Course Description

Numerical modeling is an important tool in almost all areas of modern astrophysics. In particular, in theoretical astrophysics 3D magneto- hydrodynamic models in combination with N-body codes (to model gas, stars, and dark matter), heating & cooling, radiative transfer, etc. are required to study the formation of deeply embedded, young stars; the impact of Supernovae on the interstellar medium; the formation and evolution of molecular clouds; the formation and evolution of galaxies; the accretion of gas onto black holes and the associated AGN feedback; re-ionization of the Universe from the first population of stars; and the cosmological formation of galaxies and galaxy clusters starting from primordial density fluctuations in the early Universe.

Often the time and spatial scales involved in a particular problem are extreme.

This requires sophisticated numerical techniques including adaptive resolution and time stepping, which run on the world’s largest supercomputers.

In this course we will give an overview of the numerical techniques often used in modern astrophysical codes. This involves the theoretical background about the underlying physical problem to be solved and a discussion on possible solutions as well as their pros and cons.

The course aims to be a “hands-on” experience and therefore every afternoon will be filled with practice sessions, where we will introduce the adaptive-mesh refinement MHD code FLASH as well as an SPH method and a radiative transfer tool for post-processing 3D simulation data.

Contents of the course

1. 1.General overview: Eulerian vs. Lagrangian methods for astrophysical gases
   

2. 2.Space-/Time-Adaptivity; Criteria for timestepping and space/time-adaptivity; parallelisation
   

3. 3. (Magneto-) Hydrodynamics; Riemann Problem; SPH formulation
   

4. 4.Gravity; Tree-based methods vs. multigrid methods
   

5. 5.Heating & Cooling; Chemical Networks; Stiff ODEs;
   

6. 6.Radiative transfer; Ray tracing

Teaching Methods

1. 1.Mornings: Lectures / Seminar
   

2. 2.Afternoons: Computer simulations: Practical sessions where we use different codes to model problems in star formation and radiative transfer.
   

3. 3.Programming skills are required for all practice session! However we will work in groups, so if you have no coding experience it is good to team up with somebody who does.
   

4. 4.Feedback round: Every evening each group should briefly summarize what they have done and how far they got with one particular example.

Prerequisites

1. 1.The course is aimed for graduate students in the Master programme, but Bachelor students with good programming skills and a successful participation in Astrophysics I are welcome too.
   

2. 2.Preliminary knowledge in Astrophysics (on the level of the basic Astrophysics courses) is needed
   

3. 3.It is beneficial to know basic linux commands and  to have basic programming skills

Lecturers

1. 1.Stefanie Walch-Gassner
   

2. 2.Daniel Seifried

Credit Points

Full participation will be awarded with 4 CPS.

In case you would like to use the CPS for one of your areas of specialization you will need to get a grade. This will be possible by taking an oral exam.