Hydrodynamics in Astrophysics: Fundamentals, Numerical Methods and Application

Module PH2079

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.

Basic Information

PH2079 is a semester module in German or English language at Master’s level which is offered irregular.

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

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

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 40 h 5 CP

Responsible coordinator of the module PH2079 is Ewald Müller.

Content, Learning Outcome and Preconditions


This module provides an overview of the fundamentals of hydrodynamics and the application of hydrodynamical methods in astrophysics. After deriving the equations of Newtonian hydrodynamics from classical statistical physics,  the equations of relativistic hydrodynamics and magneto-hydrodynamics are discussed. Then the mathematical properties of the hydrodynamical eqautions are studied, whereby specifically characteristics, weak solutions, flow discontinuities and the Riemann problem are discussed. Subsequently, numerical methods are presented to integrate the hydrodynamical equations. The behavior of these methods is illustrated with examples. Finally, three applications from astrophysics are presented: hydrodynamical simulations of (i) mixing processes in supernova envelopes, (ii) thermonuclear burning in white dwarfs, and (iii)  relativistic jets.


Learning Outcome

After successful participation in this module the student is able to:

1. to comprehend and explain the basic physical and mathematical properties of the equations of classical and relativistic hydrodynamics and magneto-hydrodynamics;

2. to name and explain numerical methods and algorithms used in state-of-the-art computational fluid dynamics;

3. to understand the importance and the impact of computational fluid dynamics for the simulation of multi-dimensional hydrodynamic phenomena in astrophysics


absolutely necessary: none

of advantage: basic knowledge of the theory of partial differential equations

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

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A.M.Anile, Relativistic Fluids and Magnetofluids, Cambridge University Press, 1989
G.Ecker, Theory of Fully Ionized Plasmas, Academic Press, 1972
S.N.Shore, An Introduction to Astrophysical Hydrodynamics, Academic Press, 1992
F.H.Shu, The Physics of Astrophysics Vol II: Gas Dynamics, University Science, Mill Valley, 1992

A.J.Chorin & J.E.Marsden, A Mathematical Introduction to Fluid Mechanics, Springer, 1979
R.Courant & K.O.Friedrichs, Supersonic Flow and Shock Waves, Springer, 1976
H..Goedbloed & S.Poedts, Principles of Magnetohydrodynamics, Cambridge University Press, 2004
R.J.LeVeque, Numerical Methods for Conservation Laws, Birkhaeuser, 1992                                                     E.F.Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1997

C.B.Laney, Computational Gasdynamics, Cambridge University Press, 1998
J.M.Marti and E.Mueller, Numerical Hydrodynamics in Special Relativity, Living Reviews in Relativity, lrr-2003-7,
D.Potter, Computational Physics, Wiley, 1977

E.Mueller, Simulation of Astrophysical Fluid Flow, in ``Computational methods for astrophysical fluid flow'', LeVeque, R.J., Mihalas, D., Dorfi, E.A. & Muelller, E., Springer, 1998

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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