# 325.099 Finite Element Methods for Multi-Physics II This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});});

2020S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture

## Learning outcomes

After successful completion of the course, students are able to:

• understand the physics of mechanical, electromagnetic, flow-dynamic, thermal and acoustic fields;
• understand the mathematics of the Finite Element (FE) method and have the knowledge for its computer implementation;
• perform all necessary steps by their own for a successful FE analysis starting from modelling, pre-processing, computation and post-processing;
• interpret FE simulation results in a correct physical sense to improve current and future mechatronic systems;
• identify and work on relevant topics in research.

## Subject of course

The accurate modelling of mechatronic systems leads to so-called multi-field problems, which are described by a system of non-linear partial differential equations. These systems cannot be solved analytically and thus numerical calculation schemes have to be applied. Thereby, the finite element (FE) method has been established as the standard method for numerically solving the coupled system of partial differential equations describing the physical fields including their couplings.

In detail, the course will teach the physical / mathematical modelling and its FE formulations of the following coupled fields

Aeroacoustics

• Sound generation by turbulent flows according to Lighthill's analogy
• Approximation of Lighthill's analogy for low Mach numbers
• FE formulation for the radiated sound
• Approximation of free field conditions by absorbing boundary conditions and the Perfectly Matched Layer (PML) technique
• Non-conforming finite elements

Electromagnetics-mechanics

• Maxwell's equations
• Vector potential formulation for magneto-dynamics
• Nonlinear finite elements (Newton method) using edge finite elements
• Coupling mechanism (electromagnetic forces, motional electromotive force)
• FE formulation for the coupled field problem including moving / deforming solid bodies

Electromagnetics-Heat

• Multi-harmonic ansatz for the solution of the nonlinear electromagnetic partial differential equations in the frequency domain
• Finite elements of higher order to efficiently resolve eddy currents in electric conductive structures
• Coupling mechanism (Joule's losses due to currents, temperature dependent material parameters)
• FE formulation of the coupled field problem

## Teaching methods

The course will be interactive and the knowledge will be communicated by multimedia-based presentation using practical examples. Thereby, a high priority is placed on the physical understanding.

Written and oral

## Course dates

DayTimeDateLocationDescription
Thu08:30 - 10:0005.03.2020 - 12.03.2020Seminarraum BA 05 Course
Finite Element Methods for Multi-Physics II - Single appointments
DayDateTimeLocationDescription
Thu05.03.202008:30 - 10:00Seminarraum BA 05 Course
Thu12.03.202008:30 - 10:00Seminarraum BA 05 Course

## Examination modalities

Work out questions / exercises and perform an oral exam

Not necessary

## Curricula

Study CodeSemesterPrecon.Info
066 445 Mechanical Engineering
Course requires the completion of the introductory and orientation phase
066 445 Mechanical Engineering
Course requires the completion of the introductory and orientation phase
066 445 Mechanical Engineering
Course requires the completion of the introductory and orientation phase
066 482 Mechanical Engineering - Management
Course requires the completion of the introductory and orientation phase
066 482 Mechanical Engineering - Management
Course requires the completion of the introductory and orientation phase
066 482 Mechanical Engineering - Management
Course requires the completion of the introductory and orientation phase
066 646 Computational Science and Engineering
066 646 Computational Science and Engineering

## Literature

M. Kaltenbacher. Numerical Simulation of Mechatronic Sensors and Actuators. Finite Elements for Computational Multiphysics. Springer-Verlag, Heidelberg, 2015, ISBN: 978-3-642-40169-5

## Previous knowledge

The cours Finite Element for Multi-Physics I (325.095, VU) is recommended.

English