# Case Studies Scientific Computing (MA4306)

Modern numerical methods (e.g. methods for solving ordinary and partial differential equations, methods for the iterative solution of large linear systems and inverse problems, approximation methods for scattered date, uncertainty quantification ...) are applied to application problems. These problems are obtained from other faculties, from external research institutes or from industry. The complete solution chain has to be carried out (modelling, analysis, solution, presentation).Lecture | Prof. Dr. Rainer Callies, Dr. Tobias Köppl |
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Question time | by arrangement (Email) |

Supervision | Prof. Dr. Rainer Callies Dr. Tobias Köppl Fabian Wagner |

Requirements | Basic courses on numerical mathematics: MA1304 Introduction to Numerical Linear Algebra MA2304 Numerical Methods for Ordinary Differential Equations MA3303 Numerical Methods for Partial Differential Equations |

Credits | 6 ECTS |

TUMonline | Link zum TUMonline Eintrag |

Moodle | To get access to the Moodle course, please register in TUMonline for the lecture. Afterwards you are automatically registered for the Moodle course. |

## News

- The preliminary meeting takes place on
**7th August 2019 from 11:00 am to 11:45 am in room MI 03.06.011**. - The of the prelminiary meeting
**(status 7th August)**can be found here: Slides preliminary meeting. - Kick Off Meeting:
**Wednesday 23rd October 2019 from 4:00 pm to 5:30 pm in room: MI 02.06.20**

## Basic Concept

Students participating in this module will work on a practical problem in small groups under the supervision of the lecturers. The project work typically starts with the discussion of the problem setup, an analysis of the important problem characteristics and a subsequent formulation as a mathematical model. During this phase, the students also present their challenges to a non-scientific audience, usually in the form of a poster presentation. They discuss their poster ideas with the supervisors and receive peer-feedback on their presentations. The participants then research suitable solution algorithms and receive lectures on additional skills where necessary. They discuss their solution approaches with the project supervisors and refine and implement the chosen algorithms. They assess and discuss their solutions and the practical properties of their algorithm with the supervisors and implement necessary modifications or enhancements and / or contrast the properties of different solution approaches with respect to the underlying application. During the project work the students discuss their progress with their supervisors from mathematics and from the field of application on a regular basis and give intermediate presentations of their problem, its characteristics and their solution approaches to the other participants. At the end, the results are presented in the form of conference talks to a scientific audience.## Grading

The final grade is composed of the following subtasks:- Poster presentation
- A short report about 10 to 15 pages summarizing the basic findings of the project
- Well-documented program code that has been developed during the project work
- Plan of milestones and workpackages as well as a time sheet
- Final presentation (15 minutes talk per candidate plus 5 minutes questions per candidate)

## Projects

### Project 1: Cashflow analysis of windparks (Prof. Dr. Ullmann, Wagner)

Cashflow analysis is a key element to evaluate the long-term profitability of windpark projects which serves as a decision-making basis for public, private or institutional investors. Beyond static windpark parameters and weather forecasts, cashflow analysis for windpark projects requires a long-term forecast of electricity prices, since the underlying investment period for windparks easily reaches 25 years and more. Complex and computationally intense fundamental energy models are able to forecast electricity prices on hourly resolution even beyond an investment period of 25 years. The goal is to perform a discounted cashflow analysis based on the forecasted electricity prices from a fundamental energy model from Fraunhofer-Institut für System- und Innovationsforschung, static windpark parameters, weather forecasts and initial investment costs for building the windpark. Key variables like wind forecast must be modelled using statistical distributions to obtain more realistic profitability values for the windpark. Major tasks of the project are as follows:- Understanding, summarizing and describing the comprehensive fundamental energy model from Fraunhofer-Institut für System- und Innovationsforschung and its complex mathematical optimization behind it
- Understanding the complexity of electricity short-term trading on EPEX Spot (energy exchange) in the German energy market, incl. a Know-How Onboarding through experts from FORRS Partners
- Performing a discounted cashflow analysis in Python to evaluate the profitability of a windpark to be built
- Describing the approach and the results of the cashflow analysis
- Present results of the cashflow analysis together with the essentials of the fundamental models

^{}. Experts from FORRS will meet you and provide relevant expertise upfront. During the period of the seminar, they will assist you in practical questions and keep updated with you.

### Project 2: Calibration of multi-hole probes (Dr. Köppl)

In order to enable safe operation of ships and planes, it is necessary to have an accurate knowledge on flows around them. In case of planes, probes are placed at certain distances on their wings. These probes contain several sensors that measure static and dynamic pressures as well as velocities and angles of attack. An accurate measurement of these units is achieved by calibrating each probe before it is used. The necessity for this arises from the fact that the dependence of the measured pressures on the angle of attack varies from probe to probe. This is mainly due to the manufacturing tolerances. The goal of this project is to understand and program calibration algorithms for multi-hole probes. The subtasks of this project read as follows:- Get an understanding of the fundamentals from fluid mechanics
- Study literature on the calibration of multi-hole probes
- Choose suitable numerical methods to determine the calibration parameters
- Implement a calibration algorithm in MATLAB/C++ for a multi-hole probe
- Test the MATLAB/C++ programms by means of some measurements

**Vectoflow GmbH**. Vectoflow provides measurements taken in wind tunnels. These measurements should be used to test the MATLAB/C++ programms mentioned above. Furthermore, you are assisted by vectoflow to get a better understanding of the different issues related to the project. Contact:

**Vectoflow GmbH**, Friedrichshafener Straße 1, 82205 Gilching, https://www.vectoflow.de

^{}.

### Project 3: Simulation of heat transfer in a concentrated solar powerplant (Dr. Köppl)

The use of solar energy plays a major role in the generation of renewable and sustainable energy. One way of harnessing solar energy is to build concentrated solar powerplants. Thereby, mirrors or lenses are used to concentrate a large area of sunlight, onto a small tube located in the focal point of the mirrors or lenses. The tube is filled with a fluid consisting mostly of saltwater. At the inlet the fluid enters with a low temperature which is heated as long as the tube is irradiated. After heating the fluid, the stored thermal energy can be used to produce electricity or it can be directly used for the production of chemical products. The propagation of heat within the tube is governed by the heat transfer equation. This equation consists of a time derivative, a convective term governed by the fluid velocity, a diffusive term as well as a possible source term. In order to determine the fluid velocity, a flow model like the Navier-Stokes equations can be considered. The subtasks of this project read as follows:- Derive a one-dimensional model for flow and heat transfer within the tube in order to decrease the complexity of the issue
- Choose suitable numerical methods to solve the models arising in the first subtask
- Implement a numerical solver in MATLAB/C++

### Project 4: Fast driving subject to safety restrictions (Prof. Dr. Callies)

## Registration

Registration for this course is mandatory and has to be done before the**deadline: 21st October 2019.**

The registration is done by email to koeppl@ma.tum.de providing the following information:

- last name, first name, student ID
- curriculum (of your master's studies)
- ranking of the projects (which do you find most interesting, which would be a good alternative etc.); please rank all projects. (Example: (1) Project 3, (2) Project 1, (2) Project 4, (3) Project 2 - note that you can rate multiple projects with the same value)
- list of scientific computing related lectures (numerics, numerical engineering, computer science and engineering, etc.) that you have attended (for lectures from other faculties or universities. Please provide the grades you obtained in context of these lectures and give a short description of the topics covered so that we know about your expertise in the field)
- programming skills (programming languages and other programming related skills)
- persons you would like to work with as a team

**Please note that there is only a limited number of places for this module, since for each project we can only accept up to three students. The application process for this module starts after the preliminary meeting.**

## Preliminary Meeting

The first meeting takes place on**7th August 2019 from 11:00 am to 11:45 am in room MI 03.06.011**.

The topics of this meeting are

- presentation of the projects and structure of the module
- grading system
- rough time table