Rechnergestützte Astrophysik
Computational Astrophysics

The subject of astrophysics are complex objects and phenomena. Seeking for a theoretical understanding, a realistic description is required. To this end, computers have become a major tool of research and with ever more powerful computational resources and modern numerical techniques, a detailed modeling of astrophysical objects and phenomena has become feasible. Based on general strategies to numerically model astrophysical objects and phenomena, the course aims at providing an overview of numerical methods used in computational astrophysics and will discuss some examples of recent applications of these methods in astrophysics.

Covered topics are
  * Astrophysical concepts
  * Numerical concepts
  * Modeling gravity
  * Computational fluid dynamics (CFD)
  * Relativistic CFD
  * Magnetohydrodynamics
  * Modeling nuclear reactions
  * Modeling radiative transfer

After successful participation in the module the student has attained the following abilities. The student

* understands the basics of numerical methods used in astrophysics    

* knows several numerical methods to calculate the gravitational potential of self-gravitating bodies                             

* knows how to simulate hydrodynamic flows involving shock waves                                                                          

* has obtained a basic understanding of numerical methods used to simulate magetohydrodynamic and relativistic flows

* is able to apply numerical schemes for describing astrophysical processes, like e.g. nuclear burning

* has aquired expertise to develop numerical astrophysics codes that involve as basic building blocks one or several of the topics discussed in the course

Keine Vorkenntnisse nötig, die über die Zulassungsvoraussetzungen zum Masterstudium hinausgehen. Die vorhergehende Teilnahme an der Vorlesung "Theoretische Astrophysik" (Modul PH2080) ist von Vorteil, aber nicht zwingend erforderlich.

In classroom lectures the teaching and learning content is presented and explained in a didactical, structured, and comprehensive form. This includes basic knowledge as well as selected current topics from a very broad research field.  Crucial facts are conveyed by involving the students in scientific discussions to develop their intellectual power and to stimulate their analytic thinking. Regular attendance of the lectures is therefore highly recommended.

The presentation of the learning content is enhanced by several homework problems that the student should work on using Jupyter Notebooks provided on the lecture webpage. The successful handling of these homework problems by the student substitutes the oral exam. The homework problems are intended to deepen the students' understanding and to help their learning of the course material. They can be discussed with the teacher upon request.

The homework problems as well as regular self-study of personal notes from the lectures and of textbooks and recent review articles referenced in the course are an important part of the learning process by the students. Such post-processing and practising of the teaching content is indispensable to achieve the intended learning results that the students develop the ability of explaining and applying the learned knowledge independently.

Beamer-Praesentation, Vorlesungsskript, Hausaufgaben die mit Jupyter Notebooks bearbeitet werden sollen anstatt einer muendlichen Pruefung, begeleitende Internetseite

P. Bodenheimer, G.P. Laughlin, M. Rozycka, and H.W. Yorke: Numerical Methods in Astrophysics, Taylor & Francis,200       

W.H. Press, S.A. Teukolsky. W.T. Vetterling, and B.P. Flannery: Numerical Recipes (third edition), Cambridge University Press, 2007

J.M. Thijssen: Computational Physics (2nd edition), Cambridge University Press, 2007

D. Potter: Computational Physics, Wiley, 1973

J.M.Stewart: Python for Scientists, Cambridge Univ. Press, 2017

W. Hillebrandt, E. Mueller, and F. Kupka: Einfuehrung in die Theoretische Astrophysik,                                        http://www.mpa-garching.mpg.de/lectures/TASTRO_SS08

T. Padmanabhan: An Invitation to Astrophysics, World Scientific, 2006

There will be neither an oral exam nor a written exam. Instead students are asked to handle a set of homework problems during the course of the lecture using Jupyter Notebooks provided on the lecture webpage

The homework problems cover various aspects of the material taught during the lecture course, e.g.,

* study the behavior of different numerical schemes to solve the one-dimensional diffusion equation, and determine whether the schemes are consistent, convergent and stable
* study the behavior of different numerical schemes to solve the one-dimensional linear advection equation, and determine the stability property of the schemes
* study the shock tube problem encountered in Newtonian and special-relativistic hydrodynamic simulations using Riemann solvers to handle flow discontinuities.