Advanced Numerical Methods in Coupled Multiphysics Problems

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mechanics

Synopsis:

The aim of the course is to solve coupled multiphysics problems, e.g. thermoelasticity, coupled heat and moisture transfer, thermo-hydro-mechanical problem, electordiffusion, etc. First, the balance equations together with constitutive laws will be summarized for selected coupled multiphysics problems. Discretization in space and time (Galerkin-Bubnov method, Galerkin-Petrov 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 (Newton-Raphson method, the arc-length 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 mechanics-moisture transport with influence of temperature.

8. Transport of chlorides.

9. Galerkin-Bubnov method for diffusion problems.

10. Galerkin-Petrov method for diffusion-advection problem.

11. Integration in time (generalized trapezoidal rule).

12. Systems of nonlinear algebraic equations, Newton-Raphson 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 mechanics-moisture transport with influence of temperature.

8. Transport of chlorides.

9. Galerkin-Bubnov method for diffusion problems.

10. Galerkin-Petrov method for diffusion-advection problem.

11. Integration in time (generalized trapezoidal rule).

12. Systems of nonlinear algebraic equations, Newton-Raphson method.

13. Introduction of methods for solution of systems of linear algebraic equations.

Study Objective:

Introduction into multi-physics 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.

Note:

Further information:

http://mech.fsv.cvut.cz/~jk

No time-table has been prepared for this course

The course is a part of the following study plans: