# UE Fundamentals of Numerical Thermo-Fluid Dynamics, 322.061

This course in TISS

The course will take place online via TUWEL, starting on 3rd March 2021. Study material is already available.

## Requirements & Assessment

Examples for home preparation are released one week before each exercise (except from the first week). Participants are asked to solve at least half of the examples and submit their solutions via TUWEL before the start of each exercise. Each example will then be presented by a different student of the group in a video conference using screen-sharing. Every participant must present at least one example over the semester, which constitutes

**20%**of the overall grade.A team project (see below) has to be done by groups of two to three people and submitted until Friday, 16th July 2021. The project involves solving a certain mathematical problem numerically, using the methods covered during the exercises. The team project contributes by

**40%**to the overall grade.The remaining

**40%**of the grade correspond to a final examination after the end of the course.- Attendance in the weekly video conference is required. A maximum of two absences per semester is allowed.
Some examples involve writing a simple script for MatLab or Octave. For introduction to MatLab consider this Simple MatLab tutorial and More MatLab tutorials in German.

Your solutions would preferably be written using Word / LibreOffice / LaTeX / (MATLAB) Markup / MATLAB LiveScript / Jupyter ... but clear handwritten scanned sheets are also accepted.

## Outline

*3rd March 2021: Classification of partial differential equations, Method of characteristics*- Recommended literature: [1, 3, 4, 11], Additional resources: [2, 5, 6]

*10th March 2021: Finite Difference Method for boundary value problems*- Recommended literature: [1], Additional resources: [5]

*24th March 2021: Stability of Finite Difference schemes*- Additional resources: [7, 8, 9, 10]

*14th April 2021: Explicit schemes for spatio-temporal discretization**21st April 2021: Implicit schemes for spatio-temporal discretization**28th April 2021: 2D time-dependent problems and systems of PDEs**5th May 2021: Non-linear problems**12th May 2021: Bonus examples**19th May 2021: Questions and Answers*

## Team Project

The assignment of the team project will be released within the first weeks of the course.

This assignment has to be done by groups of two or three (too long otherwise !).

Some template codes are provided, they have to be filled in and submitted together with the final report.

**Report instructions**

The report should be sent no later than

*Friday 16th, July 2021 at 8:00 a.m.*to lukas.babor@tuwien.ac.at with the Subject "E322061_NAME1_NAME2_NAME3",- with an enclosed file named 'Report_NAME1_NAME2_NAME3.pdf'
- with a zip file similar to one downloadable above with the name 'Codes_NAME1_NAME2_NAME3.zip'.

- There is no limit of number of pages.
**No oral presentation**of the work will be required.

## Recommended literature

[1] Lecture notes for the course LVA-Nr. 302.017: Grundlagen der numerischen Methoden der Stömungs- und Wärmetechnik, TU Wien

[11] Wilhelm Schneider, Mathematische Methoden der Strömungsmechanik, 1. Auflage Braunschweig, Vieweg 1978, ISBN 3-528-03574-0

## Additional resources

[5] 'CFD Education Center - Vienna', URL: http://cfdblogvienna.blogspot.com/

[7] Seibold, B. (2009), 'Numerical Methods for Partial Differential Equations', Course No. 18.336, Lecture notes, MIT. Shared under this license.