Fundamental and advanced numerical methods used in commercial and open-source CFD codes will be explained. The main focus is on numerical methods for conservation laws with discontinuities, which is relevant for trans- and hypersonic gas dynamics problems, but also CFD of incompressible flows, Direct Simulation Monte Carlo and the Lattice Boltzmann method are explained.

The bachelor's thesis is the culmination of the program. The students develop, enhance, and demonstrate their methodological abilities to independently tackle and solve a given research problem. The thesis furnishes the students with their first major research experience, and is a further development of the work done in the basis courses, and usually, the focused study.

Introduction to the fluid dynamics of the human body and the modeling of physiological flow processes (biomedical fluid dynamics).

Topics: unsteady one-dimensional subsonic and supersonic flows, acoustics, sound propagation, supersonic flows with shocks and Prandtl-Meyer expansions, flow around slender bodies, shock tubes, reaction fronts (deflagration and detonation).Mathematical tools: method of characteristics and selected numerical methods.

This course introduces students to numerical methods commonly used in engineering with a focus on finite element (FE) analysis. Starting with finite differences and ending with static and dynamic FE problems, students will learn the fundamental concepts of finite elements as well as their implementation and application.

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An introduction to the physical and mathematical foundations of fluid dynamics is given. Topics include dimensional analysis, integral and differential conservation laws, inviscid and viscous flows, Navier-Stokes equations, boundary layers, turbulence, potential flows, unsteady flows, aerodynamic concepts, vorticity dynamics, compressible flows.

Two-dimensional irrotational (potential) flows: stream function and potential, singularity method, unsteady flow, aerodynamic concepts.Vorticity dynamics: vorticity and circulation, vorticity equation, vortex theorems of Helmholtz and Kelvin.Compressible flows: isentropic flow along stream tube, normal and oblique shocks, Laval nozzle, Prandtl-Meyer expansion, viscous effects.

Students develop and build a product from A-Z! They work in teams and independently, learn to structure problems, to identify solutions, system analysis and simulations, as well as presentation and documentation techniques. They build the product with access to a machine shop and state of the art engineering tools (Matlab, Simulink, etc).

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Enlarged knowledge and practical abilities in fundamentals and applications of Computational Fluid Dynamics

Current advanced research activities in the areas of thermo- and fluid dynamics are presented and discussed, mostly by external speakers.

In the study of turbulent flows the objective is to obtain a tractable quantitative theory or model to calculate quantities of interest. A century of expertise has shown the 'turbulence problem' to be notoriously difficult, and there are no prospects of a simple analytic theory. In this class, five of the leading computational approaches to turbulent flows are described and examined.

Laminar and turbulent flows, instability and origin of turbulence - Statistical description: averaging, turbulent energy, dissipation, closure problem - Scalings. Homogeneous isotropic turbulence, correlations, Fourier representation, energy spectrum - Free turbulence: wake, jet, mixing layer - Wall turbulence: Channel and boundary layer - Computation and modelling of turbulent flows