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# Numerical Methods for Fluid-Structure Interaction

## Module MA5514

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Basic Information

MA5514 is a semester module in English language at Master’s level which is offered once.

This module description is valid from SS 2015 to SS 2015.

150 h 45 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

1) Basic concepts in continuum mechanics
2) Modeling of fluid flows and solid mechanics
3) FSI-modeling: coupling techniques of fluids and solids,
transformations between Eulerian and Lagrangian
coordinate systems
4) Discretization: Time, space (FEM), nonlinear and
linear solvers
5) Sensitivity analysis for FSI: a posteriori error estimation,

#### Learning Outcome

After successful completion of the module, students are able to formulate, couple, discretize and simulate coupled PDE systems in which one (the fluid) is formulated in Eulerian coordinates and the other (the solid) in Lagrangian coordinates.

In this class, students will learn about coupling conditions for interface problems. They will get an understanding about the properties of the single subsystems (i.e., their mathematical properties and related types of discretization).

#### Preconditions

- MA3001 Functional analysis (would be helpful; but not mandatory)
- MA3005 Partial differential equations (if possible)
- MA3303 Numerical methods for partial differential equations (required)
- Concepts of continuum mechanics (if possible)

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

Class and exercise

#### Media

Blackboard, Beamer, Exercise sheets

#### Literature

1) Numerical treatment of partial differential equations
by Ch. Grossmann, H.-G. Roos, M. Stynes
(for basics in FEM)
2) Numerische Mathematik 3 Numerische Methoden für
Probleme der Kontinuumsmechanik
by R. Rannacher (Online script at Heidelberg
University, in german)
3) Numerische Methoden in der Stroemungsmechanik,
Universität Heidelberg, 2014 by T. Richter
(Online script, in german)
4) Lecture notes to this class by T. Wick; will be
prepared this winter and during the class (in english)

### Module Exam

#### Description of exams and course work

Oral exam at the end of the semester

#### Exam Repetition

The exam may be repeated at the end of the semester.

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