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Computational Astrophysics

Module PH2077

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2020/1 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2020/1WS 2010/1

Basic Information

PH2077 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 30 h 5 CP

Responsible coordinator of the module PH2077 is Ewald Müller.

Content, Learning Outcome and Preconditions


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

Learning Outcome

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


No preconditions in addition to the requirements for the Master’s program in Physics. Previous attendance of the introductory lecture course "Theoretical Astrophysics" (Module 2080) is of advantage, but not required.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Computational Astrophysics Janka, H. Müller, E. Fri, 14:00–16:00, PH HS3

Learning and Teaching Methods

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 presentation, online script, homework problems to be handled using Jupyter notebooks instead of oral exam, accompanying internet site


P. Bodenheimer, G.P. Laughlin, M. Rozycka, and H.W. Yorke: Numerical Methods in Astrophysics, Taylor & Francis, 2007

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,                             

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

Module Exam

Description of exams and course work

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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