. Taylor: The Finite Element Method. Volume 1 The Basis. Butterworth Heinemann, 2000, Oxford, UK, 5th edition.
O.C. Zienkiewicz, R.L. Taylor: The Finite Element Method. Volume 2: Solid Mechanics.Butterworth Heinemann, 2000, Oxford, UK, 5th edition.
O.C. Zienkiewicz, R.L. Taylor: The Finite Element Method. Volume 3: Fluid Dynamics. Butterworth Heinemann, 2000, Oxford, UK, 5th edition.
J. Kruis: Domain Decomposition Methods for Distributed Computing. SaxeCoburg Publications, 2006, Stirling, Scotland, UK.
 Note:
 Further information:
 http://mech.fsv.cvut.cz/~jk
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: