Hydrodynamics
WS 2025/26

This course will introduce the basic concepts of hydrodynamics and how they are applied to astrophysical simulations.

Lectures

Suggested Literature

• Principles of Astrophysical Fluid Dynamics, C. J. Clarke and R. F. Carswell
• Simulation Techniques for Cosmological Simulations, K. Dolag, S. Borgani, S. Schindler, A. Diaferio and A. M. Bykov
• Density Estimation for Statistics and Data Analysis, B. W. Silverman
• Theoretical Fluid Dynamics, A. Feldmeier
• Computational Methods for Astrophysical Fluid Flow, R. J. LeVeque, D. Mihalas, E. A. Dorfi and E. Mueller
• The Encyclopedia of Cosmology, Volume 2: Numerical Simulations in Cosmology, Kentaro Nagamine (ed.)

Lecture Plan

• 13.10.25, L0: Introduction into Concepts of Fluid Dynamics
  Mainly based on Chapters 1 and 2 of Principles of Astrophysical Fluid Dynamics
• 20.10.25, L1: Collisionless Fluids and Gravity, N-Body simulations
  Mainly based on Chapter 2 of Simulation Techniques for Cosmological Simulations
• 27.10.25, L2: Energy Equation and Eulerian Hydrodynamics
  Mainly based on Chapter 4 of Principles of Astrophysical Fluid Dynamics
  and Chapter 3.1 of Simulation Techniques for Cosmological Simulations
• 03.11.25, L3: The Riemann Problem and Density Estimates
  Mainly based on Chapter 3.1 of Simulation Techniques for Cosmological Simulations
  and Chapters 1–3 of Density Estimation for Statistics and Data Analysis
• 10.11.25, L4: Lagrangian Hydrodynamics (SPH)
  Mainly based on Chapter 3.2 of Simulation Techniques for Cosmological Simulations
• 17.11.25, L5: Hydrostatic Equilibrium
  Mainly based on Chapters 3.5, 3.6, and 5.1 to 5.6 of Principles of Astrophysical Fluid Dynamics
• 24.11.25, L6: Waves
  Mainly based on Chapters 6.1 and 6.2 of Principles of Astrophysical Fluid Dynamics
• 01.12.25, L7: Shocks
  Mainly based on Chapters 7 and 8 of Principles of Astrophysical Fluid Dynamics
• 08.12.25, L8a: Bernoulli’s equation, Laval nozzle
  Mainly based on Chapters 9.1 and 9.2 of Principles of Astrophysical Fluid Dynamics
• 15.12.25, L8b: (Heat) Transport and Instabilities
  Mainly based on Chapter 10.1 of Principles of Astrophysical Fluid Dynamics
  as well as parts of the following publications: Section 2 of arXiv:astro-ph/0401456, Section 3.4.1 of arXiv:1412.6533, and Appendix B/C of arXiv:0812.1801.
  Note that above publications use u for internal energy and A for entropy.
• 12.01.26, L9: Viscosity
  Mainly based on Chapter 11 of Principles of Astrophysical Fluid Dynamics
• 19.01.26, L10: Plasma Physics / MHD
  Mainly based on Chapter 13 of Principles of Astrophysical Fluid Dynamics
• 26.01.26, L11: Sub-Grid Physics (star-formation)
  Mainly based on Chapters 4.1 and 4.2 of Simulation Techniques for Cosmological Simulations
  as well as parts of following publications: Sections 3.1 and 4.2 of arXiv:astro-ph/9509107 and Sections 2, 3, and 4 of arXiv:astro-ph/0206393.
• 02.02.26, L12: History of cosmology, galaxy clusters and simulations
  Some historical notes on our understanding of the cosmos,
  some notes on how galaxy clusters help us to understand our universe,
  some insights on how cosmological simulations are done.Slides.

Tutorials

In this class you will be required to write small computer programs to set up and analyze various interesting hydrodynamic flows. The simulations themselves will be done with a given hydrodynamics code and you will be given access to central computers to perform the simulations and the analysis of them. This will require some effort and lots of experimentation from your side. But keep in mind that programming is not the main aspect of these tutorials — understanding the physics of the different experiments is.

Each of the tutorials will involve a short, general discussion about some aspects of the current exercise set and the related physical and numerical issues where you are expected to have prepared yourself by answering some key questions beforehand. Handing in a short (less than one page!) written summary of answers will build up to a bonus applied towards the final exam. During the tutorials you will work on setting up the test problems and performing the hydrodynamic simulations.

You can use the same infrastructure as used for the Astrophysical Labs. Tutorial T0a will be concerned with setting up your laptops to connect to our machines, where all required software is already installed.
In case you want to work directly on your laptop, you will need:

• a C++ compiler
• a text editor (such as emacs or vim)
• a program to produce graphs (for example, gnuplot or Python+matplotlib)

For the Tutorials you will be assigned to one computing resource. Forming groups of 2 or 3 students to jointly work on the tutorials is recommended.

Tutorial schedule

• 13.10.25, T0a: Introduction Computer: shell, command-line, connecting, editing, plotting
  (Will be together with the Gravitational Dynamics Tutorials from 14:00 to 16:00 !)
• 13.10.25, T0b: Introduction Tutorials: compiling, running, reading data
• 20.10.25, T1: Free-fall collapse
  
• 27.10.25, T2: Generating field lines
• 03.11.25, T3: Density estimates
• 10.11.25, T4: The Riemann problem
• 17.11.25, T5: A collapsing gas cloud
• 24.11.25, T6: Propagating sound waves
• 01.12.25, T7a: Blast wave
• 08.12.25, T7b: Flow through a Nozzle
• 15.12.25, T8a: Equilibration using heat transport
  (Extra for fun: T8b: Adiabatic cooling)
• 12.01.26, T9a: Viscous flow between two plates
  
• 19.01.26, T9b: Viscous fluid mixing and instabilities
  
• 26.01.26, T10: Running a MHD test problem
• 02.02.26, T11: Simulating a disk galaxy and reproducing the SK relation

Grading

As Hausarbeit is not longer possible since WS23/24, there will be a written exam as already last time!

The exam is planned to be on 16.02.26 (date can still change) and will be at the same time and location as the lecture, so 10–12, USM Lecture hall. Some bonus points from the submitted discussion sheets at the beginning of the Tutorials will be incorporated.