Hydrodynamics in Astrophysics: Fundamentals, Numerical Methods and Application

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.

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

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,
http://relativity.livingreviews.org/Articles/lrr-2003-7/index.html
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
 

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.